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

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



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

procedure dns_table_pkg.DNS_Table_Type.InsertRRSIGRecord






@@@@@@@@@@  VC: procedure_insertrrsigrecord_1.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
%%%  Simplified H37 on reading formula in, to give:
     %%%  H37:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(to_lower(key), [i___1]) and element(
          to_lower(key), [i___1]) <= character__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H37).
***  Proved C1:  hash(to_lower(key)) >= rr_type__numbucketsindextype__first
     using hypothesis H39.
***  Proved C2:  hash(to_lower(key)) <= rr_type__numbucketsindextype__last
     using hypothesis H40.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_2.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
%%%  Simplified H37 on reading formula in, to give:
     %%%  H37:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(to_lower(key), [i___1]) and element(
          to_lower(key), [i___1]) <= character__last)
---  Hypothesis H38 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H41 has been replaced by "true".  (It is already present, as 
          H39).
---  Hypothesis H42 has been replaced by "true".  (It is already present, as 
          H40).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified C20 on reading formula in, to give:
     %%%  C20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified C21 on reading formula in, to give:
     %%%  C21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified C28 on reading formula in, to give:
     %%%  C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified C30 on reading formula in, to give:
     %%%  C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C31 on reading formula in, to give:
     %%%  C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C32 on reading formula in, to give:
     %%%  C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified C33 on reading formula in, to give:
     %%%  C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified C36 on reading formula in, to give:
     %%%  C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
%%%  Simplified C37 on reading formula in, to give:
     %%%  C37:  true
%%%  Simplified C39 on reading formula in, to give:
     %%%  C39:  true
***  Proved C1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
     using hypothesis H1.
***  Proved C2:  fld_ttlinseconds(fld_inherit(therecord)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H2.
***  Proved C3:  fld_ttlinseconds(fld_inherit(therecord)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H3.
***  Proved C4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
     using hypothesis H4.
***  Proved C5:  fld_class(fld_inherit(therecord)) <= rr_type__classtype__last
     using hypothesis H5.
***  Proved C6:  dns_types__query_type__first <= fld_typecovered(therecord)
     using hypothesis H6.
***  Proved C7:  fld_typecovered(therecord) <= dns_types__query_type__last
     using hypothesis H7.
***  Proved C8:  fld_algorithm(therecord) >= unsigned_types__unsigned8__first
     using hypothesis H8.
***  Proved C9:  fld_algorithm(therecord) <= unsigned_types__unsigned8__last
     using hypothesis H9.
***  Proved C10:  fld_numlabels(therecord) >= unsigned_types__unsigned8__first
     using hypothesis H10.
***  Proved C11:  fld_numlabels(therecord) <= unsigned_types__unsigned8__last
     using hypothesis H11.
***  Proved C12:  fld_origttl(therecord) >= unsigned_types__unsigned32__first
     using hypothesis H12.
***  Proved C13:  fld_origttl(therecord) <= unsigned_types__unsigned32__last
     using hypothesis H13.
***  Proved C14:  fld_sigexpiration(therecord) >= 
          unsigned_types__unsigned32__first
     using hypothesis H14.
***  Proved C15:  fld_sigexpiration(therecord) <= 
          unsigned_types__unsigned32__last
     using hypothesis H15.
***  Proved C16:  fld_siginception(therecord) >= 
          unsigned_types__unsigned32__first
     using hypothesis H16.
***  Proved C17:  fld_siginception(therecord) <= 
          unsigned_types__unsigned32__last
     using hypothesis H17.
***  Proved C18:  fld_keytag(therecord) >= unsigned_types__unsigned16__first
     using hypothesis H18.
***  Proved C19:  fld_keytag(therecord) <= unsigned_types__unsigned16__last
     using hypothesis H19.
***  Proved C20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
     using hypothesis H20.
***  Proved C21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
     using hypothesis H21.
***  Proved C22:  fld_signaturelength(therecord) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H22.
***  Proved C23:  fld_signaturelength(therecord) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H23.
***  Proved C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
     using hypothesis H24.
***  Proved C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
     using hypothesis H25.
***  Proved C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
     using hypothesis H26.
***  Proved C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
     using hypothesis H27.
***  Proved C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
     using hypothesis H28.
***  Proved C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
     using hypothesis H29.
***  Proved C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
     using hypothesis H30.
***  Proved C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
     using hypothesis H31.
***  Proved C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
     using hypothesis H32.
***  Proved C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
     using hypothesis H33.
***  Proved C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
     using hypothesis H34.
***  Proved C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
     using hypothesis H35.
***  Proved C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
     using hypothesis H36.
