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                       Semantic Analysis of SPARK Text
                             Examiner GPL Edition

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SPARK Simplifier GPL 2012
Copyright (C) 2012 Altran Praxis Limited, Bath, U.K.

procedure Process_Dns_Request.Set_TTL_Data_RRSIG






@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_1.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
***  Proved C1:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C2:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H6.
***  Proved C3:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C4:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C5:  start_byte <= 8177
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C5:  start_byte <= 8177
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_2.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New C2:  true
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte <= 8176
<S>  New C5:  start_byte <= 8175
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C6:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C7:  start_byte <= 2147483643
***  Proved C1:  true
***  Proved C2:  true
***  Proved C7:  start_byte <= 2147483643
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C4:  start_byte <= 8176
     using hypothesis H1.
***  Proved C5:  start_byte <= 8175
     using hypothesis H1.
***  Proved C6:  start_byte >= - 2147483652
     using hypothesis H3.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_3.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
***  Proved C1:  start_byte + 6 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New C2:  start_byte <= 2147483641
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C2:  start_byte <= 2147483641
     using hypothesis H4.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_4.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  true
***  Proved C3:  start_byte + 6 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C8:  true
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New C1:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C6:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New C2:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
<S>  New C7:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte <= 8174
<S>  New C5:  start_byte <= 8173
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New C1:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New C6:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New C2:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
<S>  New C7:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C4:  start_byte <= 8174
     using hypothesis H1.
***  Proved C5:  start_byte <= 8173
     using hypothesis H1.
***  Proved C1:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
***  Proved C6:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
---  Eliminated hypothesis H27 (true-hypothesis).
---  Eliminated hypothesis H28 (true-hypothesis).
---  Eliminated hypothesis H29 (true-hypothesis).
---  Eliminated hypothesis H30 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H4 (redundant, given H1).
---  Eliminated hypothesis H31 (redundant, given H1).
---  Eliminated hypothesis H35 (redundant, given H3).
---  Eliminated hypothesis H36 (redundant, given H1).
---  Eliminated hypothesis H37 (redundant, given H1).
---  Eliminated hypothesis H38 (redundant, given H3).
---  Eliminated hypothesis H39 (redundant, given H1).
---  Eliminated hypothesis H41 (redundant, given H3).
---  Eliminated hypothesis H42 (redundant, given H1).
---  Eliminated conclusion C7, which is a duplicate of C2.
***  Proved C2:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_5.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
***  Proved C5:  start_byte + 8 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C7:  start_byte + 8 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New C1:  fld_algorithm(rrsig_record) >= 0
<S>  New C3:  fld_algorithm(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New C2:  fld_algorithm(rrsig_record) <= 255
<S>  New C4:  fld_algorithm(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes, [i___1]) and element(
          bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes__1, [i___1]) and 
          element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes__2, [i___1]) and 
          element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes__3, [i___1]) and 
          element(bytes__3, [i___1]) <= 255)
<S>  New C6:  start_byte <= 8172
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New C8:  start_byte <= 2147483639
***  Proved C8:  start_byte <= 2147483639
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  fld_algorithm(rrsig_record) >= 0
     using hypothesis H11.
***  Proved C3:  fld_algorithm(rrsig_record) >= 0
     using hypothesis H11.
***  Proved C2:  fld_algorithm(rrsig_record) <= 255
     using hypothesis H12.
***  Proved C4:  fld_algorithm(rrsig_record) <= 255
     using hypothesis H12.
***  Proved C6:  start_byte <= 8172
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_6.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
***  Proved C5:  start_byte + 9 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C7:  start_byte + 9 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New C1:  fld_numlabels(rrsig_record) >= 0
<S>  New C3:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New C2:  fld_numlabels(rrsig_record) <= 255
<S>  New C4:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes, [i___1]) and element(
          bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes__1, [i___1]) and 
          element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes__2, [i___1]) and 
          element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> 0 <= element(bytes__3, [i___1]) and 
          element(bytes__3, [i___1]) <= 255)
<S>  New C6:  start_byte <= 8171
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New C8:  start_byte <= 2147483638
***  Proved C8:  start_byte <= 2147483638
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H56:  start_byte >= - 7
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  fld_numlabels(rrsig_record) >= 0
     using hypothesis H13.
***  Proved C3:  fld_numlabels(rrsig_record) >= 0
     using hypothesis H13.
***  Proved C2:  fld_numlabels(rrsig_record) <= 255
     using hypothesis H14.
***  Proved C4:  fld_numlabels(rrsig_record) <= 255
     using hypothesis H14.
***  Proved C6:  start_byte <= 8171
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_7.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
***  Proved C1:  fld_origttl(rrsig_record) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C2:  fld_origttl(rrsig_record) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C3:  start_byte + 10 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C6:  start_byte + 10 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New C4:  start_byte <= 8170
<S>  New C5:  start_byte <= 8167
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New C7:  start_byte <= 2147483637
***  Proved C7:  start_byte <= 2147483637
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C4:  start_byte <= 8170
     using hypothesis H1.
***  Proved C5:  start_byte <= 8167
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_8.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
***  Proved C1:  fld_sigexpiration(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C2:  fld_sigexpiration(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C3:  start_byte + 14 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C6:  start_byte + 14 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte <= 8166
<S>  New C5:  start_byte <= 8163
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New C7:  start_byte <= 2147483633
***  Proved C7:  start_byte <= 2147483633
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C4:  start_byte <= 8166
     using hypothesis H1.
***  Proved C5:  start_byte <= 8163
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_9.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
***  Proved C1:  fld_siginception(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C2:  fld_siginception(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C3:  start_byte + 18 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C6:  start_byte + 18 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte <= 8162
<S>  New C5:  start_byte <= 8159
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New C7:  start_byte <= 2147483629
***  Proved C7:  start_byte <= 2147483629
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C4:  start_byte <= 8162
     using hypothesis H1.
***  Proved C5:  start_byte <= 8159
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_10.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
***  Proved C1:  fld_keytag(rrsig_record) >= unsigned_types__unsigned16__first
     using hypothesis H21.
***  Proved C2:  fld_keytag(rrsig_record) <= unsigned_types__unsigned16__last
     using hypothesis H22.
***  Proved C3:  start_byte + 22 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C6:  start_byte + 22 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New C4:  start_byte <= 8158
<S>  New C5:  start_byte <= 8157
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New C7:  start_byte <= 2147483625
***  Proved C7:  start_byte <= 2147483625
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C4:  start_byte <= 8158
     using hypothesis H1.
***  Proved C5:  start_byte <= 8157
     using hypothesis H1.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_11.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
***  Proved C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= rr_type__wirestringtypeindex__first
     using hypothesis H102.
***  Proved C2:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
     using hypothesis H103.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_12.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New C3:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New C4:  true
***  Proved C3:  true
***  Proved C4:  true
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
     using hypothesis H102.
***  Proved C2:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
     using hypothesis H103.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_13.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
***  Proved C1:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 
          rr_type__wirestringtypeindex__first and rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          rr_type__wirestringtypeindex__last
     using hypotheses H102 & H103.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
<S>  New C2:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
<S>  New C2:  true
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_14.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [j_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [j_]) <= 255)
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified C14 on reading formula in, to give:
     %%%  C14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified C28 on reading formula in, to give:
     %%%  C28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  true
***  Proved C3:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H103 & H113.
***  Proved C4:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= rr_type__wirestringtypeindex__first
     using hypothesis H102.
***  Proved C5:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
     using hypothesis H103.
***  Proved C7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
     using hypothesis H99.
***  Proved C8:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C9:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H4.
***  Proved C10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H6.
***  Proved C12:  rr_type__classtype__first <= fld_class(fld_inherit(
          rrsig_record))
     using hypothesis H7.
***  Proved C13:  fld_class(fld_inherit(rrsig_record)) <= 
          rr_type__classtype__last
     using hypothesis H8.
***  Proved C14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
     using hypothesis H9.
***  Proved C15:  fld_typecovered(rrsig_record) <= dns_types__query_type__last
     using hypothesis H10.
***  Proved C16:  fld_algorithm(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C17:  fld_algorithm(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C18:  fld_numlabels(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H13.
***  Proved C19:  fld_numlabels(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H14.
***  Proved C20:  fld_origttl(rrsig_record) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C21:  fld_origttl(rrsig_record) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C22:  fld_sigexpiration(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C23:  fld_sigexpiration(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C24:  fld_siginception(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C25:  fld_siginception(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C26:  fld_keytag(rrsig_record) >= unsigned_types__unsigned16__first
     using hypothesis H21.
***  Proved C27:  fld_keytag(rrsig_record) <= unsigned_types__unsigned16__last
     using hypothesis H22.
***  Proved C28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
     using hypothesis H24.
***  Proved C30:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H25.
***  Proved C31:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H26.
***  Proved C32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H1.
***  Proved C34:  1 <= rr_type__wirestringtypeindex__last
     using hypotheses H103 & H113.
***  Proved C35:  true
***  Proved C36:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))
     using hypothesis H113.
***  Proved C37:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= rr_type__wirestringtypeindex__first
     using hypothesis H102.
***  Proved C38:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
     using hypothesis H103.
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New C2:  true
<S>  New C6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [j_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [j_]) <= 255)
<S>  New C33:  true
***  Proved C2:  true
***  Proved C33:  true
+++  Using "A->B, A |- B" on hypotheses H111 & H113 yields a new hypothesis:
     +++  H114:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1 and rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          rr_type__wirestringtypeindex__last
+++  Using "A->B, A |- B" on hypotheses H112 & H113 yields a new hypothesis:
     +++  H115:  1 <= rr_type__wirestringtypeindex__last
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
<S>  New C1:  start_byte <= 8156 - rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)))
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H114:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1 and rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 129
<S>  New H115:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
<S>  New C6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [j_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  start_byte <= 8156 - rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)))
     using hypotheses H1 & H103.
***  Proved C6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [j_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [j_]) <= 255)
     using hypothesis H100.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_15.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(update(bytes, [start_byte + 24 - 1 
          + loop__1__i], element(wireversion, [loop__1__i])), [i___1]) and 
          element(update(bytes, [start_byte + 24 - 1 + loop__1__i], element(
          wireversion, [loop__1__i])), [i___1]) <= dns_types__byte__last)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified C14 on reading formula in, to give:
     %%%  C14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified C28 on reading formula in, to give:
     %%%  C28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  loop__1__i >= 0
***  Proved C1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          current_name_length
     using hypothesis H1.
***  Proved C2:  loop__1__i + 1 >= rr_type__wirestringtypeindex__first
     using hypothesis H2.
***  Proved C4:  current_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H4.
***  Proved C5:  current_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H5.
***  Proved C6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= 
          j_ and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
     using hypothesis H6.
***  Proved C7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(update(bytes, [start_byte + 24 - 1 
          + loop__1__i], element(wireversion, [loop__1__i])), [i___1]) and 
          element(update(bytes, [start_byte + 24 - 1 + loop__1__i], element(
          wireversion, [loop__1__i])), [i___1]) <= dns_types__byte__last)
     using hypotheses H7, H39, H40, H45 & H46.
***  Proved C8:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H8.
***  Proved C9:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H9.
***  Proved C10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H11.
***  Proved C12:  rr_type__classtype__first <= fld_class(fld_inherit(
          rrsig_record))
     using hypothesis H12.
***  Proved C13:  fld_class(fld_inherit(rrsig_record)) <= 
          rr_type__classtype__last
     using hypothesis H13.
***  Proved C14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
     using hypothesis H14.
***  Proved C15:  fld_typecovered(rrsig_record) <= dns_types__query_type__last
     using hypothesis H15.
***  Proved C16:  fld_algorithm(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H16.
***  Proved C17:  fld_algorithm(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H17.
***  Proved C18:  fld_numlabels(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H18.
***  Proved C19:  fld_numlabels(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H19.
***  Proved C20:  fld_origttl(rrsig_record) >= unsigned_types__unsigned32__first
     using hypothesis H20.
***  Proved C21:  fld_origttl(rrsig_record) <= unsigned_types__unsigned32__last
     using hypothesis H21.
***  Proved C22:  fld_sigexpiration(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H22.
***  Proved C23:  fld_sigexpiration(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H23.
***  Proved C24:  fld_siginception(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H24.
***  Proved C25:  fld_siginception(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H25.
***  Proved C26:  fld_keytag(rrsig_record) >= unsigned_types__unsigned16__first
     using hypothesis H26.
***  Proved C27:  fld_keytag(rrsig_record) <= unsigned_types__unsigned16__last
     using hypothesis H27.
***  Proved C28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
     using hypothesis H28.
***  Proved C29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
     using hypothesis H29.
