*****************************************************************************
                       Semantic Analysis of SPARK Text
                             Examiner GPL Edition

*****************************************************************************



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

procedure Parser_Utilities.AddToKeyR






@@@@@@@@@@  VC: procedure_addtokeyr_1.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> character__first <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
<S>  New H24:  length >= 1
<S>  New C1:  true
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H25:  length <= 256
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 
          character__first <= element(s, [i___1]) and element(s, [i___1]) <= 
          character__last)
<S>  New C2:  true
***  Proved C1:  true
***  Proved C2:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_2.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
***  Proved C1:  1 < length -> 1 >= rr_type__linelengthindex__first and 1 <= 
          rr_type__linelengthindex__last
     using hypotheses H26 & H27.
***  Proved C2:  1 < length -> 1 >= rr_type__linelengthindex__first and 1 <= 
          rr_type__linelengthindex__last
     using hypotheses H26 & H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_3.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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).
***  Proved C1:  begidx + 1 < length -> begidx + 1 >= 
          rr_type__linelengthindex__first and begidx + 1 <= 
          rr_type__linelengthindex__last
     using hypotheses H30 & H31.
***  Proved C2:  begidx + 1 < length -> begidx + 1 >= 
          rr_type__linelengthindex__first and begidx + 1 <= 
          rr_type__linelengthindex__last
     using hypotheses H30 & H31.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_4.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  true
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C21 on reading formula in, to give:
     %%%  C21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C22 on reading formula in, to give:
     %%%  C22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  true
***  Proved C2:  1 < length
     using hypothesis H32.
***  Proved C3:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H1.
***  Proved C4:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H2.
***  Proved C5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H3.
***  Proved C6:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H4.
***  Proved C7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H5.
***  Proved C8:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H6.
***  Proved C9:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H7.
***  Proved C10:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H8.
***  Proved C11:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C12:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C13:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H11.
***  Proved C14:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H12.
***  Proved C15:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C16:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C17:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C18:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C19:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H17.
***  Proved C20:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H18.
***  Proved C21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H19.
***  Proved C22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H20.
***  Proved C23:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H21.
***  Proved C24:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H22.
***  Proved C25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C26:  length >= rr_type__linelengthindex__first
     using hypothesis H24.
***  Proved C27:  length <= rr_type__linelengthindex__last
     using hypothesis H25.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_5.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx >= 0
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C21 on reading formula in, to give:
     %%%  C21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C22 on reading formula in, to give:
     %%%  C22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  begidx >= 0
     using hypothesis H1.
***  Proved C2:  begidx + 1 < length
     using hypothesis H36.
***  Proved C3:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H3.
***  Proved C4:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H4.
***  Proved C5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H5.
***  Proved C6:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H6.
***  Proved C7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H7.
***  Proved C8:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H8.
***  Proved C9:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C10:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C11:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C12:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C13:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C14:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C15:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C16:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C17:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C18:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C19:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H19.
***  Proved C20:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H20.
***  Proved C21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H21.
***  Proved C22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H22.
***  Proved C23:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H23.
***  Proved C24:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H24.
***  Proved C25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H25.
***  Proved C26:  length >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C27:  length <= rr_type__linelengthindex__last
     using hypothesis H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_6.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  begidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H28.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H27:  length <= 256
<S>  New H29:  begidx <= 256
<S>  New C2:  begidx <= 255
***  Proved C2:  begidx <= 255
     using hypotheses H2 & H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_7.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
***  Proved C1:  1 >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C2:  1 <= rr_type__linelengthindex__last
     using hypothesis H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_8.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
***  Proved C1:  begidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H30.
***  Proved C2:  begidx + 1 <= rr_type__linelengthindex__last
     using hypothesis H31.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_9.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
***  Proved C1:  1 < length -> 1 >= rr_type__linelengthindex__first and 1 <= 
          rr_type__linelengthindex__last
     using hypothesis H30.
***  Proved C2:  1 < length -> 1 >= rr_type__linelengthindex__first and 1 <= 
          rr_type__linelengthindex__last
     using hypothesis H30.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_10.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
***  Proved C1:  begidx + 1 < length -> begidx + 1 >= 
          rr_type__linelengthindex__first and begidx + 1 <= 
          rr_type__linelengthindex__last
     using hypothesis H34.
***  Proved C2:  begidx + 1 < length -> begidx + 1 >= 
          rr_type__linelengthindex__first and begidx + 1 <= 
          rr_type__linelengthindex__last
     using hypothesis H34.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_11.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
***  Proved C1:  endidx + 1 < length -> endidx + 1 >= 
          rr_type__linelengthindex__first and endidx + 1 <= 
          rr_type__linelengthindex__last
     using hypotheses H32 & H33.
***  Proved C2:  endidx + 1 < length -> endidx + 1 >= 
          rr_type__linelengthindex__first and endidx + 1 <= 
          rr_type__linelengthindex__last
     using hypotheses H32 & H33.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_12.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  true
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  true
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C23 on reading formula in, to give:
     %%%  C23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  true
***  Proved C2:  true
***  Proved C3:  true
***  Proved C4:  1 < length
     using hypothesis H41.
***  Proved C5:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H1.
***  Proved C6:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H2.
***  Proved C7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H3.
***  Proved C8:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H4.
***  Proved C9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H5.
***  Proved C10:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H6.
***  Proved C11:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H7.
***  Proved C12:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H8.
***  Proved C13:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C14:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C15:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H11.
***  Proved C16:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H12.
***  Proved C17:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C18:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C19:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C20:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C21:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H17.
***  Proved C22:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H18.
***  Proved C23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H19.
***  Proved C24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H20.
***  Proved C25:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H21.
***  Proved C26:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H22.
***  Proved C27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C28:  length >= rr_type__linelengthindex__first
     using hypothesis H24.
***  Proved C29:  length <= rr_type__linelengthindex__last
     using hypothesis H25.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_13.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx >= 0
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  true
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  begidx >= 0
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C23 on reading formula in, to give:
     %%%  C23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  begidx >= 0
     using hypothesis H1.
***  Proved C2:  true
***  Proved C3:  begidx >= 0
     using hypothesis H1.
***  Proved C4:  begidx + 1 < length
     using hypothesis H45.
***  Proved C5:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H3.
***  Proved C6:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H4.
***  Proved C7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H5.
***  Proved C8:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H6.
***  Proved C9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H7.
***  Proved C10:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H8.
***  Proved C11:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C12:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C13:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C14:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C15:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C16:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C17:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C18:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C19:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C20:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C21:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H19.
***  Proved C22:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H20.
***  Proved C23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H21.
***  Proved C24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H22.
***  Proved C25:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H23.
***  Proved C26:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H24.
***  Proved C27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H25.
***  Proved C28:  length >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C29:  length <= rr_type__linelengthindex__last
     using hypothesis H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_14.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  endidx >= 0
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C23 on reading formula in, to give:
     %%%  C23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  begidx >= 1
     using hypothesis H1.
***  Proved C2:  begidx <= endidx + 1
     using hypothesis H2.
***  Proved C3:  endidx >= 0
     using hypothesis H3.
***  Proved C4:  endidx + 1 < length
     using hypothesis H38.
***  Proved C5:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C6:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H6.
***  Proved C7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H7.
***  Proved C8:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H8.
***  Proved C9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H9.
***  Proved C10:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H10.
***  Proved C11:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C12:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C13:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H13.
***  Proved C14:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H14.
***  Proved C15:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C16:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C17:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C18:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C19:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C20:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C21:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H21.
***  Proved C22:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H22.
***  Proved C23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H24.
***  Proved C25:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H25.
***  Proved C26:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H26.
***  Proved C27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H27.
***  Proved C28:  length >= rr_type__linelengthindex__first
     using hypothesis H28.