***  Proved C37:  true
***  Proved C39:  true
-S-  Applied substitution rule insertrrsigr_rules(136).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> rr_type__classtype__first 
          <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
<S>  New H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__returnedrecordsindextype__last -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
<S>  New C38:  1 <= rr_type__returnedrecordsindextype__last
<S>  New C40:  1 <= rr_type__returnedrecordsindextype__last
-S-  Applied substitution rule insertrrsigr_rules(137).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, rr_type__domainnamestringtypeindex__first <= i___3 and i___3 
          <= rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
<S>  New H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
<S>  New C38:  true
<S>  New C40:  true
***  Proved C38:  true
***  Proved C40:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_3.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H42).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(lower_key, [i___1]) and element(
          lower_key, [i___1]) <= character__last)
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H42).
---  Hypothesis H53 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H54 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H55 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H56 has been replaced by "true".  (It is already present, as 
          H42).
%%%  Simplified H58 on reading formula in, to give:
     %%%  H58:  false
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified C20 on reading formula in, to give:
     %%%  C20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified C21 on reading formula in, to give:
     %%%  C21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) <= rr_type__classtype__last))
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified C28 on reading formula in, to give:
     %%%  C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C30 on reading formula in, to give:
     %%%  C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) and fld_sigexpiration(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C31 on reading formula in, to give:
     %%%  C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C32 on reading formula in, to give:
     %%%  C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned16__last))
%%%  Simplified C33 on reading formula in, to give:
     %%%  C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= character__last)))
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= character__last)))
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified C36 on reading formula in, to give:
     %%%  C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(update(dns_table_type__rrsigrecordkeys, [bucket], 
          update(element(dns_table_type__rrsigrecordkeys, [bucket]), [
          loop__1__i], lower_key)), [i___1]), [i___2]), [i___3]) and element(
          element(element(update(dns_table_type__rrsigrecordkeys, [bucket], 
          update(element(dns_table_type__rrsigrecordkeys, [bucket]), [
          loop__1__i], lower_key)), [i___1]), [i___2]), [i___3]) <= 
          character__last)))
***  Proved C1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
     using hypothesis H1.
***  Proved C2:  fld_ttlinseconds(fld_inherit(therecord)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H2.
***  Proved C3:  fld_ttlinseconds(fld_inherit(therecord)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H3.
***  Proved C4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
     using hypothesis H4.
***  Proved C5:  fld_class(fld_inherit(therecord)) <= rr_type__classtype__last
     using hypothesis H5.
***  Proved C6:  dns_types__query_type__first <= fld_typecovered(therecord)
     using hypothesis H6.
***  Proved C7:  fld_typecovered(therecord) <= dns_types__query_type__last
     using hypothesis H7.
***  Proved C8:  fld_algorithm(therecord) >= unsigned_types__unsigned8__first
     using hypothesis H8.
***  Proved C9:  fld_algorithm(therecord) <= unsigned_types__unsigned8__last
     using hypothesis H9.
***  Proved C10:  fld_numlabels(therecord) >= unsigned_types__unsigned8__first
     using hypothesis H10.
***  Proved C11:  fld_numlabels(therecord) <= unsigned_types__unsigned8__last
     using hypothesis H11.
***  Proved C12:  fld_origttl(therecord) >= unsigned_types__unsigned32__first
     using hypothesis H12.
***  Proved C13:  fld_origttl(therecord) <= unsigned_types__unsigned32__last
     using hypothesis H13.
***  Proved C14:  fld_sigexpiration(therecord) >= 
          unsigned_types__unsigned32__first
     using hypothesis H14.
***  Proved C15:  fld_sigexpiration(therecord) <= 
          unsigned_types__unsigned32__last
     using hypothesis H15.
***  Proved C16:  fld_siginception(therecord) >= 
          unsigned_types__unsigned32__first
     using hypothesis H16.
***  Proved C17:  fld_siginception(therecord) <= 
          unsigned_types__unsigned32__last
     using hypothesis H17.
***  Proved C18:  fld_keytag(therecord) >= unsigned_types__unsigned16__first
     using hypothesis H18.
***  Proved C19:  fld_keytag(therecord) <= unsigned_types__unsigned16__last
     using hypothesis H19.
***  Proved C20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
     using hypothesis H20.
***  Proved C21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
     using hypothesis H21.
