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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_DNSKEY






@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
***  Proved C1:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C2:  fld_ttlinseconds(fld_inherit(dnskey_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(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H4:  start_byte <= 8180
<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(24).
     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(25).
     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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
---  Eliminated hypothesis H4 (redundant, given H1 & H16).
     +++  New H18:  integer__size >= 0
     +++  New H19:  character__size >= 0
     +++  New H20:  positive__size >= 0
     +++  New H21:  dns_types__packet_bytes_range__size >= 0
     +++  New H22:  unsigned_types__unsigned8__size >= 0
     +++  New H23:  unsigned_types__unsigned16__size >= 0
     +++  New H24:  unsigned_types__unsigned32__size >= 0
     +++  New H25:  rr_type__classtype__size >= 0
     +++  New H26:  rr_type__resourcerecordtype__size >= 0
     +++  New H27:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H28:  rr_type__dnskey_record_type__dnskeystringtypeindex__size >= 
          0
     +++  New H29:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H30:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
<S>  New C1:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New C6:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
<S>  New C2:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New C7:  fld_keylength(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<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 H22:  start_byte <= 8177
<S>  New H23:  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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C8:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C9:  start_byte <= 2147483643
***  Proved C9:  start_byte <= 2147483643
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H23:  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(24).
     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 H23:  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(25).
     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 H23:  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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New C1:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
<S>  New C2:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C6:  fld_keylength(dnskey_record) >= 0
     using hypothesis H16.
***  Proved C7:  fld_keylength(dnskey_record) <= 65535
     using hypothesis H17.
***  Proved C8:  start_byte >= - 2147483652
     using hypothesis H3.
***  Proved C1:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
***  Proved C2:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
---  Eliminated hypothesis H18 (true-hypothesis).
---  Eliminated hypothesis H19 (true-hypothesis).
---  Eliminated hypothesis H20 (true-hypothesis).
---  Eliminated hypothesis H21 (true-hypothesis).
---  Eliminated hypothesis H4 (redundant, given H22).
---  Eliminated hypothesis H22 (redundant, given H1 & H16).
     +++  New H24:  integer__size >= 0
     +++  New H25:  character__size >= 0
     +++  New H26:  positive__size >= 0
     +++  New H27:  dns_types__packet_bytes_range__size >= 0
     +++  New H28:  unsigned_types__unsigned8__size >= 0
     +++  New H29:  unsigned_types__unsigned16__size >= 0
     +++  New H30:  unsigned_types__unsigned32__size >= 0
     +++  New H31:  rr_type__classtype__size >= 0
     +++  New H32:  rr_type__resourcerecordtype__size >= 0
     +++  New H33:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H34:  rr_type__dnskey_record_type__dnskeystringtypeindex__size >= 
          0
     +++  New H35:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H36:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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:  fld_flags(dnskey_record) >= unsigned_types__unsigned16__first
     using hypothesis H9.
***  Proved C2:  fld_flags(dnskey_record) <= unsigned_types__unsigned16__last
     using hypothesis H10.
***  Proved C3:  start_byte + 6 >= dns_types__packet_bytes_range__first
     using hypothesis H3.
***  Proved C6:  start_byte + 6 >= dns_types__packet_bytes_range__base__first
     using hypothesis H31.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<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 H22:  start_byte <= 8177
<S>  New H23:  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 H27:  start_byte <= 8176
<S>  New H28:  start_byte <= 8175
<S>  New H33:  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(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H32:  start_byte <= 2147483643
<S>  New C7:  start_byte <= 2147483641
***  Proved C7:  start_byte <= 2147483641
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H23:  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 H26:  start_byte >= - 3
<S>  New H33:  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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H31:  start_byte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H23:  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 H33:  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(25).
     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 H23:  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 H33:  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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H29:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H30:  fld_keylength(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
---  Eliminated hypothesis H18 (true-hypothesis).
---  Eliminated hypothesis H19 (true-hypothesis).
---  Eliminated hypothesis H20 (true-hypothesis).
---  Eliminated hypothesis H21 (true-hypothesis).
---  Eliminated hypothesis H29 (duplicate of H16).
---  Eliminated hypothesis H4 (redundant, given H22).
---  Eliminated hypothesis H22 (redundant, given H27).
---  Eliminated hypothesis H26 (redundant, given H3).
---  Eliminated hypothesis H27 (redundant, given H28).
---  Eliminated hypothesis H28 (redundant, given H1 & H16).
---  Eliminated hypothesis H30 (redundant, given H17).
---  Eliminated hypothesis H31 (redundant, given H3).
---  Eliminated hypothesis H32 (redundant, given H1 & H16).
%%%  Simplified H24 further (given H16 & H17), to give:
     %%%  H24:  fld_keylength(dnskey_record) >= - 4
%%%  Simplified H25 further (given H16 & H17), to give:
     %%%  H25:  fld_keylength(dnskey_record) <= 65531
     +++  New H34:  integer__size >= 0
     +++  New H35:  character__size >= 0
     +++  New H36:  positive__size >= 0
     +++  New H37:  dns_types__packet_bytes_range__size >= 0
     +++  New H38:  unsigned_types__unsigned8__size >= 0
     +++  New H39:  unsigned_types__unsigned16__size >= 0
     +++  New H40:  unsigned_types__unsigned32__size >= 0
     +++  New H41:  rr_type__classtype__size >= 0
     +++  New H42:  rr_type__resourcerecordtype__size >= 0
     +++  New H43:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H44:  rr_type__dnskey_record_type__dnskeystringtypeindex__size >= 
          0
     +++  New H45:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H46:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H31.
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H23:  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 H33:  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 H41:  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_protocol(dnskey_record) >= 0
<S>  New C3:  fld_protocol(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     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 H23:  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 H33:  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 H41:  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_protocol(dnskey_record) <= 255
<S>  New C4:  fld_protocol(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H4:  start_byte <= 8180
<S>  New H22:  start_byte <= 8177
<S>  New H27:  start_byte <= 8176
<S>  New H28:  start_byte <= 8175
<S>  New H37:  start_byte <= 8174
<S>  New H38:  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 H23:  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 H33:  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 H41:  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(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H32:  start_byte <= 2147483643
<S>  New H40:  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(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H23:  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 H26:  start_byte >= - 3
<S>  New H33:  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 H36:  start_byte >= - 5
<S>  New H41:  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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H31:  start_byte >= - 2147483652
<S>  New H39:  start_byte >= - 2147483654
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H29:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H30:  fld_keylength(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C1:  fld_protocol(dnskey_record) >= 0
     using hypothesis H11.
***  Proved C3:  fld_protocol(dnskey_record) >= 0
     using hypothesis H11.
***  Proved C2:  fld_protocol(dnskey_record) <= 255
     using hypothesis H12.
***  Proved C4:  fld_protocol(dnskey_record) <= 255
     using hypothesis H12.
---  Eliminated hypothesis H18 (true-hypothesis).
---  Eliminated hypothesis H19 (true-hypothesis).
---  Eliminated hypothesis H20 (true-hypothesis).
---  Eliminated hypothesis H21 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (true-hypothesis).
---  Eliminated hypothesis H29 (duplicate of H16).
---  Eliminated hypothesis H4 (redundant, given H22).
---  Eliminated hypothesis H22 (redundant, given H27).
---  Eliminated hypothesis H26 (redundant, given H3).
---  Eliminated hypothesis H27 (redundant, given H28).
---  Eliminated hypothesis H28 (redundant, given H37).
---  Eliminated hypothesis H30 (redundant, given H17).
---  Eliminated hypothesis H31 (redundant, given H3).
---  Eliminated hypothesis H32 (redundant, given H37).
---  Eliminated hypothesis H36 (redundant, given H3).
---  Eliminated hypothesis H37 (redundant, given H38).
---  Eliminated hypothesis H38 (redundant, given H1 & H16).
---  Eliminated hypothesis H39 (redundant, given H3).
---  Eliminated hypothesis H40 (redundant, given H1 & H16).