***  Proved C29:  length <= rr_type__linelengthindex__last
     using hypothesis H29.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_15.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  endidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H30.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H29:  length <= 256
<S>  New H31:  endidx <= 256
<S>  New C2:  endidx <= 255
***  Proved C2:  endidx <= 255
     using hypotheses H4 & H29.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_16.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  1 >= integer__base__first
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  1 <= integer__base__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  0 >= integer__base__first
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  0 <= integer__base__last
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C1:  fld_signaturelength(rrsig_rec) >= - 2147483649
<S>  New C3:  true
<S>  New C5:  true
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C2:  fld_signaturelength(rrsig_rec) <= 2147483646
<S>  New C4:  true
<S>  New C6:  true
***  Proved C3:  true
***  Proved C5:  true
***  Proved C4:  true
***  Proved C6:  true
>>>  Restructured hypothesis H32 into:
     >>>  H32:  length <= 1 or element(s, [1]) <> blank and element(s, [1]) <> 
          tab
>>>  Restructured hypothesis H41 into:
     >>>  H41:  length <= 1 or (element(s, [1]) = blank or element(s, [1]) = 
          tab)
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H32:  length <= 1 or element(s, [1]) <> 32 and element(s, [1]) <> tab
<S>  New H41:  length <= 1 or (element(s, [1]) = 32 or element(s, [1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H32:  length <= 1 or element(s, [1]) <> 32 and element(s, [1]) <> 9
<S>  New H41:  length <= 1 or (element(s, [1]) = 32 or element(s, [1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H5:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H6:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H7:  fld_algorithm(rrsig_rec) >= 0
<S>  New H9:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H8:  fld_algorithm(rrsig_rec) <= 255
<S>  New H10:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H17:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H18:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H1:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H11:  fld_origttl(rrsig_rec) >= 0
<S>  New H13:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H15:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H2:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H12:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H14:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H16:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H3:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H4:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H24:  length >= 1
<S>  New H26:  true
<S>  New H30:  1 < length -> 1 <= rr_type__linelengthindex__last
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H25:  length <= 256
<S>  New H27:  true
<S>  New H30:  true
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H19:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H19:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H20:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H21:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H22:  fld_signaturelength(rrsig_rec) <= 1365
***  Proved C1:  fld_signaturelength(rrsig_rec) >= - 2147483649
     using hypothesis H21.
***  Proved C2:  fld_signaturelength(rrsig_rec) <= 2147483646
     using hypothesis H22.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_17.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  1 >= integer__base__first
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  1 <= integer__base__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  0 >= integer__base__first
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  0 <= integer__base__last
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C1:  fld_signaturelength(rrsig_rec) >= - 2147483649
<S>  New C3:  true
<S>  New C5:  true
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C2:  fld_signaturelength(rrsig_rec) <= 2147483646
<S>  New C4:  true
<S>  New C6:  true
***  Proved C3:  true
***  Proved C5:  true
***  Proved C4:  true
***  Proved C6:  true
>>>  Restructured hypothesis H36 into:
     >>>  H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> blank and 
          element(s, [begidx + 1]) <> tab
>>>  Restructured hypothesis H45 into:
     >>>  H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = blank or 
          element(s, [begidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> 32 and 
          element(s, [begidx + 1]) <> tab
<S>  New H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = 32 or 
          element(s, [begidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> 32 and 
          element(s, [begidx + 1]) <> 9
<S>  New H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = 32 or 
          element(s, [begidx + 1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H7:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H8:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H9:  fld_algorithm(rrsig_rec) >= 0
<S>  New H11:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H10:  fld_algorithm(rrsig_rec) <= 255
<S>  New H12:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H19:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H20:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H3:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H13:  fld_origttl(rrsig_rec) >= 0
<S>  New H15:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H17:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H4:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H14:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H16:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H18:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H5:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H6:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H26:  length >= 1
<S>  New H28:  begidx >= 1
<S>  New H30:  begidx >= 0
<S>  New H34:  begidx + 1 < length -> begidx >= 0 and begidx + 1 <= 
          rr_type__linelengthindex__last
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H27:  length <= 256
<S>  New H29:  begidx <= 256
<S>  New H31:  begidx <= 255
<S>  New H34:  begidx + 1 < length -> begidx >= 0 and begidx <= 255
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H21:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H21:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H22:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H22:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H23:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H24:  fld_signaturelength(rrsig_rec) <= 1365
***  Proved C1:  fld_signaturelength(rrsig_rec) >= - 2147483649
     using hypothesis H23.
***  Proved C2:  fld_signaturelength(rrsig_rec) <= 2147483646
     using hypothesis H24.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_18.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C1:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) >= - 
          2147483648
<S>  New C3:  endidx + 1 - begidx >= - 2147483649
<S>  New C5:  endidx + 1 - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C2:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          2147483647
<S>  New C4:  endidx + 1 - begidx <= 2147483646
<S>  New C6:  endidx + 1 - begidx <= 2147483647
***  Proved C3:  endidx + 1 - begidx >= - 2147483649
     using hypothesis H2.
***  Proved C5:  endidx + 1 - begidx >= - 2147483648
     using hypothesis H2.
>>>  Restructured hypothesis H38 into:
     >>>  H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = blank or 
          element(s, [endidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = 32 or 
          element(s, [endidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = 32 or 
          element(s, [endidx + 1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_rec) >= 0
<S>  New H13:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_rec) <= 255
<S>  New H14:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H15:  fld_origttl(rrsig_rec) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H19:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H28:  length >= 1
<S>  New H30:  endidx >= 1
<S>  New H32:  endidx >= 0
<S>  New H36:  endidx + 1 < length -> endidx >= 0 and endidx + 1 <= 
          rr_type__linelengthindex__last
<S>  New H39:  begidx >= 1
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H29:  length <= 256
<S>  New H31:  endidx <= 256
<S>  New H33:  endidx <= 255
<S>  New H40:  begidx <= 256
<S>  New H36:  endidx + 1 < length -> endidx >= 0 and endidx <= 255
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_rec) <= 1365
***  Proved C1:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) >= 
          - 2147483648
     using hypotheses H2 & H25.
***  Proved C2:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          2147483647
     using hypotheses H1, H26 & H31.
***  Proved C4:  endidx + 1 - begidx <= 2147483646
     using hypotheses H1 & H31.
***  Proved C6:  endidx + 1 - begidx <= 2147483647
     using hypotheses H1 & H31.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_19.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  true
<S>  New C3:  true
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  true
<S>  New C4:  true
***  Proved C1:  true
***  Proved C3:  true
***  Proved C2:  true
***  Proved C4:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_20.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  begidx >= - 2147483649
<S>  New C3:  begidx >= - 2147483649
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  begidx <= 2147483646
<S>  New C4:  begidx <= 2147483646
***  Proved C1:  begidx >= - 2147483649
     using hypothesis H1.
***  Proved C3:  begidx >= - 2147483649
     using hypothesis H1.
>>>  Restructured hypothesis H36 into:
     >>>  H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> blank and 
          element(s, [begidx + 1]) <> tab
>>>  Restructured hypothesis H45 into:
     >>>  H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = blank or 
          element(s, [begidx + 1]) = tab)
>>>  Restructured hypothesis H56 into:
     >>>  H56:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H56:  fld_signaturelength(rrsig_rec) <= 1364
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> 32 and 
          element(s, [begidx + 1]) <> tab
<S>  New H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = 32 or 
          element(s, [begidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> 32 and 
          element(s, [begidx + 1]) <> 9
<S>  New H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = 32 or 
          element(s, [begidx + 1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H50:  fld_signaturelength(rrsig_rec) >= - 2147483649
<S>  New H52:  true
<S>  New H54:  true
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H51:  fld_signaturelength(rrsig_rec) <= 2147483646
<S>  New H53:  true
<S>  New H55:  true
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H7:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H8:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H9:  fld_algorithm(rrsig_rec) >= 0
<S>  New H11:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H10:  fld_algorithm(rrsig_rec) <= 255
<S>  New H12:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H19:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H20:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H3:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H13:  fld_origttl(rrsig_rec) >= 0
<S>  New H15:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H17:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H4:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H14:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H16:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H18:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H5:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H6:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H26:  length >= 1
<S>  New H28:  begidx >= 1
<S>  New H30:  begidx >= 0
<S>  New H34:  begidx + 1 < length -> begidx >= 0 and begidx + 1 <= 
          rr_type__linelengthindex__last
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H27:  length <= 256
<S>  New H29:  begidx <= 256
<S>  New H31:  begidx <= 255
<S>  New H34:  begidx + 1 < length -> begidx >= 0 and begidx <= 255
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H21:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H21:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H22:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H22:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H23:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H24:  fld_signaturelength(rrsig_rec) <= 1365
***  Proved C2:  begidx <= 2147483646
     using hypothesis H29.
***  Proved C4:  begidx <= 2147483646
     using hypothesis H29.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_21.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New C1:  endidx >= - 2147483649
<S>  New C3:  begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New C2:  endidx <= 2147483646
<S>  New C4:  begidx <= 2147483647
***  Proved C1:  endidx >= - 2147483649
     using hypothesis H3.
***  Proved C3:  begidx >= - 2147483648
     using hypothesis H1.