***  Proved C22:  fld_signaturelength(therecord) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H22.
***  Proved C23:  fld_signaturelength(therecord) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H23.
***  Proved C37:  loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
***  Proved C39:  loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
-S-  Applied substitution rule insertrrsigr_rules(137).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__classtype__first <= fld_class(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          rr_type__classtype__last))
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__query_type__first <= fld_typecovered(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_typecovered(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) <= dns_types__query_type__last))
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned8__first <= fld_algorithm(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned8__first <= fld_numlabels(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_origttl(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) and fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          unsigned_types__unsigned32__last))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) and fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          unsigned_types__unsigned32__last))
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned16__first <= fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_keytag(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned16__last))
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
<S>  New H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
<S>  New H38:  loop__1__i <= 64
<S>  New H59:  not loop__1__i = 64
<S>  New C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_ttlinseconds(fld_inherit(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) <= unsigned_types__unsigned32__last)
          )
<S>  New C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__classtype__first <= fld_class(fld_inherit(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) <= 
          rr_type__classtype__last))
<S>  New C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__query_type__first <= fld_typecovered(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_typecovered(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 
          dns_types__query_type__last))
<S>  New C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned8__first <= fld_algorithm(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_algorithm(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 
          unsigned_types__unsigned8__last))
<S>  New C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned8__first <= fld_numlabels(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_numlabels(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 
          unsigned_types__unsigned8__last))
<S>  New C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= fld_origttl(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_origttl(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned16__first <= fld_keytag(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_keytag(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= unsigned_types__unsigned16__last))
<S>  New C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= character__last)))
<S>  New C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= character__last)))
<S>  New C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(update(dns_table_type__rrsigrecordkeys, [bucket], 
          update(element(dns_table_type__rrsigrecordkeys, [bucket]), [
          loop__1__i], lower_key)), [i___1]), [i___2]), [i___3]) and element(
          element(element(update(dns_table_type__rrsigrecordkeys, [bucket], 
          update(element(dns_table_type__rrsigrecordkeys, [bucket]), [
          loop__1__i], lower_key)), [i___1]), [i___2]), [i___3]) <= 
          character__last)))
<S>  New C38:  loop__1__i <= 63
<S>  New C40:  loop__1__i <= 63
***  Proved C38:  loop__1__i <= 63
     using hypotheses H38 & H59.
***  Proved C40:  loop__1__i <= 63
     using hypotheses H38 & H59.
>>>  Restructured hypothesis H59 into:
     >>>  H59:  loop__1__i <> 64
-S-  Applied substitution rule insertrrsigr_rules(9).
     This was achieved by replacing all occurrences of character__first by:
          0.
<S>  New H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          key, [i___1]) and element(key, [i___1]) <= character__last)
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(therecord), [i___1]) and element(fld_signername(
          therecord), [i___1]) <= character__last)
<S>  New H21:  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(therecord), [i___2]) and element(
          fld_signature(therecord), [i___2]) <= character__last)
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]
          ) <= character__last)))
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) and 
          element(element(element(dns_table_type__rrsigrecordkeys, [i___1]), [
          i___2]), [i___3]) <= character__last)))
<S>  New H48:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          lower_key, [i___1]) and element(lower_key, [i___1]) <= 
          character__last)
<S>  New C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= character__last)))
<S>  New C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= character__last)))
<S>  New C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(element(element(
          update(dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= character__last)))
-S-  Applied substitution rule insertrrsigr_rules(10).
     This was achieved by replacing all occurrences of character__last by:
          255.
<S>  New H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          key, [i___1]) and element(key, [i___1]) <= 255)
<S>  New H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(therecord), [i___1]) and element(fld_signername(
          therecord), [i___1]) <= 255)
<S>  New H21:  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(therecord), [i___2]) and element(
          fld_signature(therecord), [i___2]) <= 255)
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]
          ) <= 255)))
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          255)))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) and 
          element(element(element(dns_table_type__rrsigrecordkeys, [i___1]), [
          i___2]), [i___3]) <= 255)))
<S>  New H48:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
          lower_key, [i___1]) and element(lower_key, [i___1]) <= 255)
<S>  New C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S>  New C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= 255)))
<S>  New C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(element(element(
          update(dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(20).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__first by:
          dns_types__a.
<S>  New H6:  dns_types__a <= fld_typecovered(therecord)
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__a <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
<S>  New C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__a <= fld_typecovered(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= dns_types__query_type__last))
-S-  Applied substitution rule insertrrsigr_rules(21).
     This was achieved by replacing all occurrences of 
          dns_types__query_type__last by:
          dns_types__unimplemented.
<S>  New H7:  fld_typecovered(therecord) <= dns_types__unimplemented
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__a <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__unimplemented))
<S>  New C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__a <= fld_typecovered(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= dns_types__unimplemented))
-S-  Applied substitution rule insertrrsigr_rules(77).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__first by:
          0.
<S>  New H8:  fld_algorithm(therecord) >= 0
<S>  New H10:  fld_numlabels(therecord) >= 0
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned8__last))
-S-  Applied substitution rule insertrrsigr_rules(78).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned8__last by:
          255.
<S>  New H9:  fld_algorithm(therecord) <= 255
<S>  New H11:  fld_numlabels(therecord) <= 255
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 255))
<S>  New C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 255))
-S-  Applied substitution rule insertrrsigr_rules(83).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__first by:
          0.
<S>  New H18:  fld_keytag(therecord) >= 0
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
<S>  New C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned16__last))
-S-  Applied substitution rule insertrrsigr_rules(84).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned16__last by:
          65535.
<S>  New H19:  fld_keytag(therecord) <= 65535
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= 65535))
<S>  New C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 65535))
-S-  Applied substitution rule insertrrsigr_rules(89).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__first by:
          0.