***  Proved C30:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H30.
***  Proved C31:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H31.
***  Proved C32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H32.
***  Proved C33:  loop__1__i + 1 >= rr_type__wirestringtypeindex__first
     using hypothesis H2.
***  Proved C35:  loop__1__i >= 0
     using hypothesis H35.
***  Proved C37:  current_name_length__entry__loop__1 >= 
          rr_type__wirestringtypeindex__first
     using hypothesis H37.
***  Proved C38:  current_name_length__entry__loop__1 <= 
          rr_type__wirestringtypeindex__last
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= 129 -> 0 <= element(wireversion, [j_]) and element(
          wireversion, [j_]) <= 255)
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New C3:  loop__1__i <= 128
<S>  New C34:  loop__1__i <= 128
***  Proved C3:  loop__1__i <= 128
     using hypotheses H36, H38 & H55.
***  Proved C34:  loop__1__i <= 128
     using hypotheses H36, H38 & H55.
>>>  Restructured hypothesis H55 into:
     >>>  H55:  loop__1__i <> current_name_length__entry__loop__1
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H9:  start_byte <= 8180
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H32:  start_byte <= 6663
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
%%%  Hypotheses H36 & H55 together imply that
          loop__1__i < current_name_length__entry__loop__1.
     H36 & H55 have therefore been deleted and a new H56 added to this effect.
%%%  Simplified H51 further, to give:
     %%%  H51:  start_byte >= - 2147483671
%%%  Simplified H52 further, to give:
     %%%  H52:  start_byte <= 2147483624
***  Proved C36:  loop__1__i + 1 <= current_name_length__entry__loop__1
     via its standard form, which is:
     Std.Fm C36:  current_name_length__entry__loop__1 - loop__1__i > 0
     using hypothesis H56.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_16.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C5:  loop__1__i >= rr_type__wirestringtypeindex__first
     using hypothesis H2.
***  Proved C6:  loop__1__i <= rr_type__wirestringtypeindex__last
     using hypothesis H3.
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New C1:  element(wireversion, [loop__1__i]) >= 0
<S>  New C3:  element(wireversion, [loop__1__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C2:  element(wireversion, [loop__1__i]) <= 255
<S>  New C4:  element(wireversion, [loop__1__i]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H8:  start_byte >= 1
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New C7:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New C11:  loop__1__i >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H9:  start_byte <= 8180
<S>  New H32:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C8:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New C12:  loop__1__i <= 8180
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C9:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New C13:  start_byte + 24 >= - 2147483647
<S>  New C15:  start_byte >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C10:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New C14:  start_byte + 24 <= 2147483648
<S>  New C16:  start_byte <= 2147483623
***  Proved C1:  element(wireversion, [loop__1__i]) >= 0
     using hypotheses H2, H3 & H6.
***  Proved C3:  element(wireversion, [loop__1__i]) >= 0
     using hypotheses H2, H3 & H6.
***  Proved C2:  element(wireversion, [loop__1__i]) <= 255
     using hypotheses H2, H3 & H6.
***  Proved C4:  element(wireversion, [loop__1__i]) <= 255
     using hypotheses H2, H3 & H6.
***  Proved C7:  start_byte + 24 - 1 + loop__1__i >= 1
     using hypotheses H8 & H35.
***  Proved C11:  loop__1__i >= 1
     using hypothesis H35.
***  Proved C9:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
     using hypotheses H8 & H35.
***  Proved C13:  start_byte + 24 >= - 2147483647
     using hypothesis H8.
***  Proved C15:  start_byte >= - 2147483672
     using hypothesis H8.
***  Proved C14:  start_byte + 24 <= 2147483648
     using hypothesis H9.
***  Proved C16:  start_byte <= 2147483623
     using hypothesis H9.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C8:  start_byte + 24 - 1 + loop__1__i <= 8180
     using hypotheses H3 & H32.
***  Proved C12:  loop__1__i <= 8180
     using hypothesis H3.
***  Proved C10:  start_byte + 24 - 1 + loop__1__i <= 2147483647
     using hypotheses H3 & H9.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_17.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
***  Proved C1:  1 >= integer__first
     using hypothesis H109.
***  Proved C2:  1 <= integer__last
     using hypothesis H110.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_18.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_19.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_20.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C2:  1 <= dns_types__packet_bytes_range__last
     using hypotheses H35 & H50.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New C1:  true
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_21.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
***  Proved C1:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H25.
***  Proved C2:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H26.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_22.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C1:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H30.
***  Proved C2:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H31.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_23.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
***  Proved C6:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= dns_types__packet_bytes_range__last
     using hypotheses H113 & H117.
***  Proved C9:  start_byte + 24 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H116:  true
<S>  New C1:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
<S>  New C5:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H117:  true
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
<S>  New C3:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
<S>  New C7:  start_byte + 24 >= - 2147483647
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
<S>  New C4:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
<S>  New C8:  start_byte + 24 <= 2147483648
<S>  New C10:  start_byte <= 2147483623
***  Proved C7:  start_byte + 24 >= - 2147483647
     using hypothesis H3.
***  Proved C4:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
     using hypotheses H4 & H113.
***  Proved C8:  start_byte + 24 <= 2147483648
     using hypothesis H4.
***  Proved C10:  start_byte <= 2147483623
     using hypothesis H4.
>>>  Restructured hypothesis H113 into:
     >>>  H113:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) < 1
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
     using hypotheses H3 & H102.
***  Proved C5:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
     using hypothesis H102.
***  Proved C2:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
     using hypotheses H1 & H103.
***  Proved C3:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
     using hypotheses H3 & H107.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_24.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
***  Proved C7:  start_byte + 24 - 1 >= 
          dns_types__packet_bytes_range__base__first
     using hypothesis H51.
***  Proved C8:  start_byte + 24 - 1 <= 
          dns_types__packet_bytes_range__base__last
     using hypothesis H52.
***  Proved C9:  start_byte + 24 >= dns_types__packet_bytes_range__base__first
     using hypothesis H53.
***  Proved C10:  start_byte + 24 <= dns_types__packet_bytes_range__base__last
     using hypothesis H54.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New H58:  true
<S>  New C1:  start_byte + 24 - 1 + current_name_length >= 1
<S>  New C5:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H9:  start_byte <= 8180
<S>  New H32:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H59:  true
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  start_byte + 24 - 1 + current_name_length <= 8180
<S>  New C6:  current_name_length <= 8180
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
<S>  New C3:  start_byte + 24 - 1 + current_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
<S>  New C4:  start_byte + 24 - 1 + current_name_length <= 2147483647
>>>  Restructured hypothesis H51 into:
     >>>  H51:  start_byte >= - 2147483671
>>>  Restructured hypothesis H52 into:
     >>>  H52:  start_byte <= 2147483624
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H56:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H57:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  start_byte + 24 - 1 + current_name_length >= 1
     using hypotheses H4 & H8.
***  Proved C5:  current_name_length >= 1
     using hypothesis H4.
***  Proved C2:  start_byte + 24 - 1 + current_name_length <= 8180
     using hypotheses H5 & H32.
***  Proved C6:  current_name_length <= 8180
     using hypothesis H5.
***  Proved C3:  start_byte + 24 - 1 + current_name_length >= - 2147483648
     using hypotheses H4 & H8.
***  Proved C4:  start_byte + 24 - 1 + current_name_length <= 2147483647
     using hypotheses H5 & H9.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_25.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  4 >= integer__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  4 <= integer__base__last
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_26.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H54).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  4 >= integer__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  4 <= integer__base__last
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_27.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  srcbyte + 7 >= integer__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  srcbyte + 7 <= integer__base__last
***  Proved C1:  srcbyte + 7 >= integer__base__first
     using hypothesis H48.
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
<S>  New C2:  srcbyte <= 2147483640
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New H106:  dstbytes >= - 2
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H107:  dstbytes <= 8177
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C2:  srcbyte <= 2147483640
     using hypothesis H39.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_28.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
%%%  Simplified H130 on reading formula in, to give:
     %%%  H130:  4 >= integer__base__first
%%%  Simplified H131 on reading formula in, to give:
     %%%  H131:  4 <= integer__base__last
%%%  Simplified H132 on reading formula in, to give:
     %%%  H132:  4 <= fld_signaturelength(rrsig_record)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  4 <= fld_signaturelength(rrsig_record)
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  true
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  true
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  true
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified C15 on reading formula in, to give:
     %%%  C15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified C17 on reading formula in, to give:
     %%%  C17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified C31 on reading formula in, to give:
     %%%  C31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified C32 on reading formula in, to give:
     %%%  C32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
***  Proved C1:  4 <= fld_signaturelength(rrsig_record)
     using hypothesis H132.
***  Proved C3:  true
***  Proved C4:  true
***  Proved C5:  true
***  Proved C7:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= rr_type__wirestringtypeindex__first
     using hypothesis H102.
***  Proved C8:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
     using hypothesis H103.
***  Proved C9:  true
***  Proved C10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
     using hypothesis H99.
***  Proved C11:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C12:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H4.
***  Proved C13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H6.
***  Proved C15:  rr_type__classtype__first <= fld_class(fld_inherit(
          rrsig_record))
     using hypothesis H7.
***  Proved C16:  fld_class(fld_inherit(rrsig_record)) <= 
          rr_type__classtype__last
     using hypothesis H8.
***  Proved C17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
     using hypothesis H9.
***  Proved C18:  fld_typecovered(rrsig_record) <= dns_types__query_type__last
     using hypothesis H10.
***  Proved C19:  fld_algorithm(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C20:  fld_algorithm(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C21:  fld_numlabels(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H13.
***  Proved C22:  fld_numlabels(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H14.
***  Proved C23:  fld_origttl(rrsig_record) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C24:  fld_origttl(rrsig_record) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C25:  fld_sigexpiration(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C26:  fld_sigexpiration(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C27:  fld_siginception(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C28:  fld_siginception(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C29:  fld_keytag(rrsig_record) >= unsigned_types__unsigned16__first
     using hypothesis H21.
***  Proved C30:  fld_keytag(rrsig_record) <= unsigned_types__unsigned16__last
     using hypothesis H22.
***  Proved C31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
     using hypothesis H24.
***  Proved C33:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H25.
***  Proved C34:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H26.
***  Proved C35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H1.
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 1365
<S>  New C2:  fld_signaturelength(rrsig_record) <= 1365
>>>  Restructured hypothesis H113 into:
     >>>  H113:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) < 1
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
<S>  New C6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          fld_signaturelength(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H130:  true
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H131:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H116:  true
<S>  New H120:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
<S>  New H124:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H117:  true
<S>  New H121:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
<S>  New H125:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8180
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
<S>  New C6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
<S>  New H122:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
<S>  New H126:  start_byte + 24 >= - 2147483647
<S>  New H128:  start_byte >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
<S>  New H123:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
<S>  New H127:  start_byte + 24 <= 2147483648
<S>  New H129:  start_byte <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H126 further, to give:
     %%%  H126:  start_byte >= - 2147483671
%%%  Simplified H127 further, to give:
     %%%  H127:  start_byte <= 2147483624
***  Proved C2:  fld_signaturelength(rrsig_record) <= 1365
     using hypothesis H26.
***  Proved C6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
     using hypotheses H1 & H26.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_29.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H54).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  4 >= integer__base__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  4 <= integer__base__last
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  4 <= fld_signaturelength(rrsig_record)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  4 <= fld_signaturelength(rrsig_record)
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  true
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  true
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  true
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(update(bytes, [start_byte + 24 - 1 
          + loop__1__i], element(wireversion, [loop__1__i])), [i___1]) and 
          element(update(bytes, [start_byte + 24 - 1 + loop__1__i], element(
          wireversion, [loop__1__i])), [i___1]) <= dns_types__byte__last)
%%%  Simplified C15 on reading formula in, to give:
     %%%  C15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified C17 on reading formula in, to give:
     %%%  C17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified C31 on reading formula in, to give:
     %%%  C31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified C32 on reading formula in, to give:
     %%%  C32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
***  Proved C1:  4 <= fld_signaturelength(rrsig_record)
     using hypothesis H74.
***  Proved C3:  true
***  Proved C4:  true
***  Proved C5:  true
***  Proved C7:  current_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H4.
***  Proved C8:  current_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H5.
***  Proved C9:  true
***  Proved C10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(update(bytes, [start_byte + 24 - 1 
          + loop__1__i], element(wireversion, [loop__1__i])), [i___1]) and 
          element(update(bytes, [start_byte + 24 - 1 + loop__1__i], element(
          wireversion, [loop__1__i])), [i___1]) <= dns_types__byte__last)
     using hypotheses H7, H39, H40, H45 & H46.