%%%  Simplified H24 further (given H16 & H17), to give:
     %%%  H24:  fld_keylength(dnskey_record) >= - 4
%%%  Simplified H25 further (given H16 & H17), to give:
     %%%  H25:  fld_keylength(dnskey_record) <= 65531
     +++  New H42:  integer__size >= 0
     +++  New H43:  character__size >= 0
     +++  New H44:  positive__size >= 0
     +++  New H45:  dns_types__packet_bytes_range__size >= 0
     +++  New H46:  unsigned_types__unsigned8__size >= 0
     +++  New H47:  unsigned_types__unsigned16__size >= 0
     +++  New H48:  unsigned_types__unsigned32__size >= 0
     +++  New H49:  rr_type__classtype__size >= 0
     +++  New H50:  rr_type__resourcerecordtype__size >= 0
     +++  New H51:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H52:  rr_type__dnskey_record_type__dnskeystringtypeindex__size >= 
          0
     +++  New H53:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H54:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
***  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 H31.
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H23:  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 H33:  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 H41:  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 H42:  fld_protocol(dnskey_record) >= 0
<S>  New C1:  fld_algorithm(dnskey_record) >= 0
<S>  New C3:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H43:  fld_protocol(dnskey_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 H23:  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 H33:  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 H41:  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(dnskey_record) <= 255
<S>  New C4:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H4:  start_byte <= 8180
<S>  New H22:  start_byte <= 8177
<S>  New H27:  start_byte <= 8176
<S>  New H28:  start_byte <= 8175
<S>  New H37:  start_byte <= 8174
<S>  New H38:  start_byte <= 8173
<S>  New H47:  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 H23:  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 H33:  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 H41:  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(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H32:  start_byte <= 2147483643
<S>  New H40:  start_byte <= 2147483641
<S>  New H49:  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(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H23:  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 H26:  start_byte >= - 3
<S>  New H33:  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 H36:  start_byte >= - 5
<S>  New H41:  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 H46:  start_byte >= - 7
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H31:  start_byte >= - 2147483652
<S>  New H39:  start_byte >= - 2147483654
<S>  New H48:  start_byte >= - 2147483656
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H29:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H30:  fld_keylength(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C1:  fld_algorithm(dnskey_record) >= 0
     using hypothesis H13.
***  Proved C3:  fld_algorithm(dnskey_record) >= 0
     using hypothesis H13.
***  Proved C2:  fld_algorithm(dnskey_record) <= 255
     using hypothesis H14.
***  Proved C4:  fld_algorithm(dnskey_record) <= 255
     using hypothesis H14.
---  Eliminated hypothesis H18 (true-hypothesis).
---  Eliminated hypothesis H19 (true-hypothesis).
---  Eliminated hypothesis H20 (true-hypothesis).
---  Eliminated hypothesis H21 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H42 (duplicate of H11).
---  Eliminated hypothesis H43 (duplicate of H12).
---  Eliminated hypothesis H29 (duplicate of H16).
---  Eliminated hypothesis H4 (redundant, given H22).
---  Eliminated hypothesis H22 (redundant, given H27).
---  Eliminated hypothesis H26 (redundant, given H3).
---  Eliminated hypothesis H27 (redundant, given H28).
---  Eliminated hypothesis H28 (redundant, given H37).
---  Eliminated hypothesis H30 (redundant, given H17).
---  Eliminated hypothesis H31 (redundant, given H3).
---  Eliminated hypothesis H32 (redundant, given H37).
---  Eliminated hypothesis H36 (redundant, given H3).
---  Eliminated hypothesis H37 (redundant, given H38).
---  Eliminated hypothesis H38 (redundant, given H47).
---  Eliminated hypothesis H39 (redundant, given H3).
---  Eliminated hypothesis H40 (redundant, given H47).
---  Eliminated hypothesis H46 (redundant, given H3).
---  Eliminated hypothesis H47 (redundant, given H1 & H16).
---  Eliminated hypothesis H48 (redundant, given H3).
---  Eliminated hypothesis H49 (redundant, given H1 & H16).
%%%  Simplified H24 further (given H16 & H17), to give:
     %%%  H24:  fld_keylength(dnskey_record) >= - 4
%%%  Simplified H25 further (given H16 & H17), to give:
     %%%  H25:  fld_keylength(dnskey_record) <= 65531
     +++  New H50:  integer__size >= 0
     +++  New H51:  character__size >= 0
     +++  New H52:  positive__size >= 0
     +++  New H53:  dns_types__packet_bytes_range__size >= 0
     +++  New H54:  unsigned_types__unsigned8__size >= 0
     +++  New H55:  unsigned_types__unsigned16__size >= 0
     +++  New H56:  unsigned_types__unsigned32__size >= 0
     +++  New H57:  rr_type__classtype__size >= 0
     +++  New H58:  rr_type__resourcerecordtype__size >= 0
     +++  New H59:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H60:  rr_type__dnskey_record_type__dnskeystringtypeindex__size >= 
          0
     +++  New H61:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H62:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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).
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     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_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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).
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
<S>  New C1:  true
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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:  fld_keylength(dnskey_record) >= 
          rr_type__dnskey_record_type__keylengthvaluetype__first
     using hypothesis H16.
***  Proved C2:  fld_keylength(dnskey_record) <= 
          rr_type__dnskey_record_type__keylengthvaluetype__last
     using hypothesis H17.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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 
          H16).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H17).
%%%  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(5).
     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(6).
     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_dnskey_10.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H129 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H132).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H133).
%%%  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 H40.
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
<S>  New H113:  dstbytes <= 2147483646
<S>  New H127:  dstbytes <= 2147483645
<S>  New C2:  srcbyte <= 2147483640
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
<S>  New H132:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
<S>  New H133:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New H112:  dstbytes >= - 2147483649
<S>  New H126:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New H106:  start_byte + 9 + (dstbytes + 1) >= 1
<S>  New H110:  dstbytes >= 0
<S>  New H120:  start_byte + 9 + (dstbytes + 2) >= 1
<S>  New H124:  dstbytes >= - 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<S>  New H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<S>  New H107:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New H111:  dstbytes <= 8179
<S>  New H121:  start_byte + 9 + (dstbytes + 2) <= 8180
<S>  New H125:  dstbytes <= 8178
<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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New H108:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
<S>  New H122:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New H109:  start_byte + 9 + (dstbytes + 1) <= 2147483647
<S>  New H123:  start_byte + 9 + (dstbytes + 2) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
<S>  New H134:  dstbytes >= 0
<S>  New H136:  dstbytes >= - 3
<S>  New H140:  keylength >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
<S>  New H135:  dstbytes <= 1365
<S>  New H137:  dstbytes <= 1362
<S>  New H141:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C2:  srcbyte <= 2147483640
     using hypothesis H29.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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 
          H16).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H17).
%%%  Simplified H68 on reading formula in, to give:
     %%%  H68:  4 >= integer__base__first
%%%  Simplified H69 on reading formula in, to give:
     %%%  H69:  4 <= integer__base__last
%%%  Simplified H70 on reading formula in, to give:
     %%%  H70:  4 <= fld_keylength(dnskey_record)
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  4 <= fld_keylength(dnskey_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 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(update(bytes__3, [start_byte 
          + 8], fld_protocol(dnskey_record)), [start_byte + 9], fld_algorithm(
          dnskey_record)), [i___1]) and element(update(update(bytes__3, [
          start_byte + 8], fld_protocol(dnskey_record)), [start_byte + 9], 
          fld_algorithm(dnskey_record)), [i___1]) <= dns_types__byte__last)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  rr_type__classtype__first <= fld_class(fld_inherit(
          dnskey_record))
%%%  Simplified C20 on reading formula in, to give:
     %%%  C20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
***  Proved C1:  4 <= fld_keylength(dnskey_record)
     using hypothesis H70.
***  Proved C3:  true
***  Proved C4:  true
***  Proved C5:  true
***  Proved C6:  start_byte <= dns_types__packet_bytes_range__last - 10 - 
          fld_keylength(dnskey_record)
     using hypothesis H1.
***  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(update(bytes__3, [start_byte 
          + 8], fld_protocol(dnskey_record)), [start_byte + 9], fld_algorithm(
          dnskey_record)), [i___1]) and element(update(update(bytes__3, [
          start_byte + 8], fld_protocol(dnskey_record)), [start_byte + 9], 
          fld_algorithm(dnskey_record)), [i___1]) <= dns_types__byte__last)
     using hypotheses H41, H42, H43, H46, H47, H50, H51, H54 & H55.
***  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(dnskey_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H6.
***  Proved C12:  rr_type__classtype__first <= fld_class(fld_inherit(
          dnskey_record))
     using hypothesis H7.
***  Proved C13:  fld_class(fld_inherit(dnskey_record)) <= 
          rr_type__classtype__last
     using hypothesis H8.
***  Proved C14:  fld_flags(dnskey_record) >= unsigned_types__unsigned16__first
     using hypothesis H9.
***  Proved C15:  fld_flags(dnskey_record) <= unsigned_types__unsigned16__last
     using hypothesis H10.
***  Proved C16:  fld_protocol(dnskey_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C17:  fld_protocol(dnskey_record) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C18:  fld_algorithm(dnskey_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H13.
***  Proved C19:  fld_algorithm(dnskey_record) <= 
          unsigned_types__unsigned8__last
     using hypothesis H14.
***  Proved C20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
     using hypothesis H15.
***  Proved C21:  fld_keylength(dnskey_record) >= 
          rr_type__dnskey_record_type__keylengthvaluetype__first
     using hypothesis H16.
***  Proved C22:  fld_keylength(dnskey_record) <= 
          rr_type__dnskey_record_type__keylengthvaluetype__last
     using hypothesis H17.