<S>  New H2:  fld_ttlinseconds(fld_inherit(therecord)) >= 0
<S>  New H12:  fld_origttl(therecord) >= 0
<S>  New H14:  fld_sigexpiration(therecord) >= 0
<S>  New H16:  fld_siginception(therecord) >= 0
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_ttlinseconds(fld_inherit(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) <= unsigned_types__unsigned32__last)
          )
<S>  New C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= unsigned_types__unsigned32__last))
-S-  Applied substitution rule insertrrsigr_rules(90).
     This was achieved by replacing all occurrences of 
          unsigned_types__unsigned32__last by:
          4294967295.
<S>  New H3:  fld_ttlinseconds(fld_inherit(therecord)) <= 4294967295
<S>  New H13:  fld_origttl(therecord) <= 4294967295
<S>  New H15:  fld_sigexpiration(therecord) <= 4294967295
<S>  New H17:  fld_siginception(therecord) <= 4294967295
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= 4294967295))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 4294967295))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 4294967295))
<S>  New C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_ttlinseconds(fld_inherit(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) <= 4294967295))
<S>  New C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 4294967295))
<S>  New C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 4294967295))
<S>  New C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 0 <= fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 4294967295))
-S-  Applied substitution rule insertrrsigr_rules(95).
     This was achieved by replacing all occurrences of 
          rr_type__classtype__first by:
          rr_type__internet.
<S>  New H4:  rr_type__internet <= fld_class(fld_inherit(therecord))
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__internet <= fld_class(fld_inherit(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          rr_type__classtype__last))
<S>  New C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__internet <= fld_class(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) and fld_class(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) <= rr_type__classtype__last))
-S-  Applied substitution rule insertrrsigr_rules(96).
     This was achieved by replacing all occurrences of rr_type__classtype__last 
          by:
          rr_type__hs.
<S>  New H5:  fld_class(fld_inherit(therecord)) <= rr_type__hs
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__internet <= fld_class(fld_inherit(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= rr_type__hs)
          )
<S>  New C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__internet <= fld_class(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) and fld_class(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) <= rr_type__hs))
-S-  Applied substitution rule insertrrsigr_rules(122).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__first by:
          1.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(therecord), [i___1]) and element(fld_signername(
          therecord), [i___1]) <= 255)
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]
          ) <= 255)))
<S>  New C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> 0 <= element(
          fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(123).
     This was achieved by replacing all occurrences of 
          rr_type__domainnamestringtypeindex__last by:
          128.
<S>  New H20:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 128 -> 0 <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= 255)
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          128 -> 0 <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          255)))
<S>  New C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          128 -> 0 <= element(fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(128).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__first by:
          1.
<S>  New H1:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(key, [i___1]) and 
          element(key, [i___1]) <= 255)
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) and 
          element(element(element(dns_table_type__rrsigrecordkeys, [i___1]), [
          i___2]), [i___3]) <= 255)))
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(lower_key, [i___1])
           and element(lower_key, [i___1]) <= 255)
<S>  New C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> 0 <= element(element(element(
          update(dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(129).
     This was achieved by replacing all occurrences of 
          rr_type__wirestringtypeindex__last by:
          129.
<S>  New H1:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(key, [i___1]) and element(key, [i___1]) <= 255)
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          129 -> 0 <= element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) and element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) <= 255))
          )
<S>  New H48:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <= 
          element(lower_key, [i___1]) and element(lower_key, [i___1]) <= 255)
<S>  New C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and i___3 <= 
          129 -> 0 <= element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(136).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__first by:
          1.
<S>  New H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H37:  loop__1__i >= 1
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          255)))
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> dns_types__a <= 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) and fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          dns_types__unimplemented))
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_algorithm(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_numlabels(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_keytag(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 65535))
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_ttlinseconds(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_origttl(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 4294967295))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_sigexpiration(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 4294967295))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_siginception(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 4294967295))
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> rr_type__internet <= 
          fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__hs))
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 128 -> 0 <= element(fld_signername(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2]))
          , [i___3]) and element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          255)))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) and 
          element(element(element(dns_table_type__rrsigrecordkeys, [i___1]), [
          i___2]), [i___3]) <= 255)))
<S>  New C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= 255)))
<S>  New C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> dns_types__a <= 
          fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= dns_types__unimplemented))
<S>  New C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_algorithm(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_algorithm(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 255))
<S>  New C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_numlabels(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_numlabels(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 255))
<S>  New C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_keytag(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_keytag(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= 65535))
<S>  New C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_ttlinseconds(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) <= 4294967295))
<S>  New C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_origttl(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_origttl(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= 4294967295))
<S>  New C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_sigexpiration(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_sigexpiration(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 4294967295))
<S>  New C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_siginception(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_siginception(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 4294967295))
<S>  New C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> rr_type__internet <= 
          fld_class(fld_inherit(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) <= rr_type__hs))
<S>  New C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 128 -> 0 <= element(fld_signername(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) and element(
          fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) <= 255)))
<S>  New C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(element(element(
          update(dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(141).