***  Proved C11:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H8.
***  Proved C12:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H9.
***  Proved C13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H11.
***  Proved C15:  rr_type__classtype__first <= fld_class(fld_inherit(
          rrsig_record))
     using hypothesis H12.
***  Proved C16:  fld_class(fld_inherit(rrsig_record)) <= 
          rr_type__classtype__last
     using hypothesis H13.
***  Proved C17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
     using hypothesis H14.
***  Proved C18:  fld_typecovered(rrsig_record) <= dns_types__query_type__last
     using hypothesis H15.
***  Proved C19:  fld_algorithm(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H16.
***  Proved C20:  fld_algorithm(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H17.
***  Proved C21:  fld_numlabels(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H18.
***  Proved C22:  fld_numlabels(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H19.
***  Proved C23:  fld_origttl(rrsig_record) >= unsigned_types__unsigned32__first
     using hypothesis H20.
***  Proved C24:  fld_origttl(rrsig_record) <= unsigned_types__unsigned32__last
     using hypothesis H21.
***  Proved C25:  fld_sigexpiration(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H22.
***  Proved C26:  fld_sigexpiration(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H23.
***  Proved C27:  fld_siginception(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H24.
***  Proved C28:  fld_siginception(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H25.
***  Proved C29:  fld_keytag(rrsig_record) >= unsigned_types__unsigned16__first
     using hypothesis H26.
***  Proved C30:  fld_keytag(rrsig_record) <= unsigned_types__unsigned16__last
     using hypothesis H27.
***  Proved C31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
     using hypothesis H28.
***  Proved C32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
     using hypothesis H29.
***  Proved C33:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H30.
***  Proved C34:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H31.
***  Proved C35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H32.
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 1365
<S>  New C2:  fld_signaturelength(rrsig_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
<S>  New C6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          fld_signaturelength(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H56:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H57:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H72:  true
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H73:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New H58:  true
<S>  New H62:  start_byte + 24 - 1 + current_name_length >= 1
<S>  New H66:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H9:  start_byte <= 8180
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H59:  true
<S>  New H63:  start_byte + 24 - 1 + current_name_length <= 8180
<S>  New H67:  current_name_length <= 8180
<S>  New H32:  start_byte <= 6663
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
<S>  New H64:  start_byte + 24 - 1 + current_name_length >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
<S>  New H65:  start_byte + 24 - 1 + current_name_length <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H51 further, to give:
     %%%  H51:  start_byte >= - 2147483671
%%%  Simplified H52 further, to give:
     %%%  H52:  start_byte <= 2147483624
***  Proved C2:  fld_signaturelength(rrsig_record) <= 1365
     using hypothesis H31.
***  Proved C6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
     using hypotheses H31 & H32.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_30.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified H108 on reading formula in, to give:
     %%%  H108:  srcbyte + 7 >= integer__base__first
%%%  Simplified H109 on reading formula in, to give:
     %%%  H109:  srcbyte + 7 <= integer__base__last
%%%  Simplified H110 on reading formula in, to give:
     %%%  H110:  srcbyte + 7 <= siglength
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  srcbyte + 7 <= siglength
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  dstbytes >= - 2
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(update(update(update(bytes, [
          sigoffset + dstbytes], (lookup(element(fld_signature(rrsig_record), [
          srcbyte])) * 4 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 1])) div 16 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 1)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 1])) * 16 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 2])) div 4 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 2)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 2])) * 64 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 3]))) mod 
          dns_types__byte__modulus), [i___1]) and element(update(update(update(
          bytes, [sigoffset + dstbytes], (lookup(element(fld_signature(
          rrsig_record), [srcbyte])) * 4 mod dns_types__byte__modulus + lookup(
          element(fld_signature(rrsig_record), [srcbyte + 1])) div 16 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 1)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 1])) * 16 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 2])) div 4 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 2)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 2])) * 64 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 3]))) mod 
          dns_types__byte__modulus), [i___1]) <= dns_types__byte__last)
%%%  Simplified C15 on reading formula in, to give:
     %%%  C15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified C17 on reading formula in, to give:
     %%%  C17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified C31 on reading formula in, to give:
     %%%  C31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified C32 on reading formula in, to give:
     %%%  C32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
***  Proved C1:  srcbyte + 7 <= siglength
     using hypothesis H110.
***  Proved C2:  siglength <= rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H2.
***  Proved C3:  siglength = fld_signaturelength(rrsig_record)
     using hypothesis H3.
***  Proved C4:  dstbytes >= - 2
     using hypothesis H4.
***  Proved C6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - siglength
     using hypothesis H6.
***  Proved C7:  current_name_length >= rr_type__wirestringtypeindex__first
     using hypothesis H7.
***  Proved C8:  current_name_length <= rr_type__wirestringtypeindex__last
     using hypothesis H8.
***  Proved C9:  sigoffset = start_byte + 24 - 1 + current_name_length
     using hypothesis H9.
***  Proved C10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(update(update(update(bytes, [
          sigoffset + dstbytes], (lookup(element(fld_signature(rrsig_record), [
          srcbyte])) * 4 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 1])) div 16 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 1)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 1])) * 16 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 2])) div 4 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 2)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 2])) * 64 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 3]))) mod 
          dns_types__byte__modulus), [i___1]) and element(update(update(update(
          bytes, [sigoffset + dstbytes], (lookup(element(fld_signature(
          rrsig_record), [srcbyte])) * 4 mod dns_types__byte__modulus + lookup(
          element(fld_signature(rrsig_record), [srcbyte + 1])) div 16 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 1)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 1])) * 16 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 2])) div 4 mod 
          dns_types__byte__modulus) mod dns_types__byte__modulus), [sigoffset + 
          (dstbytes + 2)], (lookup(element(fld_signature(rrsig_record), [
          srcbyte + 2])) * 64 mod dns_types__byte__modulus + lookup(element(
          fld_signature(rrsig_record), [srcbyte + 3]))) mod 
          dns_types__byte__modulus), [i___1]) <= dns_types__byte__last)
     using hypotheses H10, H74, H75, H77, H78, H80, H81, H84, H85, H90, H91, 
          H98 & H99.
***  Proved C11:  start_byte >= dns_types__packet_bytes_range__first
     using hypothesis H11.
***  Proved C12:  start_byte <= dns_types__packet_bytes_range__last
     using hypothesis H12.
***  Proved C13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C15:  rr_type__classtype__first <= fld_class(fld_inherit(
          rrsig_record))
     using hypothesis H15.
***  Proved C16:  fld_class(fld_inherit(rrsig_record)) <= 
          rr_type__classtype__last
     using hypothesis H16.
***  Proved C17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
     using hypothesis H17.
***  Proved C18:  fld_typecovered(rrsig_record) <= dns_types__query_type__last
     using hypothesis H18.
***  Proved C19:  fld_algorithm(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H19.
***  Proved C20:  fld_algorithm(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H20.
***  Proved C21:  fld_numlabels(rrsig_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H21.
***  Proved C22:  fld_numlabels(rrsig_record) <= unsigned_types__unsigned8__last
     using hypothesis H22.
***  Proved C23:  fld_origttl(rrsig_record) >= unsigned_types__unsigned32__first
     using hypothesis H23.
***  Proved C24:  fld_origttl(rrsig_record) <= unsigned_types__unsigned32__last
     using hypothesis H24.
***  Proved C25:  fld_sigexpiration(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H25.
***  Proved C26:  fld_sigexpiration(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H26.
***  Proved C27:  fld_siginception(rrsig_record) >= 
          unsigned_types__unsigned32__first
     using hypothesis H27.
***  Proved C28:  fld_siginception(rrsig_record) <= 
          unsigned_types__unsigned32__last
     using hypothesis H28.
***  Proved C29:  fld_keytag(rrsig_record) >= unsigned_types__unsigned16__first
     using hypothesis H29.
***  Proved C30:  fld_keytag(rrsig_record) <= unsigned_types__unsigned16__last
     using hypothesis H30.
***  Proved C31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
     using hypothesis H31.
***  Proved C32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
     using hypothesis H32.
***  Proved C33:  fld_signaturelength(rrsig_record) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H33.
***  Proved C34:  fld_signaturelength(rrsig_record) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H34.
***  Proved C35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 
          rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H35.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
<S>  New H108:  srcbyte >= - 2147483655
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
<S>  New H109:  srcbyte <= 2147483640
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New H106:  dstbytes >= - 2
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H107:  dstbytes <= 8177
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C5:  dstbytes + 3 <= srcbyte + 4
     via its standard form, which is:
     Std.Fm C5:  - dstbytes + srcbyte > - 2
     using hypothesis H5.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_31.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New C1:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C2:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C3:  srcbyte >= 1
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C4:  srcbyte <= 1365
***  Proved C3:  srcbyte >= 1
     using hypotheses H4 & H5.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
     using hypotheses H1, H2, H4, H5 & H32.
***  Proved C2:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
     using hypotheses H1, H2, H4, H5 & H32.
***  Proved C4:  srcbyte <= 1365
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_32.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
***  Proved C1:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 
          dns_types__byte__first
     using hypothesis H40.
***  Proved C2:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 
          dns_types__byte__last
     using hypothesis H41.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_33.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
***  Proved C3:  srcbyte + 1 >= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first
     using hypothesis H38.
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New C1:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C2:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= 1365 -> 0 <= element(fld_signature(rrsig_record), [i___2]) 
          and element(fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C4:  srcbyte <= 1364
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C5:  srcbyte >= - 2147483649
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C6:  srcbyte <= 2147483646
***  Proved C5:  srcbyte >= - 2147483649
     using hypotheses H4 & H5.
***  Proved C6:  srcbyte <= 2147483646
     using hypothesis H39.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H38:  srcbyte >= 1
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
     using hypotheses H1, H2, H32 & H38.
***  Proved C2:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
     using hypotheses H1, H2, H32 & H38.
***  Proved C4:  srcbyte <= 1364
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_34.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
***  Proved C1:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 
          dns_types__byte__first
     using hypothesis H50.
***  Proved C2:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          dns_types__byte__last
     using hypothesis H51.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_35.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C3:  srcbyte + 2 >= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first
     using hypothesis H38.
***  Proved C5:  srcbyte + 2 >= integer__base__first
     using hypothesis H48.
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New C1:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C2:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= 1365 -> 0 <= element(fld_signature(rrsig_record), [i___2]) 
          and element(fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C4:  srcbyte <= 1363
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New C6:  srcbyte <= 2147483645
***  Proved C6:  srcbyte <= 2147483645
     using hypothesis H39.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
     using hypotheses H1, H2, H32 & H38.
***  Proved C2:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
     using hypotheses H1, H2, H32 & H38.
***  Proved C4:  srcbyte <= 1363
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_36.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
***  Proved C1:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 
          dns_types__byte__first
     using hypothesis H60.
***  Proved C2:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          dns_types__byte__last
     using hypothesis H61.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_37.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
***  Proved C3:  srcbyte + 3 >= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first
     using hypothesis H38.
***  Proved C5:  srcbyte + 3 >= integer__base__first
     using hypothesis H48.
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New C1:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C2:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= 1365 -> 0 <= element(fld_signature(rrsig_record), [i___2]) 
          and element(fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New C4:  srcbyte <= 1362
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New C6:  srcbyte <= 2147483644
***  Proved C6:  srcbyte <= 2147483644
     using hypothesis H39.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
     using hypotheses H1, H2, H32 & H38.
***  Proved C2:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
     using hypotheses H1, H2, H32 & H38.
***  Proved C4:  srcbyte <= 1362
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_38.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
***  Proved C1:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 
          dns_types__byte__first
     using hypothesis H70.
***  Proved C2:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          dns_types__byte__last
     using hypothesis H71.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_39.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
***  Proved C3:  true
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 
          mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) 
          div 16 mod 256) mod 256 >= 0
***  Proved C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 
          mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) 
          div 16 mod 256) mod 256 <= 255
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_40.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
***  Proved C3:  true
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 16 
          mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 16 
          mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) 
          div 4 mod 256) mod 256 >= 0
<S>  New C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) 
          div 4 mod 256) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
***  Proved C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_41.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 64 
          mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 64 
          mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New H11:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 64 
          mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3])))
           mod 256 >= 0
<S>  New C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 64 
          mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3])))
           mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
***  Proved C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_42.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
***  Proved C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 
          mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 1])) div 16 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= dns_types__byte__first
     using hypothesis H74.
***  Proved C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 
          mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 1])) div 16 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= dns_types__byte__last
     using hypothesis H75.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New C3:  sigoffset + dstbytes >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8156 - rr_type__maxdomainnamelength - siglength
<S>  New H12:  start_byte <= 8180
<S>  New H35:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C4:  sigoffset + dstbytes <= 8180
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C5:  sigoffset + dstbytes >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C6:  sigoffset + dstbytes <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C3:  sigoffset + dstbytes >= 1
     using hypotheses H4, H7, H9 & H11.