***  Proved C23:  start_byte <= dns_types__packet_bytes_range__last - 10 - 
          fld_keylength(dnskey_record)
     using hypothesis H1.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New C2:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H58:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H68:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H69:  true
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H23:  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 H26:  start_byte >= - 3
<S>  New H33:  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 H36:  start_byte >= - 5
<S>  New H41:  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 H46:  start_byte >= - 7
<S>  New H54:  start_byte >= - 8
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H4:  start_byte <= 8180
<S>  New H22:  start_byte <= 8177
<S>  New H27:  start_byte <= 8176
<S>  New H28:  start_byte <= 8175
<S>  New H37:  start_byte <= 8174
<S>  New H38:  start_byte <= 8173
<S>  New H47:  start_byte <= 8172
<S>  New H55:  start_byte <= 8171
<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 H23:  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 H33:  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 H41:  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-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H31:  start_byte >= - 2147483652
<S>  New H39:  start_byte >= - 2147483654
<S>  New H48:  start_byte >= - 2147483656
<S>  New H56:  start_byte >= - 2147483657
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H32:  start_byte <= 2147483643
<S>  New H40:  start_byte <= 2147483641
<S>  New H49:  start_byte <= 2147483639
<S>  New H57:  start_byte <= 2147483638
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H42:  fld_protocol(dnskey_record) >= 0
<S>  New H50:  fld_algorithm(dnskey_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 H23:  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 H33:  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 H41:  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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H43:  fld_protocol(dnskey_record) <= 255
<S>  New H51:  fld_algorithm(dnskey_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 H23:  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 H33:  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 H41:  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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H29:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H30:  fld_keylength(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
<S>  New H60:  true
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
<S>  New H61:  true
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C2:  fld_keylength(dnskey_record) <= 1365
     using hypothesis H17.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_12.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H129 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H132).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H133).
%%%  Simplified H142 on reading formula in, to give:
     %%%  H142:  srcbyte + 7 >= integer__base__first
%%%  Simplified H143 on reading formula in, to give:
     %%%  H143:  srcbyte + 7 <= integer__base__last
%%%  Simplified H144 on reading formula in, to give:
     %%%  H144:  srcbyte + 7 <= keylength
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  srcbyte + 7 <= keylength
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  dstbytes >= - 2
%%%  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(update(update(bytes, [
          start_byte + 9 + dstbytes], (lookup(element(fld_key(dnskey_record), [
          srcbyte])) * 4 mod dns_types__byte__modulus + lookup(element(fld_key(
          dnskey_record), [srcbyte + 1])) div 16 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 1)], (
          lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 2)], (lookup(
          element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus), [i___1]) and element(
          update(update(update(bytes, [start_byte + 9 + dstbytes], (lookup(
          element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 1)], (lookup(
          element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 2)], (lookup(
          element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus), [i___1]) <= 
          dns_types__byte__last)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  rr_type__classtype__first <= fld_class(fld_inherit(
          dnskey_record))
%%%  Simplified C20 on reading formula in, to give:
     %%%  C20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
***  Proved C1:  srcbyte + 7 <= keylength
     using hypothesis H144.
***  Proved C2:  keylength <= rr_type__dnskey_record_type__maxdnskeylength
     using hypothesis H2.
***  Proved C3:  keylength = fld_keylength(dnskey_record)
     using hypothesis H3.
***  Proved C4:  dstbytes >= - 2
     using hypothesis H4.
***  Proved C6:  start_byte <= dns_types__packet_bytes_range__last - 10 - 
          fld_keylength(dnskey_record)
     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(update(update(bytes, [
          start_byte + 9 + dstbytes], (lookup(element(fld_key(dnskey_record), [
          srcbyte])) * 4 mod dns_types__byte__modulus + lookup(element(fld_key(
          dnskey_record), [srcbyte + 1])) div 16 mod dns_types__byte__modulus) 
          mod dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 1)], (
          lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 2)], (lookup(
          element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus), [i___1]) and element(
          update(update(update(bytes, [start_byte + 9 + dstbytes], (lookup(
          element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 1)], (lookup(
          element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus), [start_byte + 9 + (dstbytes + 2)], (lookup(
          element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus), [i___1]) <= 
          dns_types__byte__last)
     using hypotheses H7, H74, H75, H81, H82, H88, H89, H94, H95, H106, H107, 
          H120 & H121.
***  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(dnskey_record)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H10.
***  Proved C11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H11.
***  Proved C12:  rr_type__classtype__first <= fld_class(fld_inherit(
          dnskey_record))
     using hypothesis H12.
***  Proved C13:  fld_class(fld_inherit(dnskey_record)) <= 
          rr_type__classtype__last
     using hypothesis H13.
***  Proved C14:  fld_flags(dnskey_record) >= unsigned_types__unsigned16__first
     using hypothesis H14.
***  Proved C15:  fld_flags(dnskey_record) <= unsigned_types__unsigned16__last
     using hypothesis H15.
***  Proved C16:  fld_protocol(dnskey_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H16.
***  Proved C17:  fld_protocol(dnskey_record) <= unsigned_types__unsigned8__last
     using hypothesis H17.
***  Proved C18:  fld_algorithm(dnskey_record) >= 
          unsigned_types__unsigned8__first
     using hypothesis H18.
***  Proved C19:  fld_algorithm(dnskey_record) <= 
          unsigned_types__unsigned8__last
     using hypothesis H19.
***  Proved C20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
     using hypothesis H20.
***  Proved C21:  fld_keylength(dnskey_record) >= 
          rr_type__dnskey_record_type__keylengthvaluetype__first
     using hypothesis H21.
***  Proved C22:  fld_keylength(dnskey_record) <= 
          rr_type__dnskey_record_type__keylengthvaluetype__last
     using hypothesis H22.
***  Proved C23:  start_byte <= dns_types__packet_bytes_range__last - 10 - 
          fld_keylength(dnskey_record)
     using hypothesis H6.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
<S>  New H132:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
<S>  New H133:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New H112:  dstbytes >= - 2147483649
<S>  New H126:  dstbytes >= - 2147483650
<S>  New H142:  srcbyte >= - 2147483655
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
<S>  New H113:  dstbytes <= 2147483646
<S>  New H127:  dstbytes <= 2147483645
<S>  New H143:  srcbyte <= 2147483640
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New H106:  start_byte + 9 + (dstbytes + 1) >= 1
<S>  New H110:  dstbytes >= 0
<S>  New H120:  start_byte + 9 + (dstbytes + 2) >= 1
<S>  New H124:  dstbytes >= - 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<S>  New H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<S>  New H107:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New H111:  dstbytes <= 8179
<S>  New H121:  start_byte + 9 + (dstbytes + 2) <= 8180
<S>  New H125:  dstbytes <= 8178
<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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New H108:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
<S>  New H122:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New H109:  start_byte + 9 + (dstbytes + 1) <= 2147483647
<S>  New H123:  start_byte + 9 + (dstbytes + 2) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
<S>  New H134:  dstbytes >= 0
<S>  New H136:  dstbytes >= - 3
<S>  New H140:  keylength >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
<S>  New H135:  dstbytes <= 1365
<S>  New H137:  dstbytes <= 1362
<S>  New H141:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  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_dnskey_13.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New C1:  element(fld_key(dnskey_record), [srcbyte]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New C2:  element(fld_key(dnskey_record), [srcbyte]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New C3:  srcbyte >= 1
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 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__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(18).
     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-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(24).
     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-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
***  Proved C1:  element(fld_key(dnskey_record), [srcbyte]) >= 0
     using hypotheses H1, H2, H4, H5 & H20.
***  Proved C2:  element(fld_key(dnskey_record), [srcbyte]) <= 255
     using hypotheses H1, H2, H4, H5 & H20.
***  Proved C4:  srcbyte <= 1365
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_14.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
***  Proved C1:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 
          dns_types__byte__first
     using hypothesis H30.
***  Proved C2:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 
          dns_types__byte__last
     using hypothesis H31.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_15.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C3:  srcbyte + 1 >= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first
     using hypothesis H28.
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New C1:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New C2:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= 1365 -> 0 <= element(fld_key(dnskey_record), [i___1]) 
          and element(fld_key(dnskey_record), [i___1]) <= 255)
<S>  New C4:  srcbyte <= 1364
-S-  Applied substitution rule set_ttl_data_rules(5).
     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(6).
     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 H29.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(18).
     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-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New H28:  srcbyte >= 1
***  Proved C1:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
     using hypotheses H1, H2, H20 & H28.
***  Proved C2:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
     using hypotheses H1, H2, H20 & H28.
***  Proved C4:  srcbyte <= 1364
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_16.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C1:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 
          dns_types__byte__first
     using hypothesis H42.
***  Proved C2:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 
          dns_types__byte__last
     using hypothesis H43.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_17.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C3:  srcbyte + 2 >= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first
     using hypothesis H28.
***  Proved C5:  srcbyte + 2 >= integer__base__first
     using hypothesis H40.
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New C1:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New C2:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= 1365 -> 0 <= element(fld_key(dnskey_record), [i___1]) 
          and element(fld_key(dnskey_record), [i___1]) <= 255)
<S>  New C4:  srcbyte <= 1363
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New C6:  srcbyte <= 2147483645
***  Proved C6:  srcbyte <= 2147483645
     using hypothesis H29.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
-S-  Applied substitution rule set_ttl_data_rules(18).
     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-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
***  Proved C1:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
     using hypotheses H1, H2, H20 & H28.
***  Proved C2:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
     using hypotheses H1, H2, H20 & H28.