     This was achieved by replacing all occurrences of 
          rr_type__numbucketsindextype__first by:
          1.
<S>  New H41:  bucket >= 1
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          255)))
<S>  New H26:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> dns_types__a <= fld_typecovered(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__unimplemented))
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= 65535))
<S>  New H24:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_ttlinseconds(fld_inherit(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= 4294967295))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 4294967295))
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 4294967295))
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> rr_type__internet <= fld_class(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= rr_type__hs)
          )
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and 
          i___3 <= 128 -> 0 <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          255)))
<S>  New H36:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and 
          i___3 <= 129 -> 0 <= element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) and 
          element(element(element(dns_table_type__rrsigrecordkeys, [i___1]), [
          i___2]), [i___3]) <= 255)))
<S>  New C35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New C34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 
          <= element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= 255)))
<S>  New C26:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> dns_types__a <= fld_typecovered(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) and fld_typecovered(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= dns_types__unimplemented))
<S>  New C27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_algorithm(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 255))
<S>  New C28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_numlabels(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 255))
<S>  New C32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_keytag(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 65535))
<S>  New C24:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_ttlinseconds(fld_inherit(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) <= 4294967295))
<S>  New C29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_origttl(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 4294967295))
<S>  New C30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_sigexpiration(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_sigexpiration(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 4294967295))
<S>  New C31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> 0 <= fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_siginception(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 4294967295))
<S>  New C25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> rr_type__internet <= fld_class(fld_inherit(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) <= rr_type__hs))
<S>  New C33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and 
          i___3 <= 128 -> 0 <= element(fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) and element(fld_signername(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S>  New C36:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 
          rr_type__numbucketsindextype__last -> for_all(i___2 : integer, 1 <= 
          i___2 and i___2 <= 64 -> for_all(i___3 : integer, 1 <= i___3 and 
          i___3 <= 129 -> 0 <= element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(142).
     This was achieved by replacing all occurrences of 
          rr_type__numbucketsindextype__last by:
          64.
<S>  New H42:  bucket <= 64
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          255)))
<S>  New H26:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> dns_types__a <= 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) and fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          dns_types__unimplemented))
<S>  New H27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_algorithm(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_numlabels(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 255))
<S>  New H32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_keytag(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 65535))
<S>  New H24:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_ttlinseconds(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S>  New H29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_origttl(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= 4294967295))
<S>  New H30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_sigexpiration(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 4294967295))
<S>  New H31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_siginception(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 4294967295))
<S>  New H25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> rr_type__internet <= 
          fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__hs))
<S>  New H33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 128 -> 0 <= element(fld_signername(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2]))
          , [i___3]) and element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          255)))
<S>  New H36:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(element(element(
          dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [i___3]) and 
          element(element(element(dns_table_type__rrsigrecordkeys, [i___1]), [
          i___2]), [i___3]) <= 255)))
<S>  New C35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New C34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= 255)))
<S>  New C26:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> dns_types__a <= 
          fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_typecovered(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= dns_types__unimplemented))
<S>  New C27:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_algorithm(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_algorithm(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 255))
<S>  New C28:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_numlabels(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_numlabels(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 255))
<S>  New C32:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_keytag(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_keytag(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= 65535))
<S>  New C24:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_ttlinseconds(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(
          fld_inherit(element(element(update(dns_table_type__rrsigrecordtable, [
          bucket], update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2]))) <= 4294967295))
<S>  New C29:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_origttl(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_origttl(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])) <= 4294967295))
<S>  New C30:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_sigexpiration(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_sigexpiration(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 4294967295))
<S>  New C31:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= fld_siginception(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) and fld_siginception(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])) <= 4294967295))
<S>  New C25:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> rr_type__internet <= 
          fld_class(fld_inherit(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
          update(dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2]))) <= rr_type__hs))
<S>  New C33:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 128 -> 0 <= element(fld_signername(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) and element(
          fld_signername(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___3]) <= 255)))
<S>  New C36:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___3 : 
          integer, 1 <= i___3 and i___3 <= 129 -> 0 <= element(element(element(
          update(dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) and element(element(element(update(
          dns_table_type__rrsigrecordkeys, [bucket], update(element(
          dns_table_type__rrsigrecordkeys, [bucket]), [loop__1__i], lower_key))
          , [i___1]), [i___2]), [i___3]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(146).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first by:
          1.
<S>  New H21:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(therecord), [i___2]) and element(fld_signature(
          therecord), [i___2]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, 1 <= i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          255)))
<S>  New C34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, 1 <= i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 0 <= 
          element(fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) and element(fld_signature(element(
          element(update(dns_table_type__rrsigrecordtable, [bucket], update(
          element(dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], 
          therecord)), [i___1]), [i___2])), [i___4]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(147).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last by:
          1365.