***  Proved C5:  sigoffset + dstbytes >= - 2147483648
     using hypotheses H4, H7, H9 & H11.
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H12 (redundant, given H35).
---  Eliminated hypothesis H39 (redundant, given H47).
---  Eliminated hypothesis H46 (redundant, given H38).
---  Eliminated hypothesis H47 (redundant, given H57).
---  Eliminated hypothesis H48 (redundant, given H38).
---  Eliminated hypothesis H49 (redundant, given H57).
---  Eliminated hypothesis H56 (redundant, given H38).
---  Eliminated hypothesis H57 (redundant, given H67).
---  Eliminated hypothesis H58 (redundant, given H38).
---  Eliminated hypothesis H59 (redundant, given H67).
---  Eliminated hypothesis H66 (redundant, given H38).
---  Eliminated hypothesis H68 (redundant, given H38).
---  Eliminated hypothesis H69 (redundant, given H67).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of siglength by:
          fld_signaturelength(rrsig_record).
<S>  New H1:  srcbyte + 3 <= fld_signaturelength(rrsig_record)
<S>  New H6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
<S>  New H2:  fld_signaturelength(rrsig_record) <= 1365
-S-  Eliminated hypothesis H9.
     This was achieved by replacing all occurrences of sigoffset by:
          start_byte + 24 - 1 + current_name_length.
<S>  New C4:  start_byte + 24 - 1 + current_name_length + dstbytes <= 8180
<S>  New C6:  start_byte + 24 - 1 + current_name_length + dstbytes <= 2147483647
***  Proved C4:  start_byte + 24 - 1 + current_name_length + dstbytes <= 8180
     using hypotheses H5, H8, H35 & H67.
***  Proved C6:  start_byte + 24 - 1 + current_name_length + dstbytes <= 
          2147483647
     using hypotheses H5, H8, H35 & H67.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_43.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
***  Proved C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= dns_types__byte__first
     using hypothesis H77.
***  Proved C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= dns_types__byte__last
     using hypothesis H78.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New C3:  sigoffset + (dstbytes + 1) >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8156 - rr_type__maxdomainnamelength - siglength
<S>  New H12:  start_byte <= 8180
<S>  New H35:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C4:  sigoffset + (dstbytes + 1) <= 8180
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New C5:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New C7:  dstbytes >= - 2147483649
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New C6:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New C8:  dstbytes <= 2147483646
***  Proved C7:  dstbytes >= - 2147483649
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C3:  sigoffset + (dstbytes + 1) >= 1
     via its standard form, which is:
     Std.Fm C3:  1 + (dstbytes + sigoffset) >= 1
     using hypotheses H4, H7, H9 & H11.
***  Proved C5:  sigoffset + (dstbytes + 1) >= - 2147483648
     via its standard form, which is:
     Std.Fm C5:  1 + (dstbytes + sigoffset) >= - 2147483648
     using hypotheses H4, H7, H9 & H11.
***  Proved C8:  dstbytes <= 2147483646
     using hypotheses H5 & H49.
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H12 (redundant, given H35).
---  Eliminated hypothesis H39 (redundant, given H47).
---  Eliminated hypothesis H46 (redundant, given H38).
---  Eliminated hypothesis H47 (redundant, given H57).
---  Eliminated hypothesis H48 (redundant, given H38).
---  Eliminated hypothesis H49 (redundant, given H57).
---  Eliminated hypothesis H56 (redundant, given H38).
---  Eliminated hypothesis H57 (redundant, given H67).
---  Eliminated hypothesis H58 (redundant, given H38).
---  Eliminated hypothesis H59 (redundant, given H67).
---  Eliminated hypothesis H66 (redundant, given H38).
---  Eliminated hypothesis H68 (redundant, given H38).
---  Eliminated hypothesis H69 (redundant, given H67).
---  Eliminated hypothesis H86 (redundant, given H84).
---  Eliminated hypothesis H87 (redundant, given H85).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of siglength by:
          fld_signaturelength(rrsig_record).
<S>  New H1:  srcbyte + 3 <= fld_signaturelength(rrsig_record)
<S>  New H6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
<S>  New H2:  fld_signaturelength(rrsig_record) <= 1365
-S-  Eliminated hypothesis H9.
     This was achieved by replacing all occurrences of sigoffset by:
          start_byte + 24 - 1 + current_name_length.
<S>  New H84:  start_byte + 24 - 1 + current_name_length + dstbytes >= 1
<S>  New H85:  start_byte + 24 - 1 + current_name_length + dstbytes <= 8180
<S>  New C4:  start_byte + 24 - 1 + current_name_length + (dstbytes + 1) <= 8180
<S>  New C6:  start_byte + 24 - 1 + current_name_length + (dstbytes + 1) <= 
          2147483647
***  Proved C4:  start_byte + 24 - 1 + current_name_length + (dstbytes + 1) <= 
          8180
     using hypotheses H5, H8, H35 & H67.
***  Proved C6:  start_byte + 24 - 1 + current_name_length + (dstbytes + 1) <= 
          2147483647
     using hypotheses H5, H8, H35 & H67.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_44.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
***  Proved C1:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 
          dns_types__byte__first
     using hypothesis H80.
***  Proved C2:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 
          dns_types__byte__last
     using hypothesis H81.
***  Proved C7:  dstbytes + 2 >= dns_types__packet_bytes_range__base__first
     using hypothesis H94.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New C3:  sigoffset + (dstbytes + 2) >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8156 - rr_type__maxdomainnamelength - siglength
<S>  New H12:  start_byte <= 8180
<S>  New H35:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C4:  sigoffset + (dstbytes + 2) <= 8180
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New C5:  sigoffset + (dstbytes + 2) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New C6:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New C8:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C3:  sigoffset + (dstbytes + 2) >= 1
     via its standard form, which is:
     Std.Fm C3:  2 + (dstbytes + sigoffset) >= 1
     using hypotheses H4, H7, H9 & H11.
***  Proved C5:  sigoffset + (dstbytes + 2) >= - 2147483648
     via its standard form, which is:
     Std.Fm C5:  2 + (dstbytes + sigoffset) >= - 2147483648
     using hypotheses H4, H7, H9 & H11.
***  Proved C8:  dstbytes <= 2147483645
     using hypotheses H5 & H59.
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H88 (true-hypothesis).
---  Eliminated hypothesis H89 (true-hypothesis).
---  Eliminated hypothesis H12 (redundant, given H35).
---  Eliminated hypothesis H39 (redundant, given H47).
---  Eliminated hypothesis H46 (redundant, given H38).
---  Eliminated hypothesis H47 (redundant, given H57).
---  Eliminated hypothesis H48 (redundant, given H38).
---  Eliminated hypothesis H49 (redundant, given H57).
---  Eliminated hypothesis H56 (redundant, given H38).
---  Eliminated hypothesis H57 (redundant, given H67).
---  Eliminated hypothesis H58 (redundant, given H38).
---  Eliminated hypothesis H59 (redundant, given H67).
---  Eliminated hypothesis H66 (redundant, given H38).
---  Eliminated hypothesis H68 (redundant, given H38).
---  Eliminated hypothesis H69 (redundant, given H67).
---  Eliminated hypothesis H85 (redundant, given H91).
---  Eliminated hypothesis H86 (redundant, given H84).
---  Eliminated hypothesis H87 (redundant, given H91).
---  Eliminated hypothesis H90 (redundant, given H84).
---  Eliminated hypothesis H92 (redundant, given H84).
---  Eliminated hypothesis H93 (redundant, given H91).
---  Eliminated hypothesis H94 (redundant, given H4).
---  Eliminated hypothesis H95 (redundant, given H5 & H67).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of siglength by:
          fld_signaturelength(rrsig_record).
<S>  New H1:  srcbyte + 3 <= fld_signaturelength(rrsig_record)
<S>  New H6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
<S>  New H2:  fld_signaturelength(rrsig_record) <= 1365
-S-  Eliminated hypothesis H9.
     This was achieved by replacing all occurrences of sigoffset by:
          start_byte + 24 - 1 + current_name_length.
<S>  New H84:  start_byte + 24 - 1 + current_name_length + dstbytes >= 1
<S>  New H91:  start_byte + 24 - 1 + current_name_length + (dstbytes + 1) <= 
          8180
<S>  New C4:  start_byte + 24 - 1 + current_name_length + (dstbytes + 2) <= 8180
<S>  New C6:  start_byte + 24 - 1 + current_name_length + (dstbytes + 2) <= 
          2147483647
***  Proved C4:  start_byte + 24 - 1 + current_name_length + (dstbytes + 2) <= 
          8180
     using hypotheses H5, H8, H35 & H67.
***  Proved C6:  start_byte + 24 - 1 + current_name_length + (dstbytes + 2) <= 
          2147483647
     using hypotheses H5, H8, H35 & H67.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_45.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  srcbyte <= 2147483643
***  Proved C1:  srcbyte >= - 2147483652
     using hypotheses H4 & H5.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C2:  srcbyte <= 2147483643
     using hypothesis H39.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_46.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New C1:  dstbytes >= - 2
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8156 - rr_type__maxdomainnamelength - siglength
<S>  New H12:  start_byte <= 8180
<S>  New H35:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  dstbytes <= 8177
***  Proved C1:  dstbytes >= - 2
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C2:  dstbytes <= 8177
     using hypotheses H5 & H39.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_47.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
%%%  Simplified H130 on reading formula in, to give:
     %%%  H130:  4 >= integer__base__first
%%%  Simplified H131 on reading formula in, to give:
     %%%  H131:  4 <= integer__base__last
%%%  Simplified H132 on reading formula in, to give:
     %%%  H132:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= dns_types__packet_bytes_range__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= dns_types__packet_bytes_range__last
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  0 <= dns_types__packet_bytes_range__base__last
***  Proved C1:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= dns_types__packet_bytes_range__first
     using hypothesis H124.
***  Proved C5:  1 >= dns_types__packet_bytes_range__first
     using hypothesis H116.
***  Proved C6:  1 <= dns_types__packet_bytes_range__last
     using hypothesis H117.
***  Proved C7:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= dns_types__packet_bytes_range__first
     using hypothesis H124.
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(
          bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H117:  true
<S>  New H121:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
<S>  New H125:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8180
<S>  New C2:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New C8:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
<S>  New H122:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
<S>  New H126:  start_byte + 24 >= - 2147483647
<S>  New H128:  start_byte >= - 2147483672
<S>  New C3:  true
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
<S>  New H123:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
<S>  New H127:  start_byte + 24 <= 2147483648
<S>  New H129:  start_byte <= 2147483623
<S>  New C4:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H130:  true
<S>  New C9:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H131:  true
<S>  New C10:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483623
***  Proved C2:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
     using hypothesis H113.
***  Proved C8:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
     using hypothesis H113.
***  Proved C3:  true
***  Proved C4:  true
***  Proved C10:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483623
     using hypothesis H113.
>>>  Restructured hypothesis H113 into:
     >>>  H113:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) < 1
>>>  Restructured hypothesis H126 into:
     >>>  H126:  start_byte >= - 2147483671
>>>  Restructured hypothesis H127 into:
     >>>  H127:  start_byte <= 2147483624
>>>  Restructured hypothesis H132 into:
     >>>  H132:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
<S>  New H116:  true
<S>  New H120:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
<S>  New H124:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C9:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483672
     using hypothesis H107.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_48.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H54).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  4 >= integer__base__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  4 <= integer__base__last
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  24 + current_name_length >= dns_types__packet_bytes_range__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  24 + current_name_length <= dns_types__packet_bytes_range__last
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  0 <= dns_types__packet_bytes_range__base__last
***  Proved C1:  24 + current_name_length >= 
          dns_types__packet_bytes_range__first
     using hypothesis H66.
***  Proved C5:  1 >= dns_types__packet_bytes_range__first
     using hypothesis H58.
***  Proved C6:  1 <= dns_types__packet_bytes_range__last
     using hypothesis H59.
***  Proved C7:  24 + current_name_length >= 
          dns_types__packet_bytes_range__first
     using hypothesis H66.
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H9:  start_byte <= 8180
<S>  New H32:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H59:  true
<S>  New H63:  start_byte + 24 - 1 + current_name_length <= 8180
<S>  New H67:  current_name_length <= 8180
<S>  New C2:  current_name_length <= 8156
<S>  New C8:  current_name_length <= 8156
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
<S>  New H64:  start_byte + 24 - 1 + current_name_length >= - 2147483648
<S>  New C3:  true
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
<S>  New H65:  start_byte + 24 - 1 + current_name_length <= 2147483647
<S>  New C4:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H72:  true
<S>  New C9:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H73:  true
<S>  New C10:  current_name_length <= 2147483623
***  Proved C3:  true
***  Proved C4:  true
***  Proved C10:  current_name_length <= 2147483623
     using hypothesis H67.