>>>  Restructured hypothesis H38 into:
     >>>  H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = blank or 
          element(s, [endidx + 1]) = tab)
>>>  Restructured hypothesis H49 into:
     >>>  H49:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          rr_type__rrsig_record_type__maxrrsiglength
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H49:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          1365
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = 32 or 
          element(s, [endidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = 32 or 
          element(s, [endidx + 1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H43:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) >= - 
          2147483648
<S>  New H45:  endidx + 1 - begidx >= - 2147483649
<S>  New H47:  endidx + 1 - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H44:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          2147483647
<S>  New H46:  endidx + 1 - begidx <= 2147483646
<S>  New H48:  endidx + 1 - begidx <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_rec) >= 0
<S>  New H13:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_rec) <= 255
<S>  New H14:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H15:  fld_origttl(rrsig_rec) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H19:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H28:  length >= 1
<S>  New H30:  endidx >= 1
<S>  New H32:  endidx >= 0
<S>  New H36:  endidx + 1 < length -> endidx >= 0 and endidx + 1 <= 
          rr_type__linelengthindex__last
<S>  New H39:  begidx >= 1
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H29:  length <= 256
<S>  New H31:  endidx <= 256
<S>  New H33:  endidx <= 255
<S>  New H40:  begidx <= 256
<S>  New H36:  endidx + 1 < length -> endidx >= 0 and endidx <= 255
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_rec) <= 1365
***  Proved C2:  endidx <= 2147483646
     using hypothesis H31.
***  Proved C4:  begidx <= 2147483647
     using hypothesis H40.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_22.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  1 >= integer__first and 1 <= integer__last
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  1 >= integer__first and 1 <= integer__last
***  Proved C1:  1 >= integer__first and 1 <= integer__last
     using hypotheses H57 & H58.
***  Proved C2:  1 >= integer__first and 1 <= integer__last
     using hypotheses H57 & H58.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_23.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
***  Proved C1:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
     using hypotheses H61 & H62.
***  Proved C2:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
     using hypotheses H61 & H62.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_24.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
***  Proved C1:  begidx <= endidx + 1 -> endidx + 1 >= integer__first and 
          endidx + 1 <= integer__last
     using hypotheses H54 & H55.
***  Proved C2:  begidx <= endidx + 1 -> begidx >= integer__first and begidx <= 
          integer__last
     using hypotheses H56 & H57.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_25.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H61 on reading formula in, to give:
     %%%  H61:  1 >= integer__first and 1 <= integer__last
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H67 on reading formula in, to give:
     %%%  H67:  true
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  true
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  true
%%%  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 C6 on reading formula in, to give:
     %%%  C6:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  true
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  true
***  Proved C1:  true
***  Proved C2:  true
***  Proved C3:  true
***  Proved C4:  true
***  Proved C5:  true
***  Proved C6:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H52.
***  Proved C7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H1.
***  Proved C8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H2.
***  Proved C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H3.
***  Proved C10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H4.
***  Proved C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H5.
***  Proved C12:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H6.
***  Proved C13:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H7.
***  Proved C14:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H8.
***  Proved C15:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C16:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C17:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H11.
***  Proved C18:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H12.
***  Proved C19:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C20:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C21:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C22:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C23:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H17.
***  Proved C24:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H18.
***  Proved C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H19.
***  Proved C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H20.
***  Proved C27:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H21.
***  Proved C28:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H22.
***  Proved C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C30:  length >= rr_type__linelengthindex__first
     using hypothesis H24.
***  Proved C31:  length <= rr_type__linelengthindex__last
     using hypothesis H25.
***  Proved C32:  1 >= integer__first
     using hypothesis H57.
***  Proved C33:  1 <= integer__last
     using hypothesis H58.
***  Proved C34:  true
***  Proved C35:  true
***  Proved C36:  1 >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C37:  1 <= rr_type__linelengthindex__last
     using hypothesis H27.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_26.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  true
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  true
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  true
%%%  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:  begidx >= 0
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  true
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  true
***  Proved C1:  true
***  Proved C2:  true
***  Proved C3:  true
***  Proved C4:  true
***  Proved C5:  begidx >= 0
     using hypothesis H1.
***  Proved C6:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H56.
***  Proved C7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H3.
***  Proved C8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H4.
***  Proved C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H5.
***  Proved C10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H6.
***  Proved C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H7.
***  Proved C12:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H8.
***  Proved C13:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H9.
***  Proved C14:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H10.
***  Proved C15:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C16:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C17:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H13.
***  Proved C18:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H14.
***  Proved C19:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C20:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C21:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C22:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C23:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H19.
***  Proved C24:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H20.
***  Proved C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H21.
***  Proved C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H22.
***  Proved C27:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H23.
***  Proved C28:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H24.
***  Proved C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H25.
***  Proved C30:  length >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C31:  length <= rr_type__linelengthindex__last
     using hypothesis H27.
***  Proved C32:  begidx + 1 >= integer__first
     using hypothesis H61.
***  Proved C33:  begidx + 1 <= integer__last
     using hypothesis H62.
***  Proved C34:  true
***  Proved C35:  true
***  Proved C36:  begidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H30.
***  Proved C37:  begidx + 1 <= rr_type__linelengthindex__last
     using hypothesis H31.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_27.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  true
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  true
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  true
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  true
***  Proved C1:  true
***  Proved C2:  true
***  Proved C3:  true
***  Proved C4:  begidx <= endidx + 1
     using hypothesis H64.
***  Proved C5:  begidx >= 1
     using hypothesis H1.
***  Proved C6:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H49.
***  Proved C7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H5.
***  Proved C8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H6.
***  Proved C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H7.
***  Proved C10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H8.
***  Proved C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H9.
***  Proved C12:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H10.
***  Proved C13:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H11.
***  Proved C14:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H12.
***  Proved C15:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H13.
***  Proved C16:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H14.
***  Proved C17:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H15.
***  Proved C18:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H16.
***  Proved C19:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C20:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C21:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C22:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C23:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H21.
***  Proved C24:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H22.
***  Proved C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H23.
***  Proved C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
     using hypothesis H24.
***  Proved C27:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H25.
***  Proved C28:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H26.
***  Proved C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H27.
***  Proved C30:  length >= rr_type__linelengthindex__first
     using hypothesis H28.
***  Proved C31:  length <= rr_type__linelengthindex__last
     using hypothesis H29.
***  Proved C32:  begidx >= integer__first
     using hypothesis H56.
***  Proved C33:  begidx <= integer__last
     using hypothesis H57.
***  Proved C34:  true
***  Proved C35:  begidx <= endidx + 1
     using hypothesis H64.
***  Proved C36:  endidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H32.
***  Proved C37:  endidx + 1 <= rr_type__linelengthindex__last
     using hypothesis H33.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_28.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  true
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  true
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 
          rr_type__rrsig_record_type__maxrrsiglength
%%%  Simplified C7 on reading formula in, to give:
     %%%  C7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
%%%  Simplified C8 on reading formula in, to give:
     %%%  C8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
%%%  Simplified C9 on reading formula in, to give:
     %%%  C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified C10 on reading formula in, to give:
     %%%  C10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
%%%  Simplified C11 on reading formula in, to give:
     %%%  C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified C12 on reading formula in, to give:
     %%%  C12:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
%%%  Simplified C13 on reading formula in, to give:
     %%%  C13:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
%%%  Simplified C14 on reading formula in, to give:
     %%%  C14:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
%%%  Simplified C15 on reading formula in, to give:
     %%%  C15:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
%%%  Simplified C16 on reading formula in, to give:
     %%%  C16:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
%%%  Simplified C17 on reading formula in, to give:
     %%%  C17:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
%%%  Simplified C18 on reading formula in, to give:
     %%%  C18:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
%%%  Simplified C19 on reading formula in, to give:
     %%%  C19:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
%%%  Simplified C20 on reading formula in, to give:
     %%%  C20:  fld_sigexpiration(rrsig_rec) <= unsigned_types__unsigned32__last
%%%  Simplified C21 on reading formula in, to give:
     %%%  C21:  fld_siginception(rrsig_rec) >= unsigned_types__unsigned32__first
%%%  Simplified C22 on reading formula in, to give:
     %%%  C22:  fld_siginception(rrsig_rec) <= unsigned_types__unsigned32__last
%%%  Simplified C23 on reading formula in, to give:
     %%%  C23:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(update(fld_signature(rrsig_rec), [
          fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1)], element(
          s, [loop__3__i])), [i___2]) and element(update(fld_signature(
          rrsig_rec), [fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 
          1)], element(s, [loop__3__i])), [i___2]) <= character__last)
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified C28 on reading formula in, to give:
     %%%  C28:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
***  Proved C1:  true
***  Proved C2:  endidx = endidx__entry__loop__3
     using hypothesis H2.
***  Proved C3:  loop__3__i + 1 >= begidx
     using hypothesis H3.