<S>  New H21:  for_all(i___2 : integer, 1 <= i___2 and i___2 <= 1365 -> 0 <= 
          element(fld_signature(therecord), [i___2]) and element(fld_signature(
          therecord), [i___2]) <= 255)
<S>  New H34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, 1 <= i___4 and i___4 <= 1365 -> 0 <= element(fld_signature(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2]))
          , [i___4]) and element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          255)))
<S>  New C34:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___4 : 
          integer, 1 <= i___4 and i___4 <= 1365 -> 0 <= element(fld_signature(
          element(element(update(dns_table_type__rrsigrecordtable, [bucket], 
          update(element(dns_table_type__rrsigrecordtable, [bucket]), [
          loop__1__i], therecord)), [i___1]), [i___2])), [i___4]) and element(
          fld_signature(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])), [i___4]) <= 255)))
-S-  Applied substitution rule insertrrsigr_rules(152).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__first by:
          0.
<S>  New H22:  fld_signaturelength(therecord) >= 0
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New C35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
-S-  Applied substitution rule insertrrsigr_rules(153).
     This was achieved by replacing all occurrences of 
          rr_type__rrsig_record_type__siglengthvaluetype__last by:
          1365.
<S>  New H23:  fld_signaturelength(therecord) <= 1365
<S>  New H35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 1365))
<S>  New C35:  for_all(i___1 : integer, 1 <= i___1 and i___1 <= 64 -> for_all(
          i___2 : integer, 1 <= i___2 and i___2 <= 64 -> 0 <= 
          fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) and fld_signaturelength(element(element(update(
          dns_table_type__rrsigrecordtable, [bucket], update(element(
          dns_table_type__rrsigrecordtable, [bucket]), [loop__1__i], therecord))
          , [i___1]), [i___2])) <= 1365))
%%%  Hypotheses H38 & H59 together imply that
          loop__1__i < 64.
     H38 & H59 have therefore been deleted and a new H60 added to this effect.
###  Established a contradiction [false-hypothesis] using hypothesis H58.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_4.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H42).
%%%  Simplified C1 on reading formula in, to give:
     %%%  C1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified C4 on reading formula in, to give:
     %%%  C4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified C6 on reading formula in, to give:
     %%%  C6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified C20 on reading formula in, to give:
     %%%  C20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified C21 on reading formula in, to give:
     %%%  C21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified C24 on reading formula in, to give:
     %%%  C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified C25 on reading formula in, to give:
     %%%  C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified C26 on reading formula in, to give:
     %%%  C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified C27 on reading formula in, to give:
     %%%  C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified C28 on reading formula in, to give:
     %%%  C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified C29 on reading formula in, to give:
     %%%  C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified C30 on reading formula in, to give:
     %%%  C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C31 on reading formula in, to give:
     %%%  C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified C32 on reading formula in, to give:
     %%%  C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified C33 on reading formula in, to give:
     %%%  C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified C34 on reading formula in, to give:
     %%%  C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified C35 on reading formula in, to give:
     %%%  C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified C36 on reading formula in, to give:
     %%%  C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
***  Proved C1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first 
          <= i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
     using hypothesis H1.
***  Proved C2:  fld_ttlinseconds(fld_inherit(therecord)) >= 
          unsigned_types__unsigned32__first
     using hypothesis H2.
***  Proved C3:  fld_ttlinseconds(fld_inherit(therecord)) <= 
          unsigned_types__unsigned32__last
     using hypothesis H3.
***  Proved C4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
     using hypothesis H4.
***  Proved C5:  fld_class(fld_inherit(therecord)) <= rr_type__classtype__last
     using hypothesis H5.
***  Proved C6:  dns_types__query_type__first <= fld_typecovered(therecord)
     using hypothesis H6.
***  Proved C7:  fld_typecovered(therecord) <= dns_types__query_type__last
     using hypothesis H7.
***  Proved C8:  fld_algorithm(therecord) >= unsigned_types__unsigned8__first
     using hypothesis H8.
***  Proved C9:  fld_algorithm(therecord) <= unsigned_types__unsigned8__last
     using hypothesis H9.
***  Proved C10:  fld_numlabels(therecord) >= unsigned_types__unsigned8__first
     using hypothesis H10.
***  Proved C11:  fld_numlabels(therecord) <= unsigned_types__unsigned8__last
     using hypothesis H11.
***  Proved C12:  fld_origttl(therecord) >= unsigned_types__unsigned32__first
     using hypothesis H12.
***  Proved C13:  fld_origttl(therecord) <= unsigned_types__unsigned32__last
     using hypothesis H13.
***  Proved C14:  fld_sigexpiration(therecord) >= 
          unsigned_types__unsigned32__first
     using hypothesis H14.
***  Proved C15:  fld_sigexpiration(therecord) <= 
          unsigned_types__unsigned32__last
     using hypothesis H15.
***  Proved C16:  fld_siginception(therecord) >= 
          unsigned_types__unsigned32__first
     using hypothesis H16.