***  Proved C4:  srcbyte <= 1363
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_18.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C1:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 
          dns_types__byte__first
     using hypothesis H54.
***  Proved C2:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 
          dns_types__byte__last
     using hypothesis H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_19.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C3:  srcbyte + 3 >= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first
     using hypothesis H28.
***  Proved C5:  srcbyte + 3 >= integer__base__first
     using hypothesis H40.
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New C1:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New C2:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= 1365 -> 0 <= element(fld_key(dnskey_record), [i___1]) 
          and element(fld_key(dnskey_record), [i___1]) <= 255)
<S>  New C4:  srcbyte <= 1362
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New C6:  srcbyte <= 2147483644
***  Proved C6:  srcbyte <= 2147483644
     using hypothesis H29.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(18).
     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-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
***  Proved C1:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
     using hypotheses H1, H2, H20 & H28.
***  Proved C2:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
     using hypotheses H1, H2, H20 & H28.
***  Proved C4:  srcbyte <= 1362
     using hypotheses H1 & H2.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_20.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C1:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 
          dns_types__byte__first
     using hypothesis H66.
***  Proved C2:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 
          dns_types__byte__last
     using hypothesis H67.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_21.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
***  Proved C3:  true
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New C1:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 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:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_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__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New H8:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New C1:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 + 
          lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 256)
           mod 256 >= 0
<S>  New C2:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 + 
          lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 256)
           mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C1:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 
          mod 256) mod 256 >= 0
***  Proved C2:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 
          mod 256) mod 256 <= 255
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_22.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
***  Proved C3:  true
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 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:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_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__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New H8:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New C2:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4 mod 256) mod 256 >= 0
***  Proved C2:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4 mod 256) mod 256 <= 255
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_23.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 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:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_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__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 -> 0 <= element(bytes, [i___1]) 
          and element(bytes, [i___1]) <= 255)
<S>  New H8:  start_byte >= 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New C2:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 
          256 >= 0
***  Proved C2:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 
          256 <= 255
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_24.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
***  Proved C1:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_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_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= dns_types__byte__last
     using hypothesis H75.
***  Proved C3:  start_byte + 9 + dstbytes >= 
          dns_types__packet_bytes_range__first
     using hypotheses H4 & H8.
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<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 C4:  start_byte + 9 + dstbytes <= 8180
<S>  New C8:  dstbytes <= 8180
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New C5:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New C9:  start_byte >= - 2147483657
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New C6:  start_byte + 9 + dstbytes <= 2147483647
<S>  New C10:  start_byte <= 2147483638
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 <= 8180 -> 
          dns_types__byte__first <= element(bytes, [i___1]) and element(bytes, [
          i___1]) <= dns_types__byte__last)
<S>  New C7:  dstbytes >= 1
***  Proved C5:  start_byte + 9 + dstbytes >= - 2147483648
     using hypotheses H4 & H8.
***  Proved C9:  start_byte >= - 2147483657
     using hypothesis H8.
***  Proved C10:  start_byte <= 2147483638
     using hypothesis H9.
***  Proved C7:  dstbytes >= 1
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C8:  dstbytes <= 8180
     using hypotheses H5 & H29.
***  Proved C6:  start_byte + 9 + dstbytes <= 2147483647
     via its standard form, which is:
     Std.Fm C6:  9 + (dstbytes + start_byte) <= 2147483647
     using hypotheses H5, H9 & H29.
---  Eliminated hypothesis H23 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H87 (true-hypothesis).
---  Eliminated hypothesis H90 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H9 (redundant, given H6 & H21).
---  Eliminated hypothesis H24 (redundant, given H28).
---  Eliminated hypothesis H25 (redundant, given H29).
---  Eliminated hypothesis H29 (redundant, given H39).
---  Eliminated hypothesis H38 (redundant, given H28).
---  Eliminated hypothesis H39 (redundant, given H51).
---  Eliminated hypothesis H40 (redundant, given H28).
---  Eliminated hypothesis H41 (redundant, given H51).
---  Eliminated hypothesis H50 (redundant, given H28).
---  Eliminated hypothesis H51 (redundant, given H63).
---  Eliminated hypothesis H52 (redundant, given H28).
---  Eliminated hypothesis H53 (redundant, given H63).
---  Eliminated hypothesis H62 (redundant, given H28).
---  Eliminated hypothesis H64 (redundant, given H28).
---  Eliminated hypothesis H65 (redundant, given H63).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of keylength by:
          fld_keylength(dnskey_record).
<S>  New H1:  srcbyte + 3 <= fld_keylength(dnskey_record)
<S>  New H2:  fld_keylength(dnskey_record) <= 1365
%%%  Simplified H74 further (given H42 & H43), to give:
     %%%  H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 >= 0
%%%  Simplified H75 further (given H42 & H43), to give:
     %%%  H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 <= 255
%%%  Simplified H81 further (given H54 & H55), to give:
     %%%  H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 >= 0
%%%  Simplified H82 further (given H54 & H55), to give:
     %%%  H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 <= 255
     +++  New H92:  integer__size >= 0
     +++  New H93:  character__size >= 0
     +++  New H94:  positive__size >= 0
     +++  New H95:  dns_types__packet_bytes_range__size >= 0
     +++  New H96:  unsigned_types__unsigned8__size >= 0
     +++  New H97:  unsigned_types__unsigned16__size >= 0
     +++  New H98:  unsigned_types__unsigned32__size >= 0
     +++  New H99:  rr_type__classtype__size >= 0
     +++  New H100:  rr_type__resourcerecordtype__size >= 0
     +++  New H101:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H102:  rr_type__dnskey_record_type__dnskeystringtypeindex__size 
          >= 0
     +++  New H103:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H104:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_25.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
***  Proved C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), 
          [srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= dns_types__byte__first
     using hypothesis H81.
***  Proved C2:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), 
          [srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= dns_types__byte__last
     using hypothesis H82.
***  Proved C7:  dstbytes + 1 >= dns_types__packet_bytes_range__first
     using hypothesis H98.
***  Proved C10:  dstbytes + 1 <= integer__base__last
     using hypotheses H5 & H41.
***  Proved C11:  start_byte + 9 >= dns_types__packet_bytes_range__base__first
     using hypothesis H100.
***  Proved C12:  start_byte + 9 <= dns_types__packet_bytes_range__base__last
     using hypothesis H101.
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New C3:  start_byte + 9 + (dstbytes + 1) >= 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<S>  New H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<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 C4:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New C8:  dstbytes <= 8179
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New C5:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New C6:  start_byte + 9 + (dstbytes + 1) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New C9:  dstbytes >= - 2147483649
***  Proved C9:  dstbytes >= - 2147483649
     using hypothesis H4.
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C3:  start_byte + 9 + (dstbytes + 1) >= 1
     via its standard form, which is:
     Std.Fm C3:  10 + (dstbytes + start_byte) >= 1
     using hypotheses H4 & H8.
***  Proved C8:  dstbytes <= 8179
     using hypotheses H5 & H29.
***  Proved C5:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
     via its standard form, which is:
     Std.Fm C5:  10 + (dstbytes + start_byte) >= - 2147483648
     using hypotheses H4 & H8.
***  Proved C6:  start_byte + 9 + (dstbytes + 1) <= 2147483647
     via its standard form, which is:
     Std.Fm C6:  10 + (dstbytes + start_byte) <= 2147483647
     using hypotheses H9 & H99.
---  Eliminated hypothesis H23 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H87 (true-hypothesis).
---  Eliminated hypothesis H90 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H103 (true-hypothesis).
---  Eliminated hypothesis H98 (duplicate of H4).
---  Eliminated hypothesis H9 (redundant, given H4 & H95).
---  Eliminated hypothesis H24 (redundant, given H28).
---  Eliminated hypothesis H25 (redundant, given H29).
---  Eliminated hypothesis H29 (redundant, given H39).
---  Eliminated hypothesis H38 (redundant, given H28).
---  Eliminated hypothesis H39 (redundant, given H51).
---  Eliminated hypothesis H40 (redundant, given H28).
---  Eliminated hypothesis H41 (redundant, given H51).
---  Eliminated hypothesis H50 (redundant, given H28).
---  Eliminated hypothesis H51 (redundant, given H63).
---  Eliminated hypothesis H52 (redundant, given H28).
---  Eliminated hypothesis H53 (redundant, given H63).
---  Eliminated hypothesis H62 (redundant, given H28).
---  Eliminated hypothesis H64 (redundant, given H28).
---  Eliminated hypothesis H65 (redundant, given H63).
---  Eliminated hypothesis H96 (redundant, given H94).
---  Eliminated hypothesis H97 (redundant, given H95).
---  Eliminated hypothesis H99 (redundant, given H5 & H63).
---  Eliminated hypothesis H100 (redundant, given H8).
---  Eliminated hypothesis H101 (redundant, given H4 & H95).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of keylength by:
          fld_keylength(dnskey_record).