>>>  Restructured hypothesis H51 into:
     >>>  H51:  start_byte >= - 2147483671
>>>  Restructured hypothesis H52 into:
     >>>  H52:  start_byte <= 2147483624
>>>  Restructured hypothesis H74 into:
     >>>  H74:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H56:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H57:  true
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New H58:  true
<S>  New H62:  start_byte + 24 - 1 + current_name_length >= 1
<S>  New H66:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C2:  current_name_length <= 8156
     using hypothesis H5.
***  Proved C8:  current_name_length <= 8156
     using hypothesis H5.
***  Proved C9:  current_name_length >= - 2147483672
     using hypothesis H66.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_49.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified H108 on reading formula in, to give:
     %%%  H108:  srcbyte + 7 >= integer__base__first
%%%  Simplified H109 on reading formula in, to give:
     %%%  H109:  srcbyte + 7 <= integer__base__last
%%%  Simplified H110 on reading formula in, to give:
     %%%  H110:  not srcbyte + 7 <= siglength
***  Proved C6:  1 <= dns_types__packet_bytes_range__last
     using hypotheses H4 & H107.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New H106:  dstbytes >= - 2
<S>  New C1:  24 + current_name_length + (dstbytes + 3 - 1) >= 1
<S>  New C5:  true
<S>  New C7:  current_name_length >= - 23
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8156 - rr_type__maxdomainnamelength - siglength
<S>  New H12:  start_byte <= 8180
<S>  New H35:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H107:  dstbytes <= 8177
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C2:  24 + current_name_length + (dstbytes + 3 - 1) <= 8180
<S>  New C8:  current_name_length <= 8156
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
<S>  New C3:  dstbytes + 3 >= - 2147483647
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
<S>  New C4:  dstbytes + 3 <= 2147483648
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
<S>  New H108:  srcbyte >= - 2147483655
<S>  New C9:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
<S>  New H109:  srcbyte <= 2147483640
<S>  New C10:  current_name_length <= 2147483623
***  Proved C5:  true
***  Proved C3:  dstbytes + 3 >= - 2147483647
     using hypothesis H102.
***  Proved C4:  dstbytes + 3 <= 2147483648
     using hypothesis H103.
>>>  Restructured hypothesis H110 into:
     >>>  H110:  siglength < srcbyte + 7
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  24 + current_name_length + (dstbytes + 3 - 1) >= 1
     via its standard form, which is:
     Std.Fm C1:  26 + (current_name_length + dstbytes) >= 1
     using hypotheses H4 & H7.
***  Proved C7:  current_name_length >= - 23
     using hypothesis H7.
***  Proved C2:  24 + current_name_length + (dstbytes + 3 - 1) <= 8180
     via its standard form, which is:
     Std.Fm C2:  26 + (current_name_length + dstbytes) <= 8180
     using hypotheses H5, H8 & H39.
***  Proved C8:  current_name_length <= 8156
     using hypothesis H8.
***  Proved C9:  current_name_length >= - 2147483672
     using hypothesis H7.
***  Proved C10:  current_name_length <= 2147483623
     using hypothesis H8.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_50.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
%%%  Simplified H130 on reading formula in, to give:
     %%%  H130:  4 >= integer__base__first
%%%  Simplified H131 on reading formula in, to give:
     %%%  H131:  4 <= integer__base__last
%%%  Simplified H132 on reading formula in, to give:
     %%%  H132:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified H133 on reading formula in, to give:
     %%%  H133:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= dns_types__packet_bytes_range__first
%%%  Simplified H134 on reading formula in, to give:
     %%%  H134:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= dns_types__packet_bytes_range__last
%%%  Simplified H135 on reading formula in, to give:
     %%%  H135:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified H136 on reading formula in, to give:
     %%%  H136:  0 <= dns_types__packet_bytes_range__base__last
---  Hypothesis H137 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H117).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 6 >= 
          dns_types__packet_bytes_range__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 6 <= 
          dns_types__packet_bytes_range__base__last
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__base__first
     using hypothesis H38.
***  Proved C4:  start_byte + 4 <= dns_types__packet_bytes_range__base__last
     using hypothesis H39.
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
<S>  New H122:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
<S>  New H126:  start_byte + 24 >= - 2147483647
<S>  New H128:  start_byte >= - 2147483672
<S>  New H135:  true
<S>  New C1:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483642
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
<S>  New H123:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
<S>  New H127:  start_byte + 24 <= 2147483648
<S>  New H129:  start_byte <= 2147483623
<S>  New H136:  true
<S>  New C2:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483653
***  Proved C2:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483653
     using hypothesis H113.
>>>  Restructured hypothesis H113 into:
     >>>  H113:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) < 1
>>>  Restructured hypothesis H126 into:
     >>>  H126:  start_byte >= - 2147483671
>>>  Restructured hypothesis H127 into:
     >>>  H127:  start_byte <= 2147483624
>>>  Restructured hypothesis H132 into:
     >>>  H132:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H130:  true
<S>  New H141:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H131:  true
<S>  New H142:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H116:  true
<S>  New H120:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
<S>  New H124:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H133:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 23
<S>  New H139:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 23
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H117:  true
<S>  New H121:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
<S>  New H125:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8180
<S>  New H134:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New H140:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified C1 further, to give:
     %%%  C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483666
***  Proved C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483666
     using hypothesis H107.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_51.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H54).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  4 >= integer__base__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  4 <= integer__base__last
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  24 + current_name_length >= dns_types__packet_bytes_range__first
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  24 + current_name_length <= dns_types__packet_bytes_range__last
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  0 <= dns_types__packet_bytes_range__base__last
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H59).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  24 + current_name_length - 6 >= 
          dns_types__packet_bytes_range__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  24 + current_name_length - 6 <= 
          dns_types__packet_bytes_range__base__last
***  Proved C4:  start_byte + 4 <= dns_types__packet_bytes_range__base__last
     using hypothesis H54.
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
<S>  New H64:  start_byte + 24 - 1 + current_name_length >= - 2147483648
<S>  New H77:  true
<S>  New C1:  24 + current_name_length >= - 2147483642
<S>  New C3:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
<S>  New H65:  start_byte + 24 - 1 + current_name_length <= 2147483647
<S>  New H78:  true
<S>  New C2:  24 + current_name_length <= 2147483653
>>>  Restructured hypothesis H51 into:
     >>>  H51:  start_byte >= - 2147483671
>>>  Restructured hypothesis H52 into:
     >>>  H52:  start_byte <= 2147483624
>>>  Restructured hypothesis H74 into:
     >>>  H74:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H56:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H57:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H72:  true
<S>  New H83:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H73:  true
<S>  New H84:  current_name_length <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New H58:  true
<S>  New H62:  start_byte + 24 - 1 + current_name_length >= 1
<S>  New H66:  current_name_length >= 1
<S>  New H75:  current_name_length >= - 23
<S>  New H81:  current_name_length >= - 23
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H9:  start_byte <= 8180
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H59:  true
<S>  New H63:  start_byte + 24 - 1 + current_name_length <= 8180
<S>  New H67:  current_name_length <= 8180
<S>  New H76:  current_name_length <= 8156
<S>  New H82:  current_name_length <= 8156
<S>  New H32:  start_byte <= 6663
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified C1 further, to give:
     %%%  C1:  current_name_length >= - 2147483666
%%%  Simplified C2 further, to give:
     %%%  C2:  current_name_length <= 2147483629
***  Proved C3:  start_byte >= - 2147483652
     using hypothesis H8.
***  Proved C1:  current_name_length >= - 2147483666
     using hypothesis H66.
***  Proved C2:  current_name_length <= 2147483629
     using hypothesis H84.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_52.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified H108 on reading formula in, to give:
     %%%  H108:  srcbyte + 7 >= integer__base__first
%%%  Simplified H109 on reading formula in, to give:
     %%%  H109:  srcbyte + 7 <= integer__base__last
%%%  Simplified H110 on reading formula in, to give:
     %%%  H110:  not srcbyte + 7 <= siglength
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
<S>  New H113:  dstbytes + 3 >= - 2147483647
<S>  New C1:  24 + current_name_length + (dstbytes + 3 - 1) >= - 2147483642
<S>  New C3:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
<S>  New H114:  dstbytes + 3 <= 2147483648
<S>  New C2:  24 + current_name_length + (dstbytes + 3 - 1) <= 2147483653
<S>  New C4:  start_byte <= 2147483643
>>>  Restructured hypothesis H110 into:
     >>>  H110:  siglength < srcbyte + 7
>>>  Restructured hypothesis H113 into:
     >>>  H113:  dstbytes >= - 2147483650
>>>  Restructured hypothesis H114 into:
     >>>  H114:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
<S>  New H108:  srcbyte >= - 2147483655
<S>  New H119:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
<S>  New H109:  srcbyte <= 2147483640
<S>  New H120:  current_name_length <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New H106:  dstbytes >= - 2
<S>  New H111:  24 + current_name_length + (dstbytes + 3 - 1) >= 1
<S>  New H115:  true
<S>  New H117:  current_name_length >= - 23
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H107:  dstbytes <= 8177
<S>  New H112:  24 + current_name_length + (dstbytes + 3 - 1) <= 8180
<S>  New H116:  true
<S>  New H118:  current_name_length <= 8156
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
***  Proved C1:  24 + current_name_length + (dstbytes + 3 - 1) >= - 2147483642
     using hypothesis H111.
***  Proved C3:  start_byte >= - 2147483652
     using hypothesis H11.
***  Proved C2:  24 + current_name_length + (dstbytes + 3 - 1) <= 2147483653
     using hypothesis H112.
***  Proved C4:  start_byte <= 2147483643
     using hypothesis H12.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_53.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
%%%  Simplified H130 on reading formula in, to give:
     %%%  H130:  4 >= integer__base__first
%%%  Simplified H131 on reading formula in, to give:
     %%%  H131:  4 <= integer__base__last
%%%  Simplified H132 on reading formula in, to give:
     %%%  H132:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified H133 on reading formula in, to give:
     %%%  H133:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= dns_types__packet_bytes_range__first
%%%  Simplified H134 on reading formula in, to give:
     %%%  H134:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= dns_types__packet_bytes_range__last
%%%  Simplified H135 on reading formula in, to give:
     %%%  H135:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified H136 on reading formula in, to give:
     %%%  H136:  0 <= dns_types__packet_bytes_range__base__last
---  Hypothesis H137 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H117).
%%%  Simplified H143 on reading formula in, to give:
     %%%  H143:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 6 >= 
          dns_types__packet_bytes_range__base__first
%%%  Simplified H144 on reading formula in, to give:
     %%%  H144:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 6 <= 
          dns_types__packet_bytes_range__base__last
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H39).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned16__last
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned16__last
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  true
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H35.
***  Proved C4:  start_byte + 4 <= dns_types__packet_bytes_range__last
     using hypothesis H36.
***  Proved C5:  start_byte + 4 <= dns_types__packet_bytes_range__last - 1
     using hypothesis H37.
***  Proved C8:  true
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C1:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus >= 0
<S>  New C6:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
<S>  New C2:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus <= 65535
<S>  New C7:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus <= 65535
>>>  Restructured hypothesis H113 into:
     >>>  H113:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) < 1
>>>  Restructured hypothesis H132 into:
     >>>  H132:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H130:  true
<S>  New H141:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H131:  true
<S>  New H142:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H116:  true
<S>  New H120:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
<S>  New H124:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H133:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 23
<S>  New H139:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 23
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H117:  true
<S>  New H121:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
<S>  New H125:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8180
<S>  New H134:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New H140:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
<S>  New H122:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
<S>  New H126:  start_byte + 24 >= - 2147483647
<S>  New H128:  start_byte >= - 2147483672
<S>  New H135:  true
<S>  New H143:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483642
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
<S>  New H123:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
<S>  New H127:  start_byte + 24 <= 2147483648
<S>  New H129:  start_byte <= 2147483623
<S>  New H136:  true
<S>  New H144:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483653
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
<S>  New C1:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 >= 0
<S>  New C6:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 >= 0
<S>  New C2:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 <= 65535
<S>  New C7:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H126 further, to give:
     %%%  H126:  start_byte >= - 2147483671
%%%  Simplified H127 further, to give:
     %%%  H127:  start_byte <= 2147483624
%%%  Simplified H143 further, to give:
     %%%  H143:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483666
%%%  Simplified H144 further, to give:
     %%%  H144:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483629
***  Proved C1:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 >= 0
***  Proved C6:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 >= 0
###  Established a contradiction [P-and-not-P] among the following hypotheses:
          H113 & H124.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_54.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H54).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  4 >= integer__base__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  4 <= integer__base__last
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  24 + current_name_length >= dns_types__packet_bytes_range__first
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  24 + current_name_length <= dns_types__packet_bytes_range__last
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  0 <= dns_types__packet_bytes_range__base__last
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H59).