***  Proved C17:  fld_siginception(therecord) <= 
          unsigned_types__unsigned32__last
     using hypothesis H17.
***  Proved C18:  fld_keytag(therecord) >= unsigned_types__unsigned16__first
     using hypothesis H18.
***  Proved C19:  fld_keytag(therecord) <= unsigned_types__unsigned16__last
     using hypothesis H19.
***  Proved C20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
     using hypothesis H20.
***  Proved C21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
     using hypothesis H21.
***  Proved C22:  fld_signaturelength(therecord) >= 
          rr_type__rrsig_record_type__siglengthvaluetype__first
     using hypothesis H22.
***  Proved C23:  fld_signaturelength(therecord) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last
     using hypothesis H23.
***  Proved C24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
     using hypothesis H24.
***  Proved C25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
     using hypothesis H25.
***  Proved C26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
     using hypothesis H26.
***  Proved C27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
     using hypothesis H27.
***  Proved C28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
     using hypothesis H28.
***  Proved C29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
     using hypothesis H29.
***  Proved C30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
     using hypothesis H30.
***  Proved C31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
     using hypothesis H31.
***  Proved C32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
     using hypothesis H32.
***  Proved C33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
     using hypothesis H33.
***  Proved C34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
     using hypothesis H34.
***  Proved C35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
     using hypothesis H35.
***  Proved C36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first 
          <= i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
     using hypothesis H36.
***  Proved C37:  loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
***  Proved C39:  loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
-S-  Applied substitution rule insertrrsigr_rules(137).
     This was achieved by replacing all occurrences of 
          rr_type__returnedrecordsindextype__last by:
          64.
<S>  New H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and 
          fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
<S>  New H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> rr_type__classtype__first <= fld_class(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          rr_type__classtype__last))
<S>  New H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> dns_types__query_type__first <= fld_typecovered(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_typecovered(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) <= dns_types__query_type__last))
<S>  New H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned8__first <= fld_algorithm(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned8__first <= fld_numlabels(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
<S>  New H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_origttl(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
<S>  New H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) and fld_sigexpiration(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          unsigned_types__unsigned32__last))
<S>  New H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned32__first <= 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) and fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          unsigned_types__unsigned32__last))
<S>  New H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> unsigned_types__unsigned16__first <= fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          and fld_keytag(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned16__last))
<S>  New H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
<S>  New H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___4 : integer, 
          rr_type__rrsig_record_type__rrsigstringtypeindex__first <= i___4 and 
          i___4 <= rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
<S>  New H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
<S>  New H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= 64 -> for_all(i___3 : integer, 
          rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
<S>  New H38:  loop__1__i <= 64
<S>  New H50:  not loop__1__i = 64
<S>  New C38:  loop__1__i <= 63
<S>  New C40:  loop__1__i <= 63
***  Proved C38:  loop__1__i <= 63
     using hypotheses H38 & H50.
***  Proved C40:  loop__1__i <= 63
     using hypotheses H38 & H50.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_5.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H38).
***  Proved C1:  loop__1__i >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
***  Proved C2:  loop__1__i <= rr_type__returnedrecordsindextype__last
     using hypothesis H38.
***  Proved C3:  bucket >= rr_type__numbucketsindextype__first
     using hypothesis H41.
***  Proved C4:  bucket <= rr_type__numbucketsindextype__last
     using hypothesis H42.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_6.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H42).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(lower_key, [i___1]) and element(
          lower_key, [i___1]) <= character__last)
***  Proved C1:  loop__1__i >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
***  Proved C2:  loop__1__i <= rr_type__returnedrecordsindextype__last
     using hypothesis H38.
***  Proved C3:  bucket >= rr_type__numbucketsindextype__first
     using hypothesis H41.