<S>  New H1:  srcbyte + 3 <= fld_keylength(dnskey_record)
<S>  New H2:  fld_keylength(dnskey_record) <= 1365
%%%  Simplified H74 further (given H42 & H43), to give:
     %%%  H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 >= 0
%%%  Simplified H75 further (given H42 & H43), to give:
     %%%  H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 <= 255
%%%  Simplified H81 further (given H54 & H55), to give:
     %%%  H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 >= 0
%%%  Simplified H82 further (given H54 & H55), to give:
     %%%  H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 <= 255
     +++  New H104:  integer__size >= 0
     +++  New H105:  character__size >= 0
     +++  New H106:  positive__size >= 0
     +++  New H107:  dns_types__packet_bytes_range__size >= 0
     +++  New H108:  unsigned_types__unsigned8__size >= 0
     +++  New H109:  unsigned_types__unsigned16__size >= 0
     +++  New H110:  unsigned_types__unsigned32__size >= 0
     +++  New H111:  rr_type__classtype__size >= 0
     +++  New H112:  rr_type__resourcerecordtype__size >= 0
     +++  New H113:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H114:  rr_type__dnskey_record_type__dnskeystringtypeindex__size 
          >= 0
     +++  New H115:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H116:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_26.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
***  Proved C1:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 
          mod dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), 
          [srcbyte + 3]))) mod dns_types__byte__modulus >= 
          dns_types__byte__first
     using hypothesis H88.
***  Proved C2:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 
          mod dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), 
          [srcbyte + 3]))) mod dns_types__byte__modulus <= dns_types__byte__last
     using hypothesis H89.
***  Proved C7:  dstbytes + 2 >= dns_types__packet_bytes_range__first
     using hypothesis H98.
***  Proved C9:  dstbytes + 2 >= integer__base__first
     using hypothesis H112.
***  Proved C10:  dstbytes + 2 <= integer__base__last
     using hypotheses H5 & H53.
***  Proved C11:  start_byte + 9 >= dns_types__packet_bytes_range__base__first
     using hypothesis H100.
***  Proved C12:  start_byte + 9 <= dns_types__packet_bytes_range__base__last
     using hypothesis H101.
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New H106:  start_byte + 9 + (dstbytes + 1) >= 1
<S>  New H110:  dstbytes >= 0
<S>  New C3:  start_byte + 9 + (dstbytes + 2) >= 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<S>  New H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<S>  New H107:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New H111:  dstbytes <= 8179
<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 C4:  start_byte + 9 + (dstbytes + 2) <= 8180
<S>  New C8:  dstbytes <= 8178
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New H108:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
<S>  New C5:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New H109:  start_byte + 9 + (dstbytes + 1) <= 2147483647
<S>  New C6:  start_byte + 9 + (dstbytes + 2) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New H112:  dstbytes >= - 2147483649
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
<S>  New H113:  dstbytes <= 2147483646
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(24).
     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 H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 0
-S-  Applied substitution rule set_ttl_data_rules(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C3:  start_byte + 9 + (dstbytes + 2) >= 1
     via its standard form, which is:
     Std.Fm C3:  11 + (dstbytes + start_byte) >= 1
     using hypotheses H4 & H8.
***  Proved C8:  dstbytes <= 8178
     using hypotheses H5 & H29.
***  Proved C5:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
     via its standard form, which is:
     Std.Fm C5:  11 + (dstbytes + start_byte) >= - 2147483648
     using hypotheses H4 & H8.
***  Proved C6:  start_byte + 9 + (dstbytes + 2) <= 2147483647
     via its standard form, which is:
     Std.Fm C6:  11 + (dstbytes + start_byte) <= 2147483647
     using hypotheses H9 & H99.
---  Eliminated hypothesis H23 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H87 (true-hypothesis).
---  Eliminated hypothesis H90 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H103 (true-hypothesis).
---  Eliminated hypothesis H104 (true-hypothesis).
---  Eliminated hypothesis H105 (true-hypothesis).
---  Eliminated hypothesis H114 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H117 (true-hypothesis).
---  Eliminated hypothesis H98 (duplicate of H4).
---  Eliminated hypothesis H9 (redundant, given H4 & H95).
---  Eliminated hypothesis H24 (redundant, given H28).
---  Eliminated hypothesis H25 (redundant, given H29).
---  Eliminated hypothesis H29 (redundant, given H39).
---  Eliminated hypothesis H38 (redundant, given H28).
---  Eliminated hypothesis H39 (redundant, given H51).
---  Eliminated hypothesis H40 (redundant, given H28).
---  Eliminated hypothesis H41 (redundant, given H51).
---  Eliminated hypothesis H50 (redundant, given H28).
---  Eliminated hypothesis H51 (redundant, given H63).
---  Eliminated hypothesis H52 (redundant, given H28).
---  Eliminated hypothesis H53 (redundant, given H63).
---  Eliminated hypothesis H62 (redundant, given H28).
---  Eliminated hypothesis H64 (redundant, given H28).
---  Eliminated hypothesis H65 (redundant, given H63).
---  Eliminated hypothesis H95 (redundant, given H107).
---  Eliminated hypothesis H96 (redundant, given H94).
---  Eliminated hypothesis H97 (redundant, given H107).
---  Eliminated hypothesis H99 (redundant, given H111).
---  Eliminated hypothesis H100 (redundant, given H8).
---  Eliminated hypothesis H101 (redundant, given H4 & H107).
---  Eliminated hypothesis H106 (redundant, given H94).
---  Eliminated hypothesis H108 (redundant, given H94).
---  Eliminated hypothesis H109 (redundant, given H107).
---  Eliminated hypothesis H110 (redundant, given H4).
---  Eliminated hypothesis H111 (redundant, given H5 & H63).
---  Eliminated hypothesis H112 (redundant, given H4).
---  Eliminated hypothesis H113 (redundant, given H5 & H63).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of keylength by:
          fld_keylength(dnskey_record).
<S>  New H1:  srcbyte + 3 <= fld_keylength(dnskey_record)
<S>  New H2:  fld_keylength(dnskey_record) <= 1365
%%%  Simplified H74 further (given H42 & H43), to give:
     %%%  H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 >= 0
%%%  Simplified H75 further (given H42 & H43), to give:
     %%%  H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 <= 255
%%%  Simplified H81 further (given H54 & H55), to give:
     %%%  H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 >= 0
%%%  Simplified H82 further (given H54 & H55), to give:
     %%%  H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 <= 255
     +++  New H118:  integer__size >= 0
     +++  New H119:  character__size >= 0
     +++  New H120:  positive__size >= 0
     +++  New H121:  dns_types__packet_bytes_range__size >= 0
     +++  New H122:  unsigned_types__unsigned8__size >= 0
     +++  New H123:  unsigned_types__unsigned16__size >= 0
     +++  New H124:  unsigned_types__unsigned32__size >= 0
     +++  New H125:  rr_type__classtype__size >= 0
     +++  New H126:  rr_type__resourcerecordtype__size >= 0
     +++  New H127:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H128:  rr_type__dnskey_record_type__dnskeystringtypeindex__size 
          >= 0
     +++  New H129:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H130:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_27.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H129 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C1:  srcbyte + 4 >= integer__first
     using hypothesis H24.
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
<S>  New C2:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New H112:  dstbytes >= - 2147483649
<S>  New H126:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
<S>  New H113:  dstbytes <= 2147483646
<S>  New H127:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New H106:  start_byte + 9 + (dstbytes + 1) >= 1
<S>  New H110:  dstbytes >= 0
<S>  New H120:  start_byte + 9 + (dstbytes + 2) >= 1
<S>  New H124:  dstbytes >= - 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<S>  New H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<S>  New H107:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New H111:  dstbytes <= 8179
<S>  New H121:  start_byte + 9 + (dstbytes + 2) <= 8180
<S>  New H125:  dstbytes <= 8178
<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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New H108:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
<S>  New H122:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New H109:  start_byte + 9 + (dstbytes + 1) <= 2147483647
<S>  New H123:  start_byte + 9 + (dstbytes + 2) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C2:  srcbyte <= 2147483643
     using hypothesis H29.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_28.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H129 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H25).
***  Proved C1:  dstbytes + 3 >= 
          rr_type__dnskey_record_type__keylengthvaluetype__first
     using hypothesis H134.
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
<S>  New H135:  dstbytes <= 1365
<S>  New C2:  dstbytes <= 1362
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
<S>  New H132:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
<S>  New H133:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New H112:  dstbytes >= - 2147483649
<S>  New H126:  dstbytes >= - 2147483650
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
<S>  New H113:  dstbytes <= 2147483646
<S>  New H127:  dstbytes <= 2147483645
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New H106:  start_byte + 9 + (dstbytes + 1) >= 1
<S>  New H110:  dstbytes >= 0
<S>  New H120:  start_byte + 9 + (dstbytes + 2) >= 1
<S>  New H124:  dstbytes >= - 1
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H9:  start_byte <= 8180
<S>  New H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<S>  New H107:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New H111:  dstbytes <= 8179
<S>  New H121:  start_byte + 9 + (dstbytes + 2) <= 8180
<S>  New H125:  dstbytes <= 8178
<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(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New H108:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
<S>  New H122:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New H109:  start_byte + 9 + (dstbytes + 1) <= 2147483647
<S>  New H123:  start_byte + 9 + (dstbytes + 2) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
<S>  New H134:  dstbytes >= 0
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C2:  dstbytes <= 1362
     using hypotheses H5 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_29.  @@@@@@@@@@
%%%  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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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 
          H16).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H17).