***  Proved C5:  begidx >= 1
     using hypothesis H5.
***  Proved C6:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 
          rr_type__rrsig_record_type__maxrrsiglength
     using hypothesis H6.
***  Proved C7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H7.
***  Proved C8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H8.
***  Proved C9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
     using hypothesis H9.
***  Proved C10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__classtype__last
     using hypothesis H10.
***  Proved C11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
     using hypothesis H11.
***  Proved C12:  fld_typecovered(rrsig_rec) <= dns_types__query_type__last
     using hypothesis H12.
***  Proved C13:  fld_algorithm(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H13.
***  Proved C14:  fld_algorithm(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H14.
***  Proved C15:  fld_numlabels(rrsig_rec) >= unsigned_types__unsigned8__first
     using hypothesis H15.
***  Proved C16:  fld_numlabels(rrsig_rec) <= unsigned_types__unsigned8__last
     using hypothesis H16.
***  Proved C17:  fld_origttl(rrsig_rec) >= unsigned_types__unsigned32__first
     using hypothesis H17.
***  Proved C18:  fld_origttl(rrsig_rec) <= unsigned_types__unsigned32__last
     using hypothesis H18.
***  Proved C19:  fld_sigexpiration(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H19.
***  Proved C20:  fld_sigexpiration(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H20.
***  Proved C21:  fld_siginception(rrsig_rec) >= 
          unsigned_types__unsigned32__first
     using hypothesis H21.
***  Proved C22:  fld_siginception(rrsig_rec) <= 
          unsigned_types__unsigned32__last
     using hypothesis H22.
***  Proved C23:  fld_keytag(rrsig_rec) >= unsigned_types__unsigned16__first
     using hypothesis H23.
***  Proved C24:  fld_keytag(rrsig_rec) <= unsigned_types__unsigned16__last
     using hypothesis H24.
***  Proved C25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
     using hypothesis H25.
***  Proved C26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(update(fld_signature(rrsig_rec), [
          fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1)], element(
          s, [loop__3__i])), [i___2]) and element(update(fld_signature(
          rrsig_rec), [fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 
          1)], element(s, [loop__3__i])), [i___2]) <= character__last)
     using hypotheses H26, H38, H39, H42 & H43.
***  Proved C27:  fld_signaturelength(rrsig_rec) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H27.
***  Proved C28:  fld_signaturelength(rrsig_rec) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H28.
***  Proved C29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
     using hypothesis H29.
***  Proved C30:  length >= rr_type__linelengthindex__first
     using hypothesis H30.
***  Proved C31:  length <= rr_type__linelengthindex__last
     using hypothesis H31.
***  Proved C32:  loop__3__i + 1 >= integer__first
     using hypothesis H32.
***  Proved C34:  loop__3__i + 1 >= begidx
     using hypothesis H3.
***  Proved C36:  endidx__entry__loop__3 >= rr_type__linelengthindex__first
     using hypothesis H36.
***  Proved C37:  endidx__entry__loop__3 <= rr_type__linelengthindex__last
     using hypothesis H37.
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H33:  loop__3__i <= 2147483647
<S>  New C33:  loop__3__i <= 2147483646
>>>  Restructured hypothesis H50 into:
     >>>  H50:  loop__3__i <> endidx__entry__loop__3
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H6:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H32:  loop__3__i >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H44:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= - 
          2147483648
<S>  New H46:  loop__3__i - begidx >= - 2147483649
<S>  New H48:  loop__3__i - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H45:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          2147483647
<S>  New H47:  loop__3__i - begidx <= 2147483646
<S>  New H49:  loop__3__i - begidx <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
<S>  New H38:  element(s, [loop__3__i]) >= 0
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H39:  element(s, [loop__3__i]) <= 255
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H11:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H12:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H13:  fld_algorithm(rrsig_rec) >= 0
<S>  New H15:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H14:  fld_algorithm(rrsig_rec) <= 255
<S>  New H16:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H23:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H24:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H17:  fld_origttl(rrsig_rec) >= 0
<S>  New H19:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H21:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H18:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H20:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H22:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H30:  length >= 1
<S>  New H36:  endidx__entry__loop__3 >= 1
<S>  New H40:  loop__3__i >= 1
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H31:  length <= 256
<S>  New H37:  endidx__entry__loop__3 <= 256
<S>  New H41:  loop__3__i <= 256
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H42:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= 1
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H43:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          1365
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H27:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H28:  fld_signaturelength(rrsig_rec) <= 1365
%%%  Hypotheses H35 & H50 together imply that
          loop__3__i < endidx__entry__loop__3.
     H35 & H50 have therefore been deleted and a new H51 added to this effect.
***  Proved C4:  loop__3__i + 1 <= endidx
     via its standard form, which is:
     Std.Fm C4:  endidx - loop__3__i > 0
     using hypotheses H2 & H51.
***  Proved C35:  loop__3__i + 1 <= endidx__entry__loop__3
     via its standard form, which is:
     Std.Fm C35:  endidx__entry__loop__3 - loop__3__i > 0
     using hypothesis H51.
***  Proved C33:  loop__3__i <= 2147483646
     using hypothesis H41.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_29.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  true
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
***  Proved C4:  loop__3__i <= rr_type__linelengthindex__last
     using hypotheses H2, H4 & H37.
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
<S>  New C1:  element(s, [loop__3__i]) >= 0
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
<S>  New C2:  element(s, [loop__3__i]) <= 255
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H30:  length >= 1
<S>  New H36:  endidx__entry__loop__3 >= 1
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
<S>  New C3:  loop__3__i >= 1
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
<S>  New C5:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= 1
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
<S>  New C6:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 1365
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New C7:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= - 
          2147483648
<S>  New C9:  loop__3__i - begidx >= - 2147483649
<S>  New C11:  loop__3__i - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New C8:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          2147483647
<S>  New C10:  loop__3__i - begidx <= 2147483646
<S>  New C12:  loop__3__i - begidx <= 2147483647
***  Proved C1:  element(s, [loop__3__i]) >= 0
     using hypotheses H2, H3, H4, H5, H29 & H37.
***  Proved C2:  element(s, [loop__3__i]) <= 255
     using hypotheses H2, H3, H4, H5, H29 & H37.
***  Proved C3:  loop__3__i >= 1
     using hypotheses H3 & H5.
***  Proved C9:  loop__3__i - begidx >= - 2147483649
     using hypothesis H3.
***  Proved C11:  loop__3__i - begidx >= - 2147483648
     using hypothesis H3.
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H6:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H32:  loop__3__i >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H33:  loop__3__i <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H11:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H12:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H13:  fld_algorithm(rrsig_rec) >= 0
<S>  New H15:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H14:  fld_algorithm(rrsig_rec) <= 255
<S>  New H16:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H23:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H24:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H17:  fld_origttl(rrsig_rec) >= 0
<S>  New H19:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H21:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H18:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H20:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H22:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
<S>  New H31:  length <= 256
<S>  New H37:  endidx__entry__loop__3 <= 256
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H27:  fld_signaturelength(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H28:  fld_signaturelength(rrsig_rec) <= 1365
***  Proved C5:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= 1
     using hypotheses H3 & H27.
***  Proved C7:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= 
          - 2147483648
     using hypotheses H3 & H27.
***  Proved C8:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          2147483647
     using hypotheses H2, H4, H5, H28 & H37.
***  Proved C10:  loop__3__i - begidx <= 2147483646
     using hypotheses H5 & H33.
***  Proved C12:  loop__3__i - begidx <= 2147483647
     using hypotheses H5 & H33.
---  Eliminated hypothesis H1 (true-hypothesis).
---  Eliminated hypothesis H34 (true-hypothesis).
---  Eliminated hypothesis H28 (redundant, given H3, H4 & H6).
---  Eliminated hypothesis H32 (redundant, given H3 & H5).
---  Eliminated hypothesis H33 (redundant, given H35 & H37).
-S-  Eliminated hypothesis H2.
     This was achieved by replacing all occurrences of endidx by:
          endidx__entry__loop__3.
<S>  New H4:  loop__3__i <= endidx__entry__loop__3
<S>  New H6:  fld_signaturelength(rrsig_rec) + (endidx__entry__loop__3 - begidx 
          + 1) <= 1365
***  Proved C6:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          1365
     via its standard form, which is:
     Std.Fm C6:  begidx - loop__3__i - fld_signaturelength(rrsig_rec) > - 1365
     using hypotheses H4 & H6.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_30.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H61 on reading formula in, to give:
     %%%  H61:  1 >= integer__first and 1 <= integer__last
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H67 on reading formula in, to give:
     %%%  H67:  false
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  1 >= integer__base__first
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  1 <= integer__base__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  0 >= integer__base__first
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  0 <= integer__base__last
***  Proved C1:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H21.
***  Proved C3:  1 >= integer__base__first
     using hypothesis H48.