%%%  Simplified H85 on reading formula in, to give:
     %%%  H85:  24 + current_name_length - 6 >= 
          dns_types__packet_bytes_range__base__first
%%%  Simplified H86 on reading formula in, to give:
     %%%  H86:  24 + current_name_length - 6 <= 
          dns_types__packet_bytes_range__base__last
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned16__last
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned16__last
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  true
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H8.
***  Proved C8:  true
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
<S>  New C1:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New C6:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
<S>  New C2:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
<S>  New C7:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H9:  start_byte <= 8180
<S>  New H32:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H59:  true
<S>  New H63:  start_byte + 24 - 1 + current_name_length <= 8180
<S>  New H67:  current_name_length <= 8180
<S>  New H76:  current_name_length <= 8156
<S>  New H82:  current_name_length <= 8156
<S>  New C4:  start_byte <= 8176
<S>  New C5:  start_byte <= 8175
>>>  Restructured hypothesis H74 into:
     >>>  H74:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H56:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H57:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H72:  true
<S>  New H83:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H73:  true
<S>  New H84:  current_name_length <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New H58:  true
<S>  New H62:  start_byte + 24 - 1 + current_name_length >= 1
<S>  New H66:  current_name_length >= 1
<S>  New H75:  current_name_length >= - 23
<S>  New H81:  current_name_length >= - 23
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
<S>  New H64:  start_byte + 24 - 1 + current_name_length >= - 2147483648
<S>  New H77:  true
<S>  New H85:  24 + current_name_length >= - 2147483642
<S>  New H87:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
<S>  New H65:  start_byte + 24 - 1 + current_name_length <= 2147483647
<S>  New H78:  true
<S>  New H86:  24 + current_name_length <= 2147483653
<S>  New H88:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New C1:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 >= 0
<S>  New C6:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 >= 0
<S>  New C2:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 <= 65535
<S>  New C7:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H51 further, to give:
     %%%  H51:  start_byte >= - 2147483671
%%%  Simplified H52 further, to give:
     %%%  H52:  start_byte <= 2147483624
%%%  Simplified H85 further, to give:
     %%%  H85:  current_name_length >= - 2147483666
%%%  Simplified H86 further, to give:
     %%%  H86:  current_name_length <= 2147483629
***  Proved C4:  start_byte <= 8176
     using hypothesis H32.
***  Proved C5:  start_byte <= 8175
     using hypothesis H32.
***  Proved C1:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 >= 0
***  Proved C6:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 >= 0
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H41 (true-hypothesis).
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H60 (true-hypothesis).
---  Eliminated hypothesis H61 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H49 (duplicate of H35).
---  Eliminated hypothesis H82 (duplicate of H76).
---  Eliminated hypothesis H81 (duplicate of H75).
---  Eliminated hypothesis H35 (duplicate of H2).
---  Eliminated hypothesis H66 (duplicate of H4).
---  Eliminated hypothesis H9 (redundant, given H32).
---  Eliminated hypothesis H31 (redundant, given H74).
---  Eliminated hypothesis H36 (redundant, given H55).
---  Eliminated hypothesis H47 (redundant, given H45).
---  Eliminated hypothesis H48 (redundant, given H46).
---  Eliminated hypothesis H50 (redundant, given H3).
---  Eliminated hypothesis H51 (redundant, given H8).
---  Eliminated hypothesis H52 (redundant, given H32).
---  Eliminated hypothesis H53 (redundant, given H8).
---  Eliminated hypothesis H54 (redundant, given H32).
---  Eliminated hypothesis H63 (redundant, given H1).
---  Eliminated hypothesis H64 (redundant, given H62).
---  Eliminated hypothesis H65 (redundant, given H1).
---  Eliminated hypothesis H67 (redundant, given H5).
---  Eliminated hypothesis H75 (redundant, given H4).
---  Eliminated hypothesis H76 (redundant, given H5).
---  Eliminated hypothesis H83 (redundant, given H4).
---  Eliminated hypothesis H84 (redundant, given H5).
---  Eliminated hypothesis H85 (redundant, given H4).
---  Eliminated hypothesis H86 (redundant, given H5).
---  Eliminated hypothesis H87 (redundant, given H8).
---  Eliminated hypothesis H88 (redundant, given H32).
-S-  Eliminated hypothesis H55.
     This was achieved by replacing all occurrences of loop__1__i by:
          current_name_length__entry__loop__1.
<S>  New H46:  start_byte + 24 - 1 + current_name_length__entry__loop__1 <= 8180
<S>  New H45:  start_byte + 24 - 1 + current_name_length__entry__loop__1 >= 1
<S>  New H39:  element(wireversion, [current_name_length__entry__loop__1]) >= 0
<S>  New H40:  element(wireversion, [current_name_length__entry__loop__1]) <= 
          255
<S>  New H2:  current_name_length__entry__loop__1 >= 1
<S>  New H3:  current_name_length__entry__loop__1 <= 129
---  Eliminated conclusion C7, which is a duplicate of C2.
***  Proved C2:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 <= 65535
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_55.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified H108 on reading formula in, to give:
     %%%  H108:  srcbyte + 7 >= integer__base__first
%%%  Simplified H109 on reading formula in, to give:
     %%%  H109:  srcbyte + 7 <= integer__base__last
%%%  Simplified H110 on reading formula in, to give:
     %%%  H110:  not srcbyte + 7 <= siglength
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  true
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H11.
***  Proved C8:  true
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
<S>  New C1:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod unsigned_types__unsigned32__modulus >= 0
<S>  New C6:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
<S>  New C2:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod unsigned_types__unsigned32__modulus <= 65535
<S>  New C7:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8156 - rr_type__maxdomainnamelength - siglength
<S>  New H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= 8180 -> dns_types__byte__first <= element(bytes, [
          i___1]) and element(bytes, [i___1]) <= dns_types__byte__last)
<S>  New H12:  start_byte <= 8180
<S>  New H35:  start_byte <= 8156 - rr_type__maxdomainnamelength - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H107:  dstbytes <= 8177
<S>  New H112:  24 + current_name_length + (dstbytes + 3 - 1) <= 8180
<S>  New H116:  true
<S>  New H118:  current_name_length <= 8156
<S>  New C4:  start_byte <= 8176
<S>  New C5:  start_byte <= 8175
>>>  Restructured hypothesis H110 into:
     >>>  H110:  siglength < srcbyte + 7
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 8028 - rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= 6663
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
<S>  New H108:  srcbyte >= - 2147483655
<S>  New H119:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
<S>  New H109:  srcbyte <= 2147483640
<S>  New H120:  current_name_length <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New H106:  dstbytes >= - 2
<S>  New H111:  24 + current_name_length + (dstbytes + 3 - 1) >= 1
<S>  New H115:  true
<S>  New H117:  current_name_length >= - 23
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
<S>  New H113:  dstbytes + 3 >= - 2147483647
<S>  New H121:  24 + current_name_length + (dstbytes + 3 - 1) >= - 2147483642
<S>  New H123:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
<S>  New H114:  dstbytes + 3 <= 2147483648
<S>  New H122:  24 + current_name_length + (dstbytes + 3 - 1) <= 2147483653
<S>  New H124:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New C1:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod 4294967296 >= 0
<S>  New C6:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod 4294967296 >= 0
<S>  New C2:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod 4294967296 <= 65535
<S>  New C7:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) - 
          6) mod 65536 mod 4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H113 further, to give:
     %%%  H113:  dstbytes >= - 2147483650
%%%  Simplified H114 further, to give:
     %%%  H114:  dstbytes <= 2147483645
***  Proved C4:  start_byte <= 8176
     using hypothesis H35.
***  Proved C5:  start_byte <= 8175
     using hypothesis H35.
***  Proved C1:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod 4294967296 >= 0
***  Proved C6:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod 4294967296 >= 0
---  Eliminated hypothesis H42 (true-hypothesis).
---  Eliminated hypothesis H43 (true-hypothesis).
---  Eliminated hypothesis H52 (true-hypothesis).
---  Eliminated hypothesis H53 (true-hypothesis).
---  Eliminated hypothesis H62 (true-hypothesis).
---  Eliminated hypothesis H63 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H82 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H88 (true-hypothesis).
---  Eliminated hypothesis H89 (true-hypothesis).
---  Eliminated hypothesis H96 (true-hypothesis).
---  Eliminated hypothesis H97 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H113 (duplicate of H102).
---  Eliminated hypothesis H114 (duplicate of H103).
---  Eliminated hypothesis H12 (redundant, given H35).
---  Eliminated hypothesis H39 (redundant, given H47).
---  Eliminated hypothesis H46 (redundant, given H38).
---  Eliminated hypothesis H47 (redundant, given H57).
---  Eliminated hypothesis H48 (redundant, given H38).
---  Eliminated hypothesis H49 (redundant, given H57).
---  Eliminated hypothesis H56 (redundant, given H38).
---  Eliminated hypothesis H57 (redundant, given H67).
---  Eliminated hypothesis H58 (redundant, given H38).
---  Eliminated hypothesis H59 (redundant, given H67).
---  Eliminated hypothesis H66 (redundant, given H38).
---  Eliminated hypothesis H68 (redundant, given H38).
---  Eliminated hypothesis H69 (redundant, given H67).
---  Eliminated hypothesis H85 (redundant, given H91).
---  Eliminated hypothesis H86 (redundant, given H84).
---  Eliminated hypothesis H87 (redundant, given H91).
---  Eliminated hypothesis H90 (redundant, given H84).
---  Eliminated hypothesis H91 (redundant, given H99).
---  Eliminated hypothesis H92 (redundant, given H84).
---  Eliminated hypothesis H93 (redundant, given H99).
---  Eliminated hypothesis H94 (redundant, given H4).
---  Eliminated hypothesis H95 (redundant, given H103).
---  Eliminated hypothesis H98 (redundant, given H84).
---  Eliminated hypothesis H100 (redundant, given H84).
---  Eliminated hypothesis H101 (redundant, given H99).
---  Eliminated hypothesis H102 (redundant, given H4).
---  Eliminated hypothesis H103 (redundant, given H107).
---  Eliminated hypothesis H104 (redundant, given H38).
---  Eliminated hypothesis H105 (redundant, given H67).
---  Eliminated hypothesis H106 (redundant, given H4).
---  Eliminated hypothesis H107 (redundant, given H5 & H67).
---  Eliminated hypothesis H108 (redundant, given H38).
---  Eliminated hypothesis H109 (redundant, given H67).
---  Eliminated hypothesis H117 (redundant, given H7).
---  Eliminated hypothesis H118 (redundant, given H8).
---  Eliminated hypothesis H119 (redundant, given H7).
---  Eliminated hypothesis H120 (redundant, given H8).
---  Eliminated hypothesis H121 (redundant, given H111).
---  Eliminated hypothesis H122 (redundant, given H112).
---  Eliminated hypothesis H123 (redundant, given H11).
---  Eliminated hypothesis H124 (redundant, given H35).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of siglength by:
          fld_signaturelength(rrsig_record).
<S>  New H1:  srcbyte + 3 <= fld_signaturelength(rrsig_record)
<S>  New H110:  fld_signaturelength(rrsig_record) < srcbyte + 7
<S>  New H6:  start_byte <= 8028 - fld_signaturelength(rrsig_record)
<S>  New H2:  fld_signaturelength(rrsig_record) <= 1365
-S-  Eliminated hypothesis H9.
     This was achieved by replacing all occurrences of sigoffset by:
          start_byte + 24 - 1 + current_name_length.
<S>  New H99:  start_byte + 24 - 1 + current_name_length + (dstbytes + 2) <= 
          8180
<S>  New H84:  start_byte + 24 - 1 + current_name_length + dstbytes >= 1
---  Eliminated conclusion C7, which is a duplicate of C2.
***  Proved C2:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod 4294967296 <= 65535
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_56.  @@@@@@@@@@
%%%  Simplified H2 on reading formula in, to give:
     %%%  H2:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H27 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H28 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H29 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H30 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
%%%  Simplified H40 on reading formula in, to give:
     %%%  H40:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H44).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  true
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H15).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H16).
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H18).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H19).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H20).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H21).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H22).