%%%  Simplified H68 on reading formula in, to give:
     %%%  H68:  4 >= integer__base__first
%%%  Simplified H69 on reading formula in, to give:
     %%%  H69:  4 <= integer__base__last
%%%  Simplified H70 on reading formula in, to give:
     %%%  H70:  not 4 <= fld_keylength(dnskey_record)
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H61).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  0 >= rr_type__dnskey_record_type__keylengthvaluetype__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  0 <= rr_type__dnskey_record_type__keylengthvaluetype__last
***  Proved C2:  0 <= rr_type__dnskey_record_type__keylengthvaluetype__last
     using hypothesis H61.
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
<S>  New H60:  true
<S>  New C1:  true
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_30.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H129 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H132).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H133).
%%%  Simplified H142 on reading formula in, to give:
     %%%  H142:  srcbyte + 7 >= integer__base__first
%%%  Simplified H143 on reading formula in, to give:
     %%%  H143:  srcbyte + 7 <= integer__base__last
%%%  Simplified H144 on reading formula in, to give:
     %%%  H144:  not srcbyte + 7 <= keylength
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H136).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H137).
***  Proved C2:  dstbytes + 3 - 1 <= 
          rr_type__dnskey_record_type__keylengthvaluetype__last
     using hypothesis H137.
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
<S>  New H134:  dstbytes >= 0
<S>  New H136:  dstbytes >= - 3
<S>  New H140:  keylength >= 0
<S>  New C1:  dstbytes + 3 >= 1
***  Proved C1:  dstbytes + 3 >= 1
     using hypothesis H4.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_31.  @@@@@@@@@@
%%%  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(dnskey_record)
          )
%%%  Simplified H15 on reading formula in, to give:
     %%%  H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H18 has been replaced by "true".  (It is already present, as H5)
          .
---  Hypothesis H19 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H20 has been replaced by "true".  (It is already present, as H3)
          .
---  Hypothesis H21 has been replaced by "true".  (It is already present, as H4)
          .
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  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 H33 on reading formula in, to give:
     %%%  H33:  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 H34 has been replaced by "true".  (It is already present, as H9)
          .
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H10).
%%%  Simplified H41 on reading formula in, to give:
     %%%  H41:  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 H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  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 
          H16).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H17).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H16).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H17).
%%%  Simplified H68 on reading formula in, to give:
     %%%  H68:  4 >= integer__base__first
%%%  Simplified H69 on reading formula in, to give:
     %%%  H69:  4 <= integer__base__last
%%%  Simplified H70 on reading formula in, to give:
     %%%  H70:  not 4 <= fld_keylength(dnskey_record)
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H60).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H61).
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  0 >= rr_type__dnskey_record_type__keylengthvaluetype__first
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  0 <= rr_type__dnskey_record_type__keylengthvaluetype__last
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H73).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H74).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  4 mod unsigned_types__unsigned16__modulus >= 
          unsigned_types__unsigned16__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  4 mod unsigned_types__unsigned16__modulus <= 
          unsigned_types__unsigned16__last
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  0 >= unsigned_types__unsigned16__first
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  0 <= unsigned_types__unsigned16__last
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H26.
***  Proved C4:  start_byte + 4 <= dns_types__packet_bytes_range__last
     using hypothesis H27.
***  Proved C5:  start_byte + 4 <= dns_types__packet_bytes_range__last - 1
     using hypothesis H28.
***  Proved C8:  start_byte + 4 >= dns_types__packet_bytes_range__base__first
     using hypothesis H31.
***  Proved C9:  start_byte + 4 <= dns_types__packet_bytes_range__base__last
     using hypothesis H32.
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H9:  fld_flags(dnskey_record) >= 0
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus >= 0
<S>  New H29:  fld_keylength(dnskey_record) >= 0
<S>  New C1:  4 mod unsigned_types__unsigned16__modulus >= 0
<S>  New C6:  true
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H10:  fld_flags(dnskey_record) <= 65535
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 
          unsigned_types__unsigned16__modulus <= 65535
<S>  New H30:  fld_keylength(dnskey_record) <= 65535
<S>  New C2:  4 mod unsigned_types__unsigned16__modulus <= 65535
<S>  New C7:  true
***  Proved C6:  true
***  Proved C7:  true
>>>  Restructured hypothesis H70 into:
     >>>  H70:  fld_keylength(dnskey_record) < 4
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H58:  true
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H59:  true
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H68:  true
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H69:  true
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H15:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H23:  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 H26:  start_byte >= - 3
<S>  New H33:  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 H36:  start_byte >= - 5
<S>  New H41:  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 H46:  start_byte >= - 7
<S>  New H54:  start_byte >= - 8
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H1:  start_byte <= 8170 - fld_keylength(dnskey_record)
<S>  New H4:  start_byte <= 8180
<S>  New H22:  start_byte <= 8177
<S>  New H27:  start_byte <= 8176
<S>  New H28:  start_byte <= 8175
<S>  New H37:  start_byte <= 8174
<S>  New H38:  start_byte <= 8173
<S>  New H47:  start_byte <= 8172
<S>  New H55:  start_byte <= 8171
<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 H23:  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 H33:  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 H41:  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-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H31:  start_byte >= - 2147483652
<S>  New H39:  start_byte >= - 2147483654
<S>  New H48:  start_byte >= - 2147483656
<S>  New H56:  start_byte >= - 2147483657
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H32:  start_byte <= 2147483643
<S>  New H40:  start_byte <= 2147483641
<S>  New H49:  start_byte <= 2147483639
<S>  New H57:  start_byte <= 2147483638
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H42:  fld_protocol(dnskey_record) >= 0
<S>  New H50:  fld_algorithm(dnskey_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 H23:  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 H33:  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 H41:  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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H43:  fld_protocol(dnskey_record) <= 255
<S>  New H51:  fld_algorithm(dnskey_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 H23:  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 H33:  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 H41:  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(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_protocol(dnskey_record) >= 0
<S>  New H13:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_protocol(dnskey_record) <= 255
<S>  New H14:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New H24:  (4 + fld_keylength(dnskey_record)) mod 65536 >= 0
<S>  New H25:  (4 + fld_keylength(dnskey_record)) mod 65536 <= 65535
<S>  New C1:  true
<S>  New C2:  true
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H16:  fld_keylength(dnskey_record) >= 0
<S>  New H60:  true
<S>  New H73:  true
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H17:  fld_keylength(dnskey_record) <= 1365
<S>  New H61:  true
<S>  New H74:  true
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H15:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_32.  @@@@@@@@@@
%%%  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(
          dnskey_record))
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> character__first <= element(fld_key(dnskey_record), [i___1]) and 
          element(fld_key(dnskey_record), [i___1]) <= character__last)
---  Hypothesis H23 has been replaced by "true".  (It is already present, as H6)
          .
---  Hypothesis H32 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H43).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  true
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H43).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H55).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  true
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H66).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H74).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H75).
---  Hypothesis H102 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H103 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H104 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H105 has been replaced by "true".  (It is already present, as 
          H82).
---  Hypothesis H114 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H115 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H116 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H117 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H118 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H119 has been replaced by "true".  (It is already present, as 
          H89).
---  Hypothesis H128 has been replaced by "true".  (It is already present, as 
          H100).
---  Hypothesis H129 has been replaced by "true".  (It is already present, as 
          H101).
---  Hypothesis H130 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H131 has been replaced by "true".  (It is already present, as 
          H25).
---  Hypothesis H138 has been replaced by "true".  (It is already present, as 
          H132).
---  Hypothesis H139 has been replaced by "true".  (It is already present, as 
          H133).
%%%  Simplified H142 on reading formula in, to give:
     %%%  H142:  srcbyte + 7 >= integer__base__first
%%%  Simplified H143 on reading formula in, to give:
     %%%  H143:  srcbyte + 7 <= integer__base__last
%%%  Simplified H144 on reading formula in, to give:
     %%%  H144:  not srcbyte + 7 <= keylength
---  Hypothesis H145 has been replaced by "true".  (It is already present, as 
          H136).
---  Hypothesis H146 has been replaced by "true".  (It is already present, as 
          H137).
---  Hypothesis H149 has been replaced by "true".  (It is already present, as 
          H147).
---  Hypothesis H150 has been replaced by "true".  (It is already present, as 
          H148).
***  Proved C3:  start_byte + 4 >= dns_types__packet_bytes_range__first
     using hypothesis H8.
***  Proved C9:  start_byte + 4 <= dns_types__packet_bytes_range__base__last
     using hypothesis H101.