***  Proved C4:  1 <= integer__base__last
     using hypothesis H49.
***  Proved C5:  0 >= integer__base__first
     using hypothesis H50.
***  Proved C6:  0 <= integer__base__last
     using hypothesis H51.
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H22:  fld_signaturelength(rrsig_rec) <= 1365
<S>  New C2:  fld_signaturelength(rrsig_rec) <= 1364
>>>  Restructured hypothesis H32 into:
     >>>  H32:  length <= 1 or element(s, [1]) <> blank and element(s, [1]) <> 
          tab
>>>  Restructured hypothesis H41 into:
     >>>  H41:  length <= 1 or (element(s, [1]) = blank or element(s, [1]) = 
          tab)
>>>  Restructured hypothesis H52 into:
     >>>  H52:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
---  Attempted addition of new hypothesis:
          1 >= integer__first
     eliminated: this already exists (as H57).
---  Attempted addition of new hypothesis:
          1 <= integer__last
     eliminated: this already exists (as H58).
>>>  Hypothesis H61 has now been split into two, giving:
     >>>  H57:  1 >= integer__first
     >>>  H58:  1 <= integer__last
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H52:  fld_signaturelength(rrsig_rec) <= 1364
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H32:  length <= 1 or element(s, [1]) <> 32 and element(s, [1]) <> tab
<S>  New H41:  length <= 1 or (element(s, [1]) = 32 or element(s, [1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H32:  length <= 1 or element(s, [1]) <> 32 and element(s, [1]) <> 9
<S>  New H41:  length <= 1 or (element(s, [1]) = 32 or element(s, [1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H57:  true
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H58:  true
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H46:  fld_signaturelength(rrsig_rec) >= - 2147483649
<S>  New H48:  true
<S>  New H50:  true
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H47:  fld_signaturelength(rrsig_rec) <= 2147483646
<S>  New H49:  true
<S>  New H51:  true
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H5:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H6:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H7:  fld_algorithm(rrsig_rec) >= 0
<S>  New H9:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H8:  fld_algorithm(rrsig_rec) <= 255
<S>  New H10:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H17:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H18:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H1:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H11:  fld_origttl(rrsig_rec) >= 0
<S>  New H13:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H15:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H2:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H12:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H14:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H16:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H3:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H4:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H24:  length >= 1
<S>  New H26:  true
<S>  New H30:  1 < length -> 1 <= rr_type__linelengthindex__last
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H25:  length <= 256
<S>  New H27:  true
<S>  New H30:  true
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H19:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H19:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H20:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H21:  fld_signaturelength(rrsig_rec) >= 0
***  Proved C2:  fld_signaturelength(rrsig_rec) <= 1364
     using hypothesis H52.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_31.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  false
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
%%%  Simplified C3 on reading formula in, to give:
     %%%  C3:  1 >= integer__base__first
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  1 <= integer__base__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  0 >= integer__base__first
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  0 <= integer__base__last
***  Proved C1:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H23.
***  Proved C3:  1 >= integer__base__first
     using hypothesis H52.
***  Proved C4:  1 <= integer__base__last
     using hypothesis H53.
***  Proved C5:  0 >= integer__base__first
     using hypothesis H54.
***  Proved C6:  0 <= integer__base__last
     using hypothesis H55.
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H24:  fld_signaturelength(rrsig_rec) <= 1365
<S>  New C2:  fld_signaturelength(rrsig_rec) <= 1364
>>>  Restructured hypothesis H36 into:
     >>>  H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> blank and 
          element(s, [begidx + 1]) <> tab
>>>  Restructured hypothesis H45 into:
     >>>  H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = blank or 
          element(s, [begidx + 1]) = tab)
>>>  Restructured hypothesis H56 into:
     >>>  H56:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__maxrrsiglength
---  Attempted addition of new hypothesis:
          begidx + 1 >= integer__first
     eliminated: this already exists (as H61).
---  Attempted addition of new hypothesis:
          begidx + 1 <= integer__last
     eliminated: this already exists (as H62).
>>>  Hypothesis H65 has now been split into two, giving:
     >>>  H61:  begidx + 1 >= integer__first
     >>>  H62:  begidx + 1 <= integer__last
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H56:  fld_signaturelength(rrsig_rec) <= 1364
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> 32 and 
          element(s, [begidx + 1]) <> tab
<S>  New H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = 32 or 
          element(s, [begidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H36:  length <= begidx + 1 or element(s, [begidx + 1]) <> 32 and 
          element(s, [begidx + 1]) <> 9
<S>  New H45:  length <= begidx + 1 or (element(s, [begidx + 1]) = 32 or 
          element(s, [begidx + 1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H61:  begidx >= - 2147483649
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H62:  begidx <= 2147483646
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H50:  fld_signaturelength(rrsig_rec) >= - 2147483649
<S>  New H52:  true
<S>  New H54:  true
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H51:  fld_signaturelength(rrsig_rec) <= 2147483646
<S>  New H53:  true
<S>  New H55:  true
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H7:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H8:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H9:  fld_algorithm(rrsig_rec) >= 0
<S>  New H11:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H10:  fld_algorithm(rrsig_rec) <= 255
<S>  New H12:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H19:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H20:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H3:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H13:  fld_origttl(rrsig_rec) >= 0
<S>  New H15:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H17:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H4:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H14:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H16:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H18:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H5:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H6:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H26:  length >= 1
<S>  New H28:  begidx >= 1
<S>  New H30:  begidx >= 0
<S>  New H34:  begidx + 1 < length -> begidx >= 0 and begidx + 1 <= 
          rr_type__linelengthindex__last
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H27:  length <= 256
<S>  New H29:  begidx <= 256
<S>  New H31:  begidx <= 255
<S>  New H34:  begidx + 1 < length -> begidx >= 0 and begidx <= 255
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H21:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H21:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H22:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H22:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H23:  fld_signaturelength(rrsig_rec) >= 0
***  Proved C2:  fld_signaturelength(rrsig_rec) <= 1364
     using hypothesis H56.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_32.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H33).
***  Proved C3:  endidx + 1 - begidx + 1 >= integer__base__first
     using hypothesis H45.
***  Proved C4:  endidx + 1 - begidx + 1 <= integer__base__last
     using hypothesis H46.
***  Proved C5:  endidx + 1 - begidx >= integer__base__first
     using hypothesis H47.
***  Proved C6:  endidx + 1 - begidx <= integer__base__last
     using hypothesis H48.
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H25:  fld_signaturelength(rrsig_rec) >= 0
<S>  New C1:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H26:  fld_signaturelength(rrsig_rec) <= 1365
<S>  New C2:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 1365
***  Proved C1:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) >= 0
     using hypotheses H2 & H25.
>>>  Restructured hypothesis H38 into:
     >>>  H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = blank or 
          element(s, [endidx + 1]) = tab)
>>>  Restructured hypothesis H49 into:
     >>>  H49:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          rr_type__rrsig_record_type__maxrrsiglength
>>>  Restructured hypothesis H64 into:
     >>>  H64:  endidx + 1 < begidx
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H49:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          1365
-S-  Applied substitution rule addtokeyr_rules(2).
     This was achieved by replacing all occurrences of blank by:
          32.
<S>  New H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = 32 or 
          element(s, [endidx + 1]) = tab)
-S-  Applied substitution rule addtokeyr_rules(3).
     This was achieved by replacing all occurrences of tab by:
          9.