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) and element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) <= character__last)
%%%  Simplified H101 on reading formula in, to give:
     %%%  H101:  for_all(i_ : integer, 
          rr_type__domainnamestringtypeindex__first <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = rr_type__maxdomainnamelength + 1 or 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H102).
---  Hypothesis H106 has been replaced by "true".  (It is already present, as 
          H103).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H109).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H110).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H26).
%%%  Simplified H130 on reading formula in, to give:
     %%%  H130:  4 >= integer__base__first
%%%  Simplified H131 on reading formula in, to give:
     %%%  H131:  4 <= integer__base__last
%%%  Simplified H132 on reading formula in, to give:
     %%%  H132:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified H133 on reading formula in, to give:
     %%%  H133:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= dns_types__packet_bytes_range__first
%%%  Simplified H134 on reading formula in, to give:
     %%%  H134:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= dns_types__packet_bytes_range__last
%%%  Simplified H135 on reading formula in, to give:
     %%%  H135:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified H136 on reading formula in, to give:
     %%%  H136:  0 <= dns_types__packet_bytes_range__base__last
---  Hypothesis H137 has been replaced by "true".  (It is already present, as 
          H116).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H117).
%%%  Simplified H143 on reading formula in, to give:
     %%%  H143:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 6 >= 
          dns_types__packet_bytes_range__base__first
%%%  Simplified H144 on reading formula in, to give:
     %%%  H144:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 6 <= 
          dns_types__packet_bytes_range__base__last
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H39).
%%%  Simplified H147 on reading formula in, to give:
     %%%  H147:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified H148 on reading formula in, to give:
     %%%  H148:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned16__last
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H35).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H151 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H152 has been replaced by "true".  (It is already present, as 
          H147).
---  Hypothesis H153 has been replaced by "true".  (It is already present, as 
          H148).
---  Hypothesis H154 has been replaced by "true".  (It is already present, as 
          H50).
%%%  Simplified H155 on reading formula in, to give:
     %%%  H155:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__8, [i___1]) and element(
          bytes__8, [i___1]) <= dns_types__byte__last)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 24 + rr_type__maxdomainnamelength + 
          rr_type__rrsig_record_type__maxrrsiglength
>>>  Restructured hypothesis H113 into:
     >>>  H113:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) < 1
>>>  Restructured hypothesis H132 into:
     >>>  H132:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New H104:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) = 129 or element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)))]) = 0 and for_all(q_ : integer, 1 <= 
          q_ and q_ <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) - 1 -> element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [q_]) 
          <> 0)
<S>  New C1:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 152 + 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H1:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
<S>  New C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 1493
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H107:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483648
<S>  New H109:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H108:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483647
<S>  New H110:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H130:  true
<S>  New H141:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H131:  true
<S>  New H142:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
<S>  New H100:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H3:  start_byte >= 1
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H35:  start_byte >= - 3
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H45:  start_byte >= - 5
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H56:  start_byte >= - 7
<S>  New H64:  start_byte >= - 8
<S>  New H70:  start_byte >= - 9
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H78:  start_byte >= - 13
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H86:  start_byte >= - 17
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H94:  start_byte >= - 21
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H116:  true
<S>  New H120:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1
<S>  New H124:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H133:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 23
<S>  New H139:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 23
<S>  New H155:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H4:  start_byte <= 8180
<S>  New H31:  start_byte <= 8177
<S>  New H36:  start_byte <= 8176
<S>  New H37:  start_byte <= 8175
<S>  New H46:  start_byte <= 8174
<S>  New H47:  start_byte <= 8173
<S>  New H57:  start_byte <= 8172
<S>  New H65:  start_byte <= 8171
<S>  New H71:  start_byte <= 8170
<S>  New H72:  start_byte <= 8167
<S>  New H79:  start_byte <= 8166
<S>  New H80:  start_byte <= 8163
<S>  New H87:  start_byte <= 8162
<S>  New H88:  start_byte <= 8159
<S>  New H95:  start_byte <= 8158
<S>  New H96:  start_byte <= 8157
<S>  New H117:  true
<S>  New H121:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          8180
<S>  New H125:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8180
<S>  New H134:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New H140:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 8156
<S>  New H1:  start_byte <= 6663
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__1, [i___1]) and element(
          bytes__1, [i___1]) <= dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__2, [i___1]) and element(
          bytes__2, [i___1]) <= dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__3, [i___1]) and element(
          bytes__3, [i___1]) <= dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__4, [i___1]) and element(
          bytes__4, [i___1]) <= dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__5, [i___1]) and element(
          bytes__5, [i___1]) <= dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__6, [i___1]) and element(
          bytes__6, [i___1]) <= dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__7, [i___1]) and element(
          bytes__7, [i___1]) <= dns_types__byte__last)
<S>  New H155:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__8, [i___1]) and element(
          bytes__8, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H38:  start_byte >= - 2147483652
<S>  New H41:  start_byte >= - 2147483654
<S>  New H58:  start_byte >= - 2147483656
<S>  New H66:  start_byte >= - 2147483657
<S>  New H73:  start_byte >= - 2147483658
<S>  New H81:  start_byte >= - 2147483662
<S>  New H89:  start_byte >= - 2147483666
<S>  New H97:  start_byte >= - 2147483670
<S>  New H122:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= - 
          2147483648
<S>  New H126:  start_byte + 24 >= - 2147483647
<S>  New H128:  start_byte >= - 2147483672
<S>  New H135:  true
<S>  New H143:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483642
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H39:  start_byte <= 2147483643
<S>  New H42:  start_byte <= 2147483641
<S>  New H59:  start_byte <= 2147483639
<S>  New H67:  start_byte <= 2147483638
<S>  New H74:  start_byte <= 2147483637
<S>  New H82:  start_byte <= 2147483633
<S>  New H90:  start_byte <= 2147483629
<S>  New H98:  start_byte <= 2147483625
<S>  New H123:  start_byte + 24 - 1 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) <= 
          2147483647
<S>  New H127:  start_byte + 24 <= 2147483648
<S>  New H129:  start_byte <= 2147483623
<S>  New H136:  true
<S>  New H144:  24 + rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483653
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H52:  fld_algorithm(rrsig_record) >= 0
<S>  New H60:  fld_numlabels(rrsig_record) >= 0
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 
          dns_types__byte__last)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 
          dns_types__byte__last)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 
          dns_types__byte__last)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 
          dns_types__byte__last)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 
          dns_types__byte__last)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 
          dns_types__byte__last)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 
          dns_types__byte__last)
<S>  New H155:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H53:  fld_algorithm(rrsig_record) <= 255
<S>  New H61:  fld_numlabels(rrsig_record) <= 255
<S>  New H2:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__1, [i___1]) and element(bytes__1, [i___1]) <= 255)
<S>  New H40:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__2, [i___1]) and element(bytes__2, [i___1]) <= 255)
<S>  New H51:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__3, [i___1]) and element(bytes__3, [i___1]) <= 255)
<S>  New H75:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__4, [i___1]) and element(bytes__4, [i___1]) <= 255)
<S>  New H83:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__5, [i___1]) and element(bytes__5, [i___1]) <= 255)
<S>  New H91:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__6, [i___1]) and element(bytes__6, [i___1]) <= 255)
<S>  New H99:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__7, [i___1]) and element(bytes__7, [i___1]) <= 255)
<S>  New H155:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_record) >= 0
<S>  New H13:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_record) <= 255
<S>  New H14:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_record) >= 0
<S>  New H33:  true
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
<S>  New H147:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_record) <= 65535
<S>  New H34:  true
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
<S>  New H148:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H15:  fld_origttl(rrsig_record) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H19:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H43:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 >= 0
<S>  New H147:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 >= 0
<S>  New H44:  from_query_type(fld_typecovered(rrsig_record)) mod 65536 mod 
          4294967296 <= 65535
<S>  New H148:  from_bytes_range(24 + rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) - 6) 
          mod 65536 mod 4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H101:  for_all(i_ : integer, 1 <= i_ and i_ <= 128 -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [i_]) 
          and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i_]) <= 255)
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H102:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= 1
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= rr_type__wirestringtypeindex__last
<S>  New H112:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> 1 <= 
          rr_type__wirestringtypeindex__last
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record)), [
          i___1]) and element(rr_type__convertdomainnametowire(fld_signername(
          rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H103:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H111:  1 <= rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) -> rr_type__wirenamelength(
          rr_type__convertdomainnametowire(fld_signername(rrsig_record))) >= 1 
          and rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 129
<S>  New H112:  true
<S>  New H100:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(rr_type__convertdomainnametowire(fld_signername(rrsig_record))
          , [i___1]) and element(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record)), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H126 further, to give:
     %%%  H126:  start_byte >= - 2147483671
%%%  Simplified H127 further, to give:
     %%%  H127:  start_byte <= 2147483624
%%%  Simplified H143 further, to give:
     %%%  H143:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) >= - 2147483666
%%%  Simplified H144 further, to give:
     %%%  H144:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 2147483629
***  Proved C1:  rr_type__wirenamelength(rr_type__convertdomainnametowire(
          fld_signername(rrsig_record))) <= 1493
     using hypothesis H113.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_57.  @@@@@@@@@@
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  for_all(j_ : integer, rr_type__wirestringtypeindex__first <= j_ 
          and j_ <= rr_type__wirestringtypeindex__last -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  for_all(i___1 : integer, dns_types__packet_bytes_range__first <= 
          i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H12 on reading formula in, to give:
     %%%  H12:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H14 on reading formula in, to give:
     %%%  H14:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H33 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as H2)
          .
---  Hypothesis H44 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H54).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  4 >= integer__base__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  4 <= integer__base__last
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  not 4 <= fld_signaturelength(rrsig_record)
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  24 + current_name_length >= dns_types__packet_bytes_range__first
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  24 + current_name_length <= dns_types__packet_bytes_range__last
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  0 >= dns_types__packet_bytes_range__base__first
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  0 <= dns_types__packet_bytes_range__base__last
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H59).
%%%  Simplified H85 on reading formula in, to give:
     %%%  H85:  24 + current_name_length - 6 >= 
          dns_types__packet_bytes_range__base__first
%%%  Simplified H86 on reading formula in, to give:
     %%%  H86:  24 + current_name_length - 6 <= 
          dns_types__packet_bytes_range__base__last
%%%  Simplified H89 on reading formula in, to give:
     %%%  H89:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified H90 on reading formula in, to give:
     %%%  H90:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 
          unsigned_types__unsigned16__last
---  Hypothesis H94 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H95 has been replaced by "true".  (It is already present, as 
          H90).