-S-  Applied substitution rule set_ttl_data_rules(36).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H14:  fld_flags(dnskey_record) >= 0
<S>  New C1:  (4 + (dstbytes + 3 - 1)) mod unsigned_types__unsigned16__modulus 
          >= 0
<S>  New C6:  dstbytes + 3 >= 1
-S-  Applied substitution rule set_ttl_data_rules(37).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H15:  fld_flags(dnskey_record) <= 65535
<S>  New C2:  (4 + (dstbytes + 3 - 1)) mod unsigned_types__unsigned16__modulus 
          <= 65535
<S>  New C7:  dstbytes + 3 <= 65536
-S-  Applied substitution rule set_ttl_data_rules(19).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__last by:
          8180.
<S>  New H6:  start_byte <= 8170 - fld_keylength(dnskey_record)
<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 H95:  start_byte + 9 + dstbytes <= 8180
<S>  New H99:  dstbytes <= 8180
<S>  New H107:  start_byte + 9 + (dstbytes + 1) <= 8180
<S>  New H111:  dstbytes <= 8179
<S>  New H121:  start_byte + 9 + (dstbytes + 2) <= 8180
<S>  New H125:  dstbytes <= 8178
<S>  New C4:  start_byte <= 8176
<S>  New C5:  start_byte <= 8175
-S-  Applied substitution rule set_ttl_data_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__first by:
          - 2147483648.
<S>  New H96:  start_byte + 9 + dstbytes >= - 2147483648
<S>  New H100:  start_byte >= - 2147483657
<S>  New H108:  start_byte + 9 + (dstbytes + 1) >= - 2147483648
<S>  New H122:  start_byte + 9 + (dstbytes + 2) >= - 2147483648
<S>  New C8:  start_byte >= - 2147483652
***  Proved C6:  dstbytes + 3 >= 1
     using hypothesis H4.
***  Proved C7:  dstbytes + 3 <= 65536
     using hypothesis H99.
>>>  Restructured hypothesis H144 into:
     >>>  H144:  keylength < srcbyte + 7
-S-  Applied substitution rule set_ttl_data_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__maxdnskeylength by:
          1365.
<S>  New H2:  keylength <= 1365
-S-  Applied substitution rule set_ttl_data_rules(3).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H24:  srcbyte >= - 2147483648
<S>  New H132:  srcbyte >= - 2147483652
-S-  Applied substitution rule set_ttl_data_rules(4).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H25:  srcbyte <= 2147483647
<S>  New H133:  srcbyte <= 2147483643
-S-  Applied substitution rule set_ttl_data_rules(5).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H40:  srcbyte >= - 2147483649
<S>  New H52:  srcbyte >= - 2147483650
<S>  New H64:  srcbyte >= - 2147483651
<S>  New H112:  dstbytes >= - 2147483649
<S>  New H126:  dstbytes >= - 2147483650
<S>  New H142:  srcbyte >= - 2147483655
-S-  Applied substitution rule set_ttl_data_rules(6).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H41:  srcbyte <= 2147483646
<S>  New H53:  srcbyte <= 2147483645
<S>  New H65:  srcbyte <= 2147483644
<S>  New H113:  dstbytes <= 2147483646
<S>  New H127:  dstbytes <= 2147483645
<S>  New H143:  srcbyte <= 2147483640
-S-  Applied substitution rule set_ttl_data_rules(8).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= character__last)
<S>  New H26:  element(fld_key(dnskey_record), [srcbyte]) >= 0
<S>  New H36:  element(fld_key(dnskey_record), [srcbyte + 1]) >= 0
<S>  New H48:  element(fld_key(dnskey_record), [srcbyte + 2]) >= 0
<S>  New H60:  element(fld_key(dnskey_record), [srcbyte + 3]) >= 0
-S-  Applied substitution rule set_ttl_data_rules(9).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H27:  element(fld_key(dnskey_record), [srcbyte]) <= 255
<S>  New H37:  element(fld_key(dnskey_record), [srcbyte + 1]) <= 255
<S>  New H49:  element(fld_key(dnskey_record), [srcbyte + 2]) <= 255
<S>  New H61:  element(fld_key(dnskey_record), [srcbyte + 3]) <= 255
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first <= i___1 
          and i___1 <= rr_type__dnskey_record_type__dnskeystringtypeindex__last 
          -> 0 <= element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(18).
     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 H94:  start_byte + 9 + dstbytes >= 1
<S>  New H98:  dstbytes >= 1
<S>  New H106:  start_byte + 9 + (dstbytes + 1) >= 1
<S>  New H110:  dstbytes >= 0
<S>  New H120:  start_byte + 9 + (dstbytes + 2) >= 1
<S>  New H124:  dstbytes >= - 1
-S-  Applied substitution rule set_ttl_data_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__packet_bytes_range__base__last by:
          2147483647.
<S>  New H97:  start_byte + 9 + dstbytes <= 2147483647
<S>  New H101:  start_byte <= 2147483638
<S>  New H109:  start_byte + 9 + (dstbytes + 1) <= 2147483647
<S>  New H123:  start_byte + 9 + (dstbytes + 2) <= 2147483647
-S-  Applied substitution rule set_ttl_data_rules(24).
     This was achieved by replacing all occurrences of dns_types__byte__first 
          by:
          0.
<S>  New H30:  lookup(element(fld_key(dnskey_record), [srcbyte])) >= 0
<S>  New H42:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) >= 0
<S>  New H54:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) >= 0
<S>  New H66:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) >= 0
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus >= 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(25).
     This was achieved by replacing all occurrences of dns_types__byte__last by:
          255.
<S>  New H31:  lookup(element(fld_key(dnskey_record), [srcbyte])) <= 255
<S>  New H43:  lookup(element(fld_key(dnskey_record), [srcbyte + 1])) <= 255
<S>  New H55:  lookup(element(fld_key(dnskey_record), [srcbyte + 2])) <= 255
<S>  New H67:  lookup(element(fld_key(dnskey_record), [srcbyte + 3])) <= 255
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 1])) div 16 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 2])) div 4 mod dns_types__byte__modulus) mod 
          dns_types__byte__modulus <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          dns_types__byte__modulus + lookup(element(fld_key(dnskey_record), [
          srcbyte + 3]))) mod dns_types__byte__modulus <= 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(28).
     This was achieved by replacing all occurrences of dns_types__byte__modulus 
          by:
          256.
<S>  New H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 >= 0
<S>  New H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 >= 0
<S>  New H88:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          >= 0
<S>  New H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16 mod 
          256) mod 256 <= 255
<S>  New H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 4 
          mod 256) mod 256 <= 255
<S>  New H89:  (lookup(element(fld_key(dnskey_record), [srcbyte + 2])) * 64 mod 
          256 + lookup(element(fld_key(dnskey_record), [srcbyte + 3]))) mod 256 
          <= 255
-S-  Applied substitution rule set_ttl_data_rules(30).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H16:  fld_protocol(dnskey_record) >= 0
<S>  New H18:  fld_algorithm(dnskey_record) >= 0
-S-  Applied substitution rule set_ttl_data_rules(31).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H17:  fld_protocol(dnskey_record) <= 255
<S>  New H19:  fld_algorithm(dnskey_record) <= 255
-S-  Applied substitution rule set_ttl_data_rules(40).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__modulus by:
          65536.
<S>  New C1:  (4 + (dstbytes + 3 - 1)) mod 65536 >= 0
<S>  New C2:  (4 + (dstbytes + 3 - 1)) mod 65536 <= 65535
-S-  Applied substitution rule set_ttl_data_rules(42).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H10:  fld_ttlinseconds(fld_inherit(dnskey_record)) >= 0
-S-  Applied substitution rule set_ttl_data_rules(43).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H11:  fld_ttlinseconds(fld_inherit(dnskey_record)) <= 4294967295
-S-  Applied substitution rule set_ttl_data_rules(48).
     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(dnskey_record))
-S-  Applied substitution rule set_ttl_data_rules(49).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H13:  fld_class(fld_inherit(dnskey_record)) <= rr_type__hs
-S-  Applied substitution rule set_ttl_data_rules(77).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__first by:
          0.
<S>  New H21:  fld_keylength(dnskey_record) >= 0
<S>  New H134:  dstbytes >= 0
<S>  New H136:  dstbytes >= - 3
<S>  New H140:  keylength >= 0
<S>  New H147:  dstbytes + 3 >= 1
-S-  Applied substitution rule set_ttl_data_rules(78).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__keylengthvaluetype__last by:
          1365.
<S>  New H22:  fld_keylength(dnskey_record) <= 1365
<S>  New H135:  dstbytes <= 1365
<S>  New H137:  dstbytes <= 1362
<S>  New H141:  keylength <= 1365
<S>  New H148:  dstbytes + 3 <= 1366
-S-  Applied substitution rule set_ttl_data_rules(82).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__first by:
          1.
<S>  New H28:  srcbyte >= 1
<S>  New H38:  srcbyte >= 0
<S>  New H50:  srcbyte >= - 1
<S>  New H62:  srcbyte >= - 2
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
-S-  Applied substitution rule set_ttl_data_rules(83).
     This was achieved by replacing all occurrences of 
          rr_type__dnskey_record_type__dnskeystringtypeindex__last by:
          1365.