<S>  New H38:  length <= endidx + 1 or (element(s, [endidx + 1]) = 32 or 
          element(s, [endidx + 1]) = 9)
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H54:  endidx >= - 2147483649
<S>  New H56:  begidx >= - 2147483648
<S>  New H58:  begidx <= endidx + 1 -> endidx >= - 2147483649 and endidx + 1 <= 
          integer__last
<S>  New H59:  begidx <= endidx + 1 -> begidx >= - 2147483648 and begidx <= 
          integer__last
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H55:  endidx <= 2147483646
<S>  New H57:  begidx <= 2147483647
<S>  New H58:  begidx <= endidx + 1 -> endidx >= - 2147483649 and endidx <= 
          2147483646
<S>  New H59:  begidx <= endidx + 1 -> begidx >= - 2147483648 and begidx <= 
          2147483647
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H43:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) >= - 
          2147483648
<S>  New H45:  endidx + 1 - begidx >= - 2147483649
<S>  New H47:  endidx + 1 - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H44:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          2147483647
<S>  New H46:  endidx + 1 - begidx <= 2147483646
<S>  New H48:  endidx + 1 - begidx <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H9:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H10:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H11:  fld_algorithm(rrsig_rec) >= 0
<S>  New H13:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H12:  fld_algorithm(rrsig_rec) <= 255
<S>  New H14:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H21:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H22:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H5:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H15:  fld_origttl(rrsig_rec) >= 0
<S>  New H17:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H19:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H6:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H16:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H18:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H20:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H7:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H8:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H28:  length >= 1
<S>  New H30:  endidx >= 1
<S>  New H32:  endidx >= 0
<S>  New H36:  endidx + 1 < length -> endidx >= 0 and endidx + 1 <= 
          rr_type__linelengthindex__last
<S>  New H39:  begidx >= 1
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H29:  length <= 256
<S>  New H31:  endidx <= 256
<S>  New H33:  endidx <= 255
<S>  New H40:  begidx <= 256
<S>  New H36:  endidx + 1 < length -> endidx >= 0 and endidx <= 255
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H23:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H24:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
***  Proved C2:  fld_signaturelength(rrsig_rec) + (endidx + 1 - begidx + 1) <= 
          1365
     using hypothesis H49.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_33.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  true
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H27:  fld_signaturelength(rrsig_rec) >= 0
<S>  New C1:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H28:  fld_signaturelength(rrsig_rec) <= 1365
<S>  New C2:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H44:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= - 
          2147483648
<S>  New H46:  loop__3__i - begidx >= - 2147483649
<S>  New H48:  loop__3__i - begidx >= - 2147483648
<S>  New C3:  endidx - begidx >= - 2147483649
<S>  New C5:  endidx - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H45:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          2147483647
<S>  New H47:  loop__3__i - begidx <= 2147483646
<S>  New H49:  loop__3__i - begidx <= 2147483647
<S>  New C4:  endidx - begidx <= 2147483646
<S>  New C6:  endidx - begidx <= 2147483647
***  Proved C1:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 0
     using hypotheses H3, H4 & H27.
***  Proved C3:  endidx - begidx >= - 2147483649
     using hypotheses H3 & H4.
***  Proved C5:  endidx - begidx >= - 2147483648
     using hypotheses H3 & H4.
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H6:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H32:  loop__3__i >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H33:  loop__3__i <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
<S>  New H38:  element(s, [loop__3__i]) >= 0
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H39:  element(s, [loop__3__i]) <= 255
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H11:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H12:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H13:  fld_algorithm(rrsig_rec) >= 0
<S>  New H15:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H14:  fld_algorithm(rrsig_rec) <= 255
<S>  New H16:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H23:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H24:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H17:  fld_origttl(rrsig_rec) >= 0
<S>  New H19:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H21:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H18:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H20:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H22:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H30:  length >= 1
<S>  New H36:  endidx__entry__loop__3 >= 1
<S>  New H40:  loop__3__i >= 1
<S>  New H51:  begidx >= 1
<S>  New H53:  endidx >= 1
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H31:  length <= 256
<S>  New H37:  endidx__entry__loop__3 <= 256
<S>  New H41:  loop__3__i <= 256
<S>  New H52:  begidx <= 256
<S>  New H54:  endidx <= 256
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H42:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= 1
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H43:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          1365
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
***  Proved C2:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
     using hypothesis H6.
***  Proved C4:  endidx - begidx <= 2147483646
     using hypotheses H5 & H54.
***  Proved C6:  endidx - begidx <= 2147483647
     using hypotheses H5 & H54.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_34.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  2 <= rr_type__linelengthindex__last
***  Proved C1:  2 >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C2:  2 <= rr_type__linelengthindex__last
     using hypotheses H25 & H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_35.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H61 on reading formula in, to give:
     %%%  H61:  1 >= integer__first and 1 <= integer__last
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H67 on reading formula in, to give:
     %%%  H67:  false
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H48).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H49).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  2 <= rr_type__linelengthindex__last
***  Proved C1:  2 >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C2:  2 <= rr_type__linelengthindex__last
     using hypotheses H25 & H80.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_36.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  begidx + 2 <= rr_type__linelengthindex__last
***  Proved C1:  begidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H28.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H27:  length <= 256
<S>  New H29:  begidx <= 256
<S>  New H31:  begidx <= 255
<S>  New H34:  begidx + 1 < length -> begidx + 1 >= 
          rr_type__linelengthindex__first and begidx <= 255
<S>  New C2:  begidx <= 254
***  Proved C2:  begidx <= 254
     using hypotheses H27 & H59.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_37.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  false
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  begidx + 2 <= rr_type__linelengthindex__last
***  Proved C1:  begidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H28.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H27:  length <= 256
<S>  New H29:  begidx <= 256
<S>  New H31:  begidx <= 255
<S>  New H34:  begidx + 1 < length -> begidx + 1 >= 
          rr_type__linelengthindex__first and begidx <= 255
<S>  New C2:  begidx <= 254
***  Proved C2:  begidx <= 254
     using hypotheses H27 & H84.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_38.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  endidx + 2 <= rr_type__linelengthindex__last
***  Proved C1:  endidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H30.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H29:  length <= 256
<S>  New H31:  endidx <= 256
<S>  New H33:  endidx <= 255
<S>  New H36:  endidx + 1 < length -> endidx + 1 >= 
          rr_type__linelengthindex__first and endidx <= 255
<S>  New H40:  begidx <= 256
<S>  New C2:  endidx <= 254
***  Proved C2:  endidx <= 254
     using hypotheses H29 & H52.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_39.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H45).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H47).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H48).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  endidx + 2 <= rr_type__linelengthindex__last
***  Proved C1:  endidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H30.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H29:  length <= 256
<S>  New H31:  endidx <= 256
<S>  New H33:  endidx <= 255
<S>  New H36:  endidx + 1 < length -> endidx + 1 >= 
          rr_type__linelengthindex__first and endidx <= 255
<S>  New H40:  begidx <= 256
<S>  New C2:  endidx <= 254
***  Proved C2:  endidx <= 254
     using hypotheses H29 & H77.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_40.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  true
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H54).
***  Proved C1:  endidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H53.
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= 256 -> character__first <= element(s, [i___1]) and 
          element(s, [i___1]) <= character__last)
<S>  New H31:  length <= 256
<S>  New H37:  endidx__entry__loop__3 <= 256
<S>  New H41:  loop__3__i <= 256
<S>  New H52:  begidx <= 256
<S>  New H54:  endidx <= 256
<S>  New C2:  endidx <= 255
***  Proved C2:  endidx <= 255
     using hypotheses H31 & H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_41.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H58 on reading formula in, to give:
     %%%  H58:  2 >= rr_type__linelengthindex__first
%%%  Simplified H59 on reading formula in, to give:
     %%%  H59:  2 <= rr_type__linelengthindex__last
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H59).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  2 <= rr_type__linelengthindex__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  2 <= length
***  Proved C1:  2 >= rr_type__linelengthindex__first
     using hypothesis H58.
***  Proved C2:  2 <= rr_type__linelengthindex__last
     using hypothesis H59.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H24.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H25.
***  Proved C5:  2 <= length
     using hypothesis H55.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_42.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H61 on reading formula in, to give:
     %%%  H61:  1 >= integer__first and 1 <= integer__last
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H67 on reading formula in, to give:
     %%%  H67:  false
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H48).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H49).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  2 >= rr_type__linelengthindex__first
%%%  Simplified H84 on reading formula in, to give:
     %%%  H84:  2 <= rr_type__linelengthindex__last
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H83).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H84).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  2 <= rr_type__linelengthindex__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  2 <= length
***  Proved C1:  2 >= rr_type__linelengthindex__first
     using hypothesis H83.
***  Proved C2:  2 <= rr_type__linelengthindex__last
     using hypothesis H84.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H24.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H25.
***  Proved C5:  2 <= length
     using hypothesis H80.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_43.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H62 on reading formula in, to give:
     %%%  H62:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  begidx + 2 <= rr_type__linelengthindex__last
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H63).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  begidx + 2 <= rr_type__linelengthindex__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  begidx + 2 <= length
***  Proved C1:  begidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H62.
***  Proved C2:  begidx + 2 <= rr_type__linelengthindex__last
     using hypothesis H63.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H27.
***  Proved C5:  begidx + 2 <= length
     using hypothesis H59.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_44.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  false
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H87 on reading formula in, to give:
     %%%  H87:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H88 on reading formula in, to give:
     %%%  H88:  begidx + 2 <= rr_type__linelengthindex__last
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H87).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H88).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  begidx + 2 <= rr_type__linelengthindex__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  begidx + 2 <= length
***  Proved C1:  begidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H87.
***  Proved C2:  begidx + 2 <= rr_type__linelengthindex__last
     using hypothesis H88.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H26.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H27.