%%%  Simplified H96 on reading formula in, to give:
     %%%  H96:  true
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__8, [i___1]) and element(
          bytes__8, [i___1]) <= dns_types__byte__last)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  24 + current_name_length <= 24 + rr_type__maxdomainnamelength + 
          rr_type__rrsig_record_type__maxrrsiglength
>>>  Restructured hypothesis H74 into:
     >>>  H74:  fld_signaturelength(rrsig_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New C1:  24 + current_name_length <= 152 + 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H32:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
<S>  New C1:  current_name_length <= 1493
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H56:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H57:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H72:  true
<S>  New H83:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H73:  true
<S>  New H84:  current_name_length <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H28:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H29:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H8:  start_byte >= 1
<S>  New H45:  start_byte + 24 - 1 + loop__1__i >= 1
<S>  New H49:  loop__1__i >= 1
<S>  New H58:  true
<S>  New H62:  start_byte + 24 - 1 + current_name_length >= 1
<S>  New H66:  current_name_length >= 1
<S>  New H75:  current_name_length >= - 23
<S>  New H81:  current_name_length >= - 23
<S>  New H91:  start_byte >= - 3
<S>  New H97:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8156 - current_name_length
<S>  New H9:  start_byte <= 8180
<S>  New H46:  start_byte + 24 - 1 + loop__1__i <= 8180
<S>  New H50:  loop__1__i <= 8180
<S>  New H59:  true
<S>  New H63:  start_byte + 24 - 1 + current_name_length <= 8180
<S>  New H67:  current_name_length <= 8180
<S>  New H76:  current_name_length <= 8156
<S>  New H82:  current_name_length <= 8156
<S>  New H92:  start_byte <= 8176
<S>  New H93:  start_byte <= 8175
<S>  New H32:  start_byte <= 6663
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H97:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__8, [i___1]) and element(
          bytes__8, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H47:  start_byte + 24 - 1 + loop__1__i >= - 2147483648
<S>  New H51:  start_byte + 24 >= - 2147483647
<S>  New H53:  start_byte >= - 2147483672
<S>  New H64:  start_byte + 24 - 1 + current_name_length >= - 2147483648
<S>  New H77:  true
<S>  New H85:  24 + current_name_length >= - 2147483642
<S>  New H87:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H48:  start_byte + 24 - 1 + loop__1__i <= 2147483647
<S>  New H52:  start_byte + 24 <= 2147483648
<S>  New H54:  start_byte <= 2147483623
<S>  New H65:  start_byte + 24 - 1 + current_name_length <= 2147483647
<S>  New H78:  true
<S>  New H86:  24 + current_name_length <= 2147483653
<S>  New H88:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H39:  element(wireversion, [loop__1__i]) >= 0
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H97:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H40:  element(wireversion, [loop__1__i]) <= 255
<S>  New H7:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H97:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H14:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H15:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_algorithm(rrsig_record) >= 0
<S>  New H18:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_algorithm(rrsig_record) <= 255
<S>  New H19:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H26:  fld_keytag(rrsig_record) >= 0
<S>  New H89:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H27:  fld_keytag(rrsig_record) <= 65535
<S>  New H90:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H20:  fld_origttl(rrsig_record) >= 0
<S>  New H22:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H24:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H21:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H23:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H25:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H89:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 >= 0
<S>  New H90:  from_bytes_range(24 + current_name_length - 6) mod 65536 mod 
          4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H12:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H2:  loop__1__i >= 1
<S>  New H4:  current_name_length >= 1
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(wireversion, [j_]) 
          and element(wireversion, [j_]) <= 255)
<S>  New H37:  current_name_length__entry__loop__1 >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H3:  loop__1__i <= 129
<S>  New H5:  current_name_length <= 129
<S>  New H38:  current_name_length__entry__loop__1 <= 129
<S>  New H6:  for_all(j_ : integer, 1 <= j_ and j_ <= 129 -> 0 <= element(
          wireversion, [j_]) and element(wireversion, [j_]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H29:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H30:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H31:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H51 further, to give:
     %%%  H51:  start_byte >= - 2147483671
%%%  Simplified H52 further, to give:
     %%%  H52:  start_byte <= 2147483624
%%%  Simplified H85 further, to give:
     %%%  H85:  current_name_length >= - 2147483666
%%%  Simplified H86 further, to give:
     %%%  H86:  current_name_length <= 2147483629
***  Proved C1:  current_name_length <= 1493
     using hypothesis H5.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_rrsig_58.  @@@@@@@@@@
%%%  Simplified H10 on reading formula in, to give:
     %%%  H10:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_record)
          )
%%%  Simplified H17 on reading formula in, to give:
     %%%  H17:  dns_types__query_type__first <= fld_typecovered(rrsig_record)
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= character__last)
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_record), [i___2]) and 
          element(fld_signature(rrsig_record), [i___2]) <= character__last)
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H70).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H71).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  true
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H77).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H78).
---  Hypothesis H96 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H97 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified H108 on reading formula in, to give:
     %%%  H108:  srcbyte + 7 >= integer__base__first
%%%  Simplified H109 on reading formula in, to give:
     %%%  H109:  srcbyte + 7 <= integer__base__last
%%%  Simplified H110 on reading formula in, to give:
     %%%  H110:  not srcbyte + 7 <= siglength
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H125).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H126).
%%%  Simplified H132 on reading formula in, to give:
     %%%  H132:  true
%%%  Simplified H133 on reading formula in, to give:
     %%%  H133:  for_all(i___1 : integer, dns_types__packet_bytes_range__first 
          <= i___1 and i___1 <= dns_types__packet_bytes_range__last -> 
          dns_types__byte__first <= element(bytes__8, [i___1]) and element(
          bytes__8, [i___1]) <= dns_types__byte__last)
>>>  Restructured hypothesis H110 into:
     >>>  H110:  siglength < srcbyte + 7
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__maxdomainnamelength by:
          128.
<S>  New H6:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          siglength
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          rr_type__rrsig_record_type__maxrrsiglength
<S>  New C1:  24 + current_name_length + (dstbytes + 3 - 1) <= 152 + 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule set_ttl_data_rules(2).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H2:  siglength <= 1365
<S>  New H35:  start_byte <= dns_types__packet_bytes_range__last - 24 - 128 - 
          1365
<S>  New C1:  24 + current_name_length + (dstbytes + 3 - 1) <= 1517
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H104:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H105:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H48:  srcbyte >= - 2147483649
<S>  New H58:  srcbyte >= - 2147483650
<S>  New H68:  srcbyte >= - 2147483651
<S>  New H108:  srcbyte >= - 2147483655
<S>  New H119:  current_name_length >= - 2147483672
-S-  Applied substitution rule set_ttl_data_rules(7).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H49:  srcbyte <= 2147483646
<S>  New H59:  srcbyte <= 2147483645
<S>  New H69:  srcbyte <= 2147483644
<S>  New H109:  srcbyte <= 2147483640
<S>  New H120:  current_name_length <= 2147483623
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= character__last)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= character__last)
<S>  New H36:  element(fld_signature(rrsig_record), [srcbyte]) >= 0
<S>  New H44:  element(fld_signature(rrsig_record), [srcbyte + 1]) >= 0
<S>  New H54:  element(fld_signature(rrsig_record), [srcbyte + 2]) >= 0
<S>  New H64:  element(fld_signature(rrsig_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H37:  element(fld_signature(rrsig_record), [srcbyte]) <= 255
<S>  New H45:  element(fld_signature(rrsig_record), [srcbyte + 1]) <= 255
<S>  New H55:  element(fld_signature(rrsig_record), [srcbyte + 2]) <= 255
<S>  New H65:  element(fld_signature(rrsig_record), [srcbyte + 3]) <= 255
<S>  New H31:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
<S>  New H32:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__first by:
          1.
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H11:  start_byte >= 1
<S>  New H84:  sigoffset + dstbytes >= 1
<S>  New H90:  sigoffset + (dstbytes + 1) >= 1
<S>  New H98:  sigoffset + (dstbytes + 2) >= 1
<S>  New H106:  dstbytes >= - 2
<S>  New H111:  24 + current_name_length + (dstbytes + 3 - 1) >= 1
<S>  New H115:  true
<S>  New H117:  current_name_length >= - 23
<S>  New H127:  start_byte >= - 3
<S>  New H133:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          dns_types__packet_bytes_range__last -> dns_types__byte__first <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H12:  start_byte <= 8180
<S>  New H85:  sigoffset + dstbytes <= 8180
<S>  New H91:  sigoffset + (dstbytes + 1) <= 8180
<S>  New H99:  sigoffset + (dstbytes + 2) <= 8180
<S>  New H107:  dstbytes <= 8177
<S>  New H112:  24 + current_name_length + (dstbytes + 3 - 1) <= 8180
<S>  New H116:  true
<S>  New H118:  current_name_length <= 8156
<S>  New H128:  start_byte <= 8176
<S>  New H129:  start_byte <= 8175
<S>  New H6:  start_byte <= 8028 - siglength
<S>  New H35:  start_byte <= 6663
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New H133:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 
          dns_types__byte__first <= element(bytes__8, [i___1]) and element(
          bytes__8, [i___1]) <= dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H86:  sigoffset + dstbytes >= - 2147483648
<S>  New H92:  sigoffset + (dstbytes + 1) >= - 2147483648
<S>  New H94:  dstbytes >= - 2147483649
<S>  New H100:  sigoffset + (dstbytes + 2) >= - 2147483648
<S>  New H102:  dstbytes >= - 2147483650
<S>  New H113:  dstbytes + 3 >= - 2147483647
<S>  New H121:  24 + current_name_length + (dstbytes + 3 - 1) >= - 2147483642
<S>  New H123:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H87:  sigoffset + dstbytes <= 2147483647
<S>  New H93:  sigoffset + (dstbytes + 1) <= 2147483647
<S>  New H95:  dstbytes <= 2147483646
<S>  New H101:  sigoffset + (dstbytes + 2) <= 2147483647
<S>  New H103:  dstbytes <= 2147483645
<S>  New H114:  dstbytes + 3 <= 2147483648
<S>  New H122:  24 + current_name_length + (dstbytes + 3 - 1) <= 2147483653
<S>  New H124:  start_byte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H40:  lookup(element(fld_signature(rrsig_record), [srcbyte])) >= 0
<S>  New H50:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) >= 0
<S>  New H60:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) >= 0
<S>  New H70:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus >= 0
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 
          dns_types__byte__last)
<S>  New H133:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 
          dns_types__byte__last)
-S-  Applied substitution rule set_ttl_data_rules(26).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H41:  lookup(element(fld_signature(rrsig_record), [srcbyte])) <= 255
<S>  New H51:  lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) <= 
          255
<S>  New H61:  lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) <= 
          255
<S>  New H71:  lookup(element(fld_signature(rrsig_record), [srcbyte + 3])) <= 
          255
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_signature(rrsig_record)
          , [srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 2])) div 4 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod dns_types__byte__modulus + lookup(element(fld_signature(
          rrsig_record), [srcbyte + 3]))) mod dns_types__byte__modulus <= 255
<S>  New H10:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes, [i___1]) and element(bytes, [i___1]) <= 255)
<S>  New H133:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 8180 -> 0 <= 
          element(bytes__8, [i___1]) and element(bytes__8, [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(29).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 >= 0
<S>  New H77:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 >= 0
<S>  New H80:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_signature(rrsig_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) div 
          16 mod 256) mod 256 <= 255
<S>  New H78:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 1])) * 
          16 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 2]
          )) div 4 mod 256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_signature(rrsig_record), [srcbyte + 2])) * 
          64 mod 256 + lookup(element(fld_signature(rrsig_record), [srcbyte + 3]
          ))) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(32).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H17:  dns_types__a <= fld_typecovered(rrsig_record)
-S-  Applied substitution rule set_ttl_data_rules(33).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H18:  fld_typecovered(rrsig_record) <= dns_types__unimplemented
-S-  Applied substitution rule set_ttl_data_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H19:  fld_algorithm(rrsig_record) >= 0
<S>  New H21:  fld_numlabels(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H20:  fld_algorithm(rrsig_record) <= 255
<S>  New H22:  fld_numlabels(rrsig_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(95).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H29:  fld_keytag(rrsig_record) >= 0
<S>  New H125:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod unsigned_types__unsigned32__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(96).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H30:  fld_keytag(rrsig_record) <= 65535
<S>  New H126:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod unsigned_types__unsigned32__modulus <= 65535
-S-  Applied substitution rule set_ttl_data_rules(101).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H13:  fld_ttlinseconds(fld_inherit(rrsig_record)) >= 0
<S>  New H23:  fld_origttl(rrsig_record) >= 0
<S>  New H25:  fld_sigexpiration(rrsig_record) >= 0
<S>  New H27:  fld_siginception(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(102).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H14:  fld_ttlinseconds(fld_inherit(rrsig_record)) <= 4294967295
<S>  New H24:  fld_origttl(rrsig_record) <= 4294967295
<S>  New H26:  fld_sigexpiration(rrsig_record) <= 4294967295
<S>  New H28:  fld_siginception(rrsig_record) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(105).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__modulus by:
          4294967296.
<S>  New H125:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod 4294967296 >= 0
<S>  New H126:  from_bytes_range(24 + current_name_length + (dstbytes + 3 - 1) 
          - 6) mod 65536 mod 4294967296 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(107).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H15:  rr_type__internet <= fld_class(fld_inherit(rrsig_record))
-S-  Applied substitution rule set_ttl_data_rules(108).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H16:  fld_class(fld_inherit(rrsig_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(134).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_record), [i___1]) and element(fld_signername(
          rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(135).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_record), [i___1]) and element(
          fld_signername(rrsig_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(140).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H7:  current_name_length >= 1
-S-  Applied substitution rule set_ttl_data_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H8:  current_name_length <= 129
-S-  Applied substitution rule set_ttl_data_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H38:  srcbyte >= 1
<S>  New H46:  srcbyte >= 0
<S>  New H56:  srcbyte >= - 1
<S>  New H66:  srcbyte >= - 2
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(148).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H39:  srcbyte <= 1365
<S>  New H47:  srcbyte <= 1364
<S>  New H57:  srcbyte <= 1363
<S>  New H67:  srcbyte <= 1362
<S>  New H32:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_record), [i___2]) and element(
          fld_signature(rrsig_record), [i___2]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H33:  fld_signaturelength(rrsig_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(154).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H34:  fld_signaturelength(rrsig_record) <= 1365
%%%  Simplified H113 further, to give:
     %%%  H113:  dstbytes >= - 2147483650
%%%  Simplified H114 further, to give:
     %%%  H114:  dstbytes <= 2147483645
***  Proved C1:  24 + current_name_length + (dstbytes + 3 - 1) <= 1517
     via its standard form, which is:
     Std.Fm C1:  26 + (current_name_length + dstbytes) <= 1517
     using hypotheses H5, H8 & H67.
***  PROVED VC.