<S>  New H29:  srcbyte <= 1365
<S>  New H39:  srcbyte <= 1364
<S>  New H51:  srcbyte <= 1363
<S>  New H63:  srcbyte <= 1362
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 1365 -> 0 <= 
          element(fld_key(dnskey_record), [i___1]) and element(fld_key(
          dnskey_record), [i___1]) <= 255)
%%%  Simplified H147 further, to give:
     %%%  H147:  dstbytes >= - 2
%%%  Simplified H148 further, to give:
     %%%  H148:  dstbytes <= 1363
***  Proved C8:  start_byte >= - 2147483652
     using hypothesis H8.
***  Proved C1:  (4 + (dstbytes + 3 - 1)) mod 65536 >= 0
***  Proved C2:  (4 + (dstbytes + 3 - 1)) mod 65536 <= 65535
---  Eliminated hypothesis H23 (true-hypothesis).
---  Eliminated hypothesis H32 (true-hypothesis).
---  Eliminated hypothesis H33 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H35 (true-hypothesis).
---  Eliminated hypothesis H44 (true-hypothesis).
---  Eliminated hypothesis H45 (true-hypothesis).
---  Eliminated hypothesis H46 (true-hypothesis).
---  Eliminated hypothesis H47 (true-hypothesis).
---  Eliminated hypothesis H56 (true-hypothesis).
---  Eliminated hypothesis H57 (true-hypothesis).
---  Eliminated hypothesis H58 (true-hypothesis).
---  Eliminated hypothesis H59 (true-hypothesis).
---  Eliminated hypothesis H68 (true-hypothesis).
---  Eliminated hypothesis H69 (true-hypothesis).
---  Eliminated hypothesis H70 (true-hypothesis).
---  Eliminated hypothesis H71 (true-hypothesis).
---  Eliminated hypothesis H72 (true-hypothesis).
---  Eliminated hypothesis H73 (true-hypothesis).
---  Eliminated hypothesis H76 (true-hypothesis).
---  Eliminated hypothesis H77 (true-hypothesis).
---  Eliminated hypothesis H78 (true-hypothesis).
---  Eliminated hypothesis H79 (true-hypothesis).
---  Eliminated hypothesis H80 (true-hypothesis).
---  Eliminated hypothesis H83 (true-hypothesis).
---  Eliminated hypothesis H84 (true-hypothesis).
---  Eliminated hypothesis H85 (true-hypothesis).
---  Eliminated hypothesis H86 (true-hypothesis).
---  Eliminated hypothesis H87 (true-hypothesis).
---  Eliminated hypothesis H90 (true-hypothesis).
---  Eliminated hypothesis H91 (true-hypothesis).
---  Eliminated hypothesis H92 (true-hypothesis).
---  Eliminated hypothesis H93 (true-hypothesis).
---  Eliminated hypothesis H102 (true-hypothesis).
---  Eliminated hypothesis H103 (true-hypothesis).
---  Eliminated hypothesis H104 (true-hypothesis).
---  Eliminated hypothesis H105 (true-hypothesis).
---  Eliminated hypothesis H114 (true-hypothesis).
---  Eliminated hypothesis H115 (true-hypothesis).
---  Eliminated hypothesis H116 (true-hypothesis).
---  Eliminated hypothesis H117 (true-hypothesis).
---  Eliminated hypothesis H118 (true-hypothesis).
---  Eliminated hypothesis H119 (true-hypothesis).
---  Eliminated hypothesis H128 (true-hypothesis).
---  Eliminated hypothesis H129 (true-hypothesis).
---  Eliminated hypothesis H130 (true-hypothesis).
---  Eliminated hypothesis H131 (true-hypothesis).
---  Eliminated hypothesis H138 (true-hypothesis).
---  Eliminated hypothesis H139 (true-hypothesis).
---  Eliminated hypothesis H145 (true-hypothesis).
---  Eliminated hypothesis H146 (true-hypothesis).
---  Eliminated hypothesis H149 (true-hypothesis).
---  Eliminated hypothesis H150 (true-hypothesis).
---  Eliminated hypothesis H98 (duplicate of H4).
---  Eliminated hypothesis H141 (duplicate of H2).
---  Eliminated hypothesis H134 (duplicate of H110).
---  Eliminated hypothesis H9 (redundant, given H4 & H95).
---  Eliminated hypothesis H24 (redundant, given H28).
---  Eliminated hypothesis H25 (redundant, given H29).
---  Eliminated hypothesis H29 (redundant, given H39).
---  Eliminated hypothesis H38 (redundant, given H28).
---  Eliminated hypothesis H39 (redundant, given H51).
---  Eliminated hypothesis H40 (redundant, given H28).
---  Eliminated hypothesis H41 (redundant, given H51).
---  Eliminated hypothesis H50 (redundant, given H28).
---  Eliminated hypothesis H51 (redundant, given H63).
---  Eliminated hypothesis H52 (redundant, given H28).
---  Eliminated hypothesis H53 (redundant, given H63).
---  Eliminated hypothesis H62 (redundant, given H28).
---  Eliminated hypothesis H64 (redundant, given H28).
---  Eliminated hypothesis H65 (redundant, given H63).
---  Eliminated hypothesis H95 (redundant, given H107).
---  Eliminated hypothesis H96 (redundant, given H94).
---  Eliminated hypothesis H97 (redundant, given H107).
---  Eliminated hypothesis H99 (redundant, given H111).
---  Eliminated hypothesis H100 (redundant, given H8).
---  Eliminated hypothesis H101 (redundant, given H4 & H107).
---  Eliminated hypothesis H106 (redundant, given H94).
---  Eliminated hypothesis H107 (redundant, given H121).
---  Eliminated hypothesis H108 (redundant, given H94).
---  Eliminated hypothesis H109 (redundant, given H121).
---  Eliminated hypothesis H110 (redundant, given H4).
---  Eliminated hypothesis H111 (redundant, given H125).
---  Eliminated hypothesis H112 (redundant, given H4).
---  Eliminated hypothesis H113 (redundant, given H125).
---  Eliminated hypothesis H120 (redundant, given H94).
---  Eliminated hypothesis H122 (redundant, given H94).
---  Eliminated hypothesis H123 (redundant, given H121).
---  Eliminated hypothesis H124 (redundant, given H4).
---  Eliminated hypothesis H125 (redundant, given H135).
---  Eliminated hypothesis H126 (redundant, given H4).
---  Eliminated hypothesis H127 (redundant, given H135).
---  Eliminated hypothesis H132 (redundant, given H28).
---  Eliminated hypothesis H133 (redundant, given H63).
---  Eliminated hypothesis H135 (redundant, given H137).
---  Eliminated hypothesis H136 (redundant, given H4).
---  Eliminated hypothesis H140 (redundant, given H1 & H28).
---  Eliminated hypothesis H142 (redundant, given H28).
---  Eliminated hypothesis H143 (redundant, given H63).
---  Eliminated hypothesis H147 (redundant, given H4).
---  Eliminated hypothesis H148 (redundant, given H137).
-S-  Eliminated hypothesis H3.
     This was achieved by replacing all occurrences of keylength by:
          fld_keylength(dnskey_record).
<S>  New H1:  srcbyte + 3 <= fld_keylength(dnskey_record)
<S>  New H144:  fld_keylength(dnskey_record) < srcbyte + 7
<S>  New H2:  fld_keylength(dnskey_record) <= 1365
%%%  Simplified H74 further (given H42 & H43), to give:
     %%%  H74:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 >= 0
%%%  Simplified H75 further (given H42 & H43), to give:
     %%%  H75:  (lookup(element(fld_key(dnskey_record), [srcbyte])) * 4 mod 256 
          + lookup(element(fld_key(dnskey_record), [srcbyte + 1])) div 16) mod 
          256 <= 255
%%%  Simplified H81 further (given H54 & H55), to give:
     %%%  H81:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 >= 0
%%%  Simplified H82 further (given H54 & H55), to give:
     %%%  H82:  (lookup(element(fld_key(dnskey_record), [srcbyte + 1])) * 16 
          mod 256 + lookup(element(fld_key(dnskey_record), [srcbyte + 2])) div 
          4) mod 256 <= 255
     +++  New H151:  integer__size >= 0
     +++  New H152:  character__size >= 0
     +++  New H153:  positive__size >= 0
     +++  New H154:  dns_types__packet_bytes_range__size >= 0
     +++  New H155:  unsigned_types__unsigned8__size >= 0
     +++  New H156:  unsigned_types__unsigned16__size >= 0
     +++  New H157:  unsigned_types__unsigned32__size >= 0
     +++  New H158:  rr_type__classtype__size >= 0
     +++  New H159:  rr_type__resourcerecordtype__size >= 0
     +++  New H160:  rr_type__dnskey_record_type__keylengthvaluetype__size >= 0
     +++  New H161:  rr_type__dnskey_record_type__dnskeystringtypeindex__size 
          >= 0
     +++  New H162:  rr_type__dnskey_record_type__dnskeystringtype__size >= 0
     +++  New H163:  rr_type__dnskey_record_type__dnskeyrecordtype__size >= 0


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_33.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_set_ttl_data_dnskey_34.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.