***  Proved C5:  begidx + 2 <= length
     using hypothesis H84.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_45.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  endidx + 2 <= rr_type__linelengthindex__last
---  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 
          H56).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  endidx + 2 <= rr_type__linelengthindex__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  endidx + 2 <= length
***  Proved C1:  endidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H55.
***  Proved C2:  endidx + 2 <= rr_type__linelengthindex__last
     using hypothesis H56.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H28.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H29.
***  Proved C5:  endidx + 2 <= length
     using hypothesis H52.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_46.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H45).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H47).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H48).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified H80 on reading formula in, to give:
     %%%  H80:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H81 on reading formula in, to give:
     %%%  H81:  endidx + 2 <= rr_type__linelengthindex__last
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H81).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified C2 on reading formula in, to give:
     %%%  C2:  endidx + 2 <= rr_type__linelengthindex__last
%%%  Simplified C5 on reading formula in, to give:
     %%%  C5:  endidx + 2 <= length
***  Proved C1:  endidx + 2 >= rr_type__linelengthindex__first
     using hypothesis H80.
***  Proved C2:  endidx + 2 <= rr_type__linelengthindex__last
     using hypothesis H81.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H28.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H29.
***  Proved C5:  endidx + 2 <= length
     using hypothesis H77.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_47.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  true
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H54).
---  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).
***  Proved C1:  endidx + 1 >= rr_type__linelengthindex__first
     using hypothesis H66.
***  Proved C2:  endidx + 1 <= rr_type__linelengthindex__last
     using hypothesis H67.
***  Proved C3:  length >= rr_type__linelengthindex__first
     using hypothesis H30.
***  Proved C4:  length <= rr_type__linelengthindex__last
     using hypothesis H31.
-S-  Applied substitution rule addtokeyr_rules(1).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__maxrrsiglength by:
          1365.
<S>  New H6:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
-S-  Applied substitution rule addtokeyr_rules(5).
     This was achieved by replacing all occurrences of integer__first by:
          - 2147483648.
<S>  New H32:  loop__3__i >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(6).
     This was achieved by replacing all occurrences of integer__last by:
          2147483647.
<S>  New H33:  loop__3__i <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(7).
     This was achieved by replacing all occurrences of integer__base__first by:
          - 2147483648.
<S>  New H44:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= - 
          2147483648
<S>  New H46:  loop__3__i - begidx >= - 2147483649
<S>  New H48:  loop__3__i - begidx >= - 2147483648
<S>  New H57:  endidx - begidx >= - 2147483649
<S>  New H59:  endidx - begidx >= - 2147483648
-S-  Applied substitution rule addtokeyr_rules(8).
     This was achieved by replacing all occurrences of integer__base__last by:
          2147483647.
<S>  New H45:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          2147483647
<S>  New H47:  loop__3__i - begidx <= 2147483646
<S>  New H49:  loop__3__i - begidx <= 2147483647
<S>  New H58:  endidx - begidx <= 2147483646
<S>  New H60:  endidx - begidx <= 2147483647
-S-  Applied substitution rule addtokeyr_rules(10).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= character__last)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= character__last)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= character__last)
<S>  New H38:  element(s, [loop__3__i]) >= 0
-S-  Applied substitution rule addtokeyr_rules(11).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H39:  element(s, [loop__3__i]) <= 255
<S>  New H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
<S>  New H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(rrsig_rec), [i___2]) and element(
          fld_signature(rrsig_rec), [i___2]) <= 255)
<S>  New H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> 0 <= element(s, [
          i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H11:  dns_types__a <= fld_typecovered(rrsig_rec)
-S-  Applied substitution rule addtokeyr_rules(22).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H12:  fld_typecovered(rrsig_rec) <= dns_types__unimplemented
-S-  Applied substitution rule addtokeyr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H13:  fld_algorithm(rrsig_rec) >= 0
<S>  New H15:  fld_numlabels(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(79).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H14:  fld_algorithm(rrsig_rec) <= 255
<S>  New H16:  fld_numlabels(rrsig_rec) <= 255
-S-  Applied substitution rule addtokeyr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H23:  fld_keytag(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(85).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H24:  fld_keytag(rrsig_rec) <= 65535
-S-  Applied substitution rule addtokeyr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H7:  fld_ttlinseconds(fld_inherit(rrsig_rec)) >= 0
<S>  New H17:  fld_origttl(rrsig_rec) >= 0
<S>  New H19:  fld_sigexpiration(rrsig_rec) >= 0
<S>  New H21:  fld_siginception(rrsig_rec) >= 0
-S-  Applied substitution rule addtokeyr_rules(91).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H8:  fld_ttlinseconds(fld_inherit(rrsig_rec)) <= 4294967295
<S>  New H18:  fld_origttl(rrsig_rec) <= 4294967295
<S>  New H20:  fld_sigexpiration(rrsig_rec) <= 4294967295
<S>  New H22:  fld_siginception(rrsig_rec) <= 4294967295
-S-  Applied substitution rule addtokeyr_rules(96).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H9:  rr_type__internet <= fld_class(fld_inherit(rrsig_rec))
-S-  Applied substitution rule addtokeyr_rules(97).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H10:  fld_class(fld_inherit(rrsig_rec)) <= rr_type__hs
-S-  Applied substitution rule addtokeyr_rules(164).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__first by:
          1.
<S>  New H30:  length >= 1
<S>  New H36:  endidx__entry__loop__3 >= 1
<S>  New H40:  loop__3__i >= 1
<S>  New H51:  begidx >= 1
<S>  New H53:  endidx >= 1
<S>  New H66:  endidx >= 0
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__linelengthindex__last -> 0 <= element(s, [i___1]) and 
          element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(165).
     This was achieved by replacing all occurrences of 
          rr_type__linelengthindex__last by:
          256.
<S>  New H31:  length <= 256
<S>  New H37:  endidx__entry__loop__3 <= 256
<S>  New H41:  loop__3__i <= 256
<S>  New H52:  begidx <= 256
<S>  New H54:  endidx <= 256
<S>  New H67:  endidx <= 255
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 256 -> 0 <= 
          element(s, [i___1]) and element(s, [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(169).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(rrsig_rec), [i___1]) and element(fld_signername(
          rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(170).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(177).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H42:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) >= 1
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(178).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H43:  fld_signaturelength(rrsig_rec) + (loop__3__i - begidx + 1) <= 
          1365
<S>  New H26:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(rrsig_rec), [i___2]) and element(fld_signature(
          rrsig_rec), [i___2]) <= 255)
-S-  Applied substitution rule addtokeyr_rules(183).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H27:  fld_signaturelength(rrsig_rec) >= 0
<S>  New H55:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 0
-S-  Applied substitution rule addtokeyr_rules(184).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H28:  fld_signaturelength(rrsig_rec) <= 1365
<S>  New H56:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 1365
***  Proved C5:  endidx + 1 <= length
     via its standard form, which is:
     Std.Fm C5:  - endidx + length > 0
     using hypothesis H63.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_48.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H58 on reading formula in, to give:
     %%%  H58:  2 >= rr_type__linelengthindex__first
%%%  Simplified H59 on reading formula in, to give:
     %%%  H59:  2 <= rr_type__linelengthindex__last
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H58).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H59).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H25).
%%%  Simplified H66 on reading formula in, to give:
     %%%  H66:  2 <= length
%%%  Simplified H70 on reading formula in, to give:
     %%%  H70:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H75 on reading formula in, to give:
     %%%  H75:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H75.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H76.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H73.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H74.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H71.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H72.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_49.  @@@@@@@@@@
%%%  Simplified H3 on reading formula in, to give:
     %%%  H3:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H19 on reading formula in, to give:
     %%%  H19:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H28 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H29 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H31 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H33 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H36 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H46 on reading formula in, to give:
     %%%  H46:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H47 on reading formula in, to give:
     %%%  H47:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  1 >= integer__base__first
%%%  Simplified H49 on reading formula in, to give:
     %%%  H49:  1 <= integer__base__last
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  0 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  0 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H57).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H58).
%%%  Simplified H61 on reading formula in, to give:
     %%%  H61:  1 >= integer__first and 1 <= integer__last
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H67 on reading formula in, to give:
     %%%  H67:  false
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H73 on reading formula in, to give:
     %%%  H73:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H48).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H49).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H50).
---  Hypothesis H77 has been replaced by "true".  (It is already present, as 
          H51).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H27).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  2 >= rr_type__linelengthindex__first
%%%  Simplified H84 on reading formula in, to give:
     %%%  H84:  2 <= rr_type__linelengthindex__last
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H83).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H84).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H83).