***  Proved C4:  bucket <= rr_type__numbucketsindextype__last
     using hypothesis H42.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_7.  @@@@@@@@@@
%%%  Simplified H1 on reading formula in, to give:
     %%%  H1:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(key, [i___1]) and element(key, [i___1]) 
          <= character__last)
%%%  Simplified H4 on reading formula in, to give:
     %%%  H4:  rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%%  Simplified H6 on reading formula in, to give:
     %%%  H6:  dns_types__query_type__first <= fld_typecovered(therecord)
%%%  Simplified H20 on reading formula in, to give:
     %%%  H20:  for_all(i___1 : integer, 
          rr_type__domainnamestringtypeindex__first <= i___1 and i___1 <= 
          rr_type__domainnamestringtypeindex__last -> character__first <= 
          element(fld_signername(therecord), [i___1]) and element(
          fld_signername(therecord), [i___1]) <= character__last)
%%%  Simplified H21 on reading formula in, to give:
     %%%  H21:  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(therecord), [i___2]) and 
          element(fld_signature(therecord), [i___2]) <= character__last)
%%%  Simplified H24 on reading formula in, to give:
     %%%  H24:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])))
           and fld_ttlinseconds(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) <= 
          unsigned_types__unsigned32__last))
%%%  Simplified H25 on reading formula in, to give:
     %%%  H25:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__classtype__first <= fld_class(fld_inherit(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2]))) and fld_class(
          fld_inherit(element(element(dns_table_type__rrsigrecordtable, [i___1])
          , [i___2]))) <= rr_type__classtype__last))
%%%  Simplified H26 on reading formula in, to give:
     %%%  H26:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          dns_types__query_type__first <= fld_typecovered(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_typecovered(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= dns_types__query_type__last))
%%%  Simplified H27 on reading formula in, to give:
     %%%  H27:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_algorithm(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_algorithm(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H28 on reading formula in, to give:
     %%%  H28:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned8__first <= fld_numlabels(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_numlabels(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned8__last))
%%%  Simplified H29 on reading formula in, to give:
     %%%  H29:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_origttl(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_origttl(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned32__last))
%%%  Simplified H30 on reading formula in, to give:
     %%%  H30:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_sigexpiration(element(
          element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_sigexpiration(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H31 on reading formula in, to give:
     %%%  H31:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned32__first <= fld_siginception(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and 
          fld_siginception(element(element(dns_table_type__rrsigrecordtable, [
          i___1]), [i___2])) <= unsigned_types__unsigned32__last))
%%%  Simplified H32 on reading formula in, to give:
     %%%  H32:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          unsigned_types__unsigned16__first <= fld_keytag(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) and fld_keytag(
          element(element(dns_table_type__rrsigrecordtable, [i___1]), [i___2])) 
          <= unsigned_types__unsigned16__last))
%%%  Simplified H33 on reading formula in, to give:
     %%%  H33:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__domainnamestringtypeindex__first <= i___3 and 
          i___3 <= rr_type__domainnamestringtypeindex__last -> character__first 
          <= element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) and 
          element(fld_signername(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___3]) <= 
          character__last)))
%%%  Simplified H34 on reading formula in, to give:
     %%%  H34:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___4 
          : integer, rr_type__rrsig_record_type__rrsigstringtypeindex__first <= 
          i___4 and i___4 <= 
          rr_type__rrsig_record_type__rrsigstringtypeindex__last -> 
          character__first <= element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) and 
          element(fld_signature(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])), [i___4]) <= 
          character__last)))
%%%  Simplified H35 on reading formula in, to give:
     %%%  H35:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> 
          rr_type__rrsig_record_type__siglengthvaluetype__first <= 
          fld_signaturelength(element(element(dns_table_type__rrsigrecordtable, 
          [i___1]), [i___2])) and fld_signaturelength(element(element(
          dns_table_type__rrsigrecordtable, [i___1]), [i___2])) <= 
          rr_type__rrsig_record_type__siglengthvaluetype__last))
%%%  Simplified H36 on reading formula in, to give:
     %%%  H36:  for_all(i___1 : integer, rr_type__numbucketsindextype__first <= 
          i___1 and i___1 <= rr_type__numbucketsindextype__last -> for_all(
          i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2 
          and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___3 
          : integer, rr_type__wirestringtypeindex__first <= i___3 and i___3 <= 
          rr_type__wirestringtypeindex__last -> character__first <= element(
          element(element(dns_table_type__rrsigrecordkeys, [i___1]), [i___2]), [
          i___3]) and element(element(element(dns_table_type__rrsigrecordkeys, [
          i___1]), [i___2]), [i___3]) <= character__last)))
---  Hypothesis H39 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H40 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H43 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H44 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H45 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H46 has been replaced by "true".  (It is already present, as 
          H42).
%%%  Simplified H48 on reading formula in, to give:
     %%%  H48:  for_all(i___1 : integer, rr_type__wirestringtypeindex__first <= 
          i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 
          character__first <= element(lower_key, [i___1]) and element(
          lower_key, [i___1]) <= character__last)
---  Hypothesis H49 has been replaced by "true".  (It is already present, as 
          H37).
---  Hypothesis H50 has been replaced by "true".  (It is already present, as 
          H38).
---  Hypothesis H51 has been replaced by "true".  (It is already present, as 
          H41).
---  Hypothesis H52 has been replaced by "true".  (It is already present, as 
          H42).
***  Proved C1:  loop__1__i >= rr_type__returnedrecordsindextype__first
     using hypothesis H37.
***  Proved C2:  loop__1__i <= rr_type__returnedrecordsindextype__last
     using hypothesis H38.
***  Proved C3:  bucket >= rr_type__numbucketsindextype__first
     using hypothesis H41.
***  Proved C4:  bucket <= rr_type__numbucketsindextype__last
     using hypothesis H42.
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_8.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_9.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_10.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_11.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_12.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.


@@@@@@@@@@  VC: procedure_insertrrsigrecord_13.  @@@@@@@@@@
***  Proved C1:  true
***  PROVED VC.