---  Hypothesis H88 has been replaced by "true".  (It is already present, as 
          H84).
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H24).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H25).
%%%  Simplified H91 on reading formula in, to give:
     %%%  H91:  2 <= length
%%%  Simplified H95 on reading formula in, to give:
     %%%  H95:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H100 on reading formula in, to give:
     %%%  H100:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H100.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H101.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H98.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H99.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H96.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H97.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_50.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H62 on reading formula in, to give:
     %%%  H62:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  begidx + 2 <= rr_type__linelengthindex__last
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H62).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H63).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H70 on reading formula in, to give:
     %%%  H70:  begidx + 2 <= length
%%%  Simplified H74 on reading formula in, to give:
     %%%  H74:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H79 on reading formula in, to give:
     %%%  H79:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H79.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H80.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H77.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H78.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H75.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H76.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_51.  @@@@@@@@@@
%%%  Simplified H5 on reading formula in, to give:
     %%%  H5:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H22 on reading formula in, to give:
     %%%  H22:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  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 H35 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H34).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H47 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H48 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H50 on reading formula in, to give:
     %%%  H50:  fld_signaturelength(rrsig_rec) + 1 >= integer__base__first
%%%  Simplified H51 on reading formula in, to give:
     %%%  H51:  fld_signaturelength(rrsig_rec) + 1 <= integer__base__last
%%%  Simplified H52 on reading formula in, to give:
     %%%  H52:  1 >= integer__base__first
%%%  Simplified H53 on reading formula in, to give:
     %%%  H53:  1 <= integer__base__last
%%%  Simplified H54 on reading formula in, to give:
     %%%  H54:  0 >= integer__base__first
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  0 <= integer__base__last
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  not fld_signaturelength(rrsig_rec) + 1 > 
          rr_type__rrsig_record_type__maxrrsiglength
---  Hypothesis H57 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H58 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H61).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H62).
%%%  Simplified H65 on reading formula in, to give:
     %%%  H65:  begidx + 1 >= integer__first and begidx + 1 <= integer__last
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H65).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H69 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H70 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H71 on reading formula in, to give:
     %%%  H71:  false
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H76 on reading formula in, to give:
     %%%  H76:  fld_signaturelength(rrsig_rec) + 1 >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H77 on reading formula in, to give:
     %%%  H77:  fld_signaturelength(rrsig_rec) + 1 <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H52).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H80 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H81 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H31).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H87 on reading formula in, to give:
     %%%  H87:  begidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H88 on reading formula in, to give:
     %%%  H88:  begidx + 2 <= rr_type__linelengthindex__last
---  Hypothesis H89 has been replaced by "true".  (It is already present, as 
          H87).
---  Hypothesis H90 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H91 has been replaced by "true".  (It is already present, as 
          H87).
---  Hypothesis H92 has been replaced by "true".  (It is already present, as 
          H88).
---  Hypothesis H93 has been replaced by "true".  (It is already present, as 
          H26).
---  Hypothesis H94 has been replaced by "true".  (It is already present, as 
          H27).
%%%  Simplified H95 on reading formula in, to give:
     %%%  H95:  begidx + 2 <= length
%%%  Simplified H99 on reading formula in, to give:
     %%%  H99:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H104 on reading formula in, to give:
     %%%  H104:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H104.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H105.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H102.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H103.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H100.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H101.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_52.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  endidx + 2 <= rr_type__linelengthindex__last
---  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 
          H56).
---  Hypothesis H59 has been replaced by "true".  (It is already present, as 
          H55).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H56).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H29).
%%%  Simplified H63 on reading formula in, to give:
     %%%  H63:  endidx + 2 <= length
%%%  Simplified H67 on reading formula in, to give:
     %%%  H67:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H72 on reading formula in, to give:
     %%%  H72:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H72.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H73.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H70.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H71.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H68.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H69.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_53.  @@@@@@@@@@
%%%  Simplified H7 on reading formula in, to give:
     %%%  H7:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H23 on reading formula in, to give:
     %%%  H23:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H35 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H37 has been replaced by "true".  (It is already present, as 
          H36).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H60 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H63 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H66 has been replaced by "true".  (It is already present, as 
          H40).
---  Hypothesis H67 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H68 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H45).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H46).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H47).
---  Hypothesis H74 has been replaced by "true".  (It is already present, as 
          H48).
---  Hypothesis H75 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H76 has been replaced by "true".  (It is already present, as 
          H33).
---  Hypothesis H78 has been replaced by "true".  (It is already present, as 
          H32).
---  Hypothesis H79 has been replaced by "true".  (It is already present, as 
          H33).
%%%  Simplified H80 on reading formula in, to give:
     %%%  H80:  endidx + 2 >= rr_type__linelengthindex__first
%%%  Simplified H81 on reading formula in, to give:
     %%%  H81:  endidx + 2 <= rr_type__linelengthindex__last
---  Hypothesis H82 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H83 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H84 has been replaced by "true".  (It is already present, as 
          H80).
---  Hypothesis H85 has been replaced by "true".  (It is already present, as 
          H81).
---  Hypothesis H86 has been replaced by "true".  (It is already present, as 
          H28).
---  Hypothesis H87 has been replaced by "true".  (It is already present, as 
          H29).
%%%  Simplified H88 on reading formula in, to give:
     %%%  H88:  endidx + 2 <= length
%%%  Simplified H92 on reading formula in, to give:
     %%%  H92:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H97 on reading formula in, to give:
     %%%  H97:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H97.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H98.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H95.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H96.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H93.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H94.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_54.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  true
%%%  Simplified H9 on reading formula in, to give:
     %%%  H9:  rr_type__classtype__first <= fld_class(fld_inherit(rrsig_rec))
%%%  Simplified H11 on reading formula in, to give:
     %%%  H11:  dns_types__query_type__first <= fld_typecovered(rrsig_rec)
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(rrsig_rec), [i___1]) and element(
          fld_signername(rrsig_rec), [i___1]) <= character__last)
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___2 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___2 and 
          i___2 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(rrsig_rec), [i___2]) and 
          element(fld_signature(rrsig_rec), [i___2]) <= character__last)
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__linelengthindex__first <= 
          i___1 and i___1 <= rr_type__linelengthindex__last -> character__first 
          <= element(s, [i___1]) and element(s, [i___1]) <= character__last)
---  Hypothesis H34 has been replaced by "true".  (It is already present, as H3)
          .
%%%  Simplified H55 on reading formula in, to give:
     %%%  H55:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
%%%  Simplified H56 on reading formula in, to give:
     %%%  H56:  fld_signaturelength(rrsig_rec) + (endidx - begidx + 1) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
---  Hypothesis H61 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H62 has been replaced by "true".  (It is already present, as 
          H54).
---  Hypothesis H64 has been replaced by "true".  (It is already present, as 
          H53).
---  Hypothesis H65 has been replaced by "true".  (It is already present, as 
          H54).
---  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 
          H66).
---  Hypothesis H71 has been replaced by "true".  (It is already present, as 
          H67).
---  Hypothesis H72 has been replaced by "true".  (It is already present, as 
          H30).
---  Hypothesis H73 has been replaced by "true".  (It is already present, as 
          H31).
%%%  Simplified H78 on reading formula in, to give:
     %%%  H78:  returnedtype__1 = rr_type__number -> for_all(i_ : integer, 
          begidx__1 <= i_ and i_ <= endidx__1 -> 48 <= element(s, [i_]) and 
          element(s, [i_]) <= 57)
%%%  Simplified H83 on reading formula in, to give:
     %%%  H83:  rr_type__rritemtype__first <= returnedtype__1
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  rr_type__rritemtype__first <= returnedtype__1
***  Proved C1:  rr_type__rritemtype__first <= returnedtype__1
     using hypothesis H83.
***  Proved C2:  returnedtype__1 <= rr_type__rritemtype__last
     using hypothesis H84.
***  Proved C3:  endidx__1 >= rr_type__linelengthindex__first
     using hypothesis H81.
***  Proved C4:  endidx__1 <= rr_type__linelengthindex__last
     using hypothesis H82.
***  Proved C5:  begidx__1 >= rr_type__linelengthindex__first
     using hypothesis H79.
***  Proved C6:  begidx__1 <= rr_type__linelengthindex__last
     using hypothesis H80.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_55.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_56.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_57.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_58.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_59.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_60.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_61.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_62.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_63.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_64.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_65.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_66.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_67.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_68.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_69.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_70.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_71.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_72.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_73.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_74.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_addtokeyr_75.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.

