ironsides/dns_table_pkg/dns_table_type/insertptrrecord.slg

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105 KiB
Plaintext

*****************************************************************************
Semantic Analysis of SPARK Text
Examiner GPL Edition
*****************************************************************************
SPARK Simplifier GPL 2011
Copyright (C) 2011 Altran Praxis Limited, Bath, U.K.
procedure dns_table_pkg.DNS_Table_Type.insertPTRRecord
@@@@@@@@@@ VC: procedure_insertptrrecord_1. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
%%% Simplified H12 on reading formula in, to give:
%%% H12: 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 H13 has been replaced by "true". (It is already present, as
H12).
*** Proved C1: hash(to_lower(key)) >= rr_type__numbucketsindextype__first
using hypothesis H14.
*** Proved C2: hash(to_lower(key)) <= rr_type__numbucketsindextype__last
using hypothesis H15.
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_2. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
%%% Simplified H12 on reading formula in, to give:
%%% H12: 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 H13 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H16 has been replaced by "true". (It is already present, as
H14).
--- Hypothesis H17 has been replaced by "true". (It is already present, as
H15).
%%% Simplified C2 on reading formula in, to give:
%%% C2: 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 C3 on reading formula in, to give:
%%% C3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified C4 on reading formula in, to give:
%%% C4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified C8 on reading formula in, to give:
%%% C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified C9 on reading formula in, to give:
%%% C9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified C10 on reading formula in, to give:
%%% C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified C11 on reading formula in, to give:
%%% C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
%%% Simplified C12 on reading formula in, to give:
%%% C12: true
%%% Simplified C14 on reading formula in, to give:
%%% C14: true
*** Proved C1: true
*** Proved C2: 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 H2.
*** Proved C3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first
<= i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__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: fld_ttlinseconds(fld_inherit(therecord)) >=
unsigned_types__unsigned32__first
using hypothesis H6.
*** Proved C7: fld_ttlinseconds(fld_inherit(therecord)) <=
unsigned_types__unsigned32__last
using hypothesis H7.
*** Proved C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first
<= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
using hypothesis H8.
*** Proved C9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
using hypothesis H9.
*** Proved C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
using hypothesis H10.
*** Proved C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first
<= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
using hypothesis H11.
*** Proved C12: true
*** Proved C14: true
-S- Applied substitution rule insertptrrec_rules(59).
This was achieved by replacing all occurrences of
rr_type__returnedrecordsindextype__first by:
1.
<S> New H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New H9: for_all(i___2 : integer, 1 <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
<S> New H10: for_all(i___2 : integer, 1 <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
<S> New H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
<S> New C13: 1 <= rr_type__returnedrecordsindextype__last
<S> New C15: 1 <= rr_type__returnedrecordsindextype__last
-S- Applied substitution rule insertptrrec_rules(60).
This was achieved by replacing all occurrences of
rr_type__returnedrecordsindextype__last by:
64.
<S> New H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New H9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, rr_type__numbucketsindextype__first <= i___1 and
i___1 <= rr_type__numbucketsindextype__last ->
rr_type__classtype__first <= fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) and fld_class(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) <= rr_type__classtype__last))
<S> New H10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, rr_type__numbucketsindextype__first <= i___1 and
i___1 <= rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
<S> New H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
<S> New C13: true
<S> New C15: true
*** Proved C13: true
*** Proved C15: true
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_3. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
--- Hypothesis H14 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H15 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H18 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H19 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H20 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H21 has been replaced by "true". (It is already present, as
H17).
%%% Simplified H23 on reading formula in, to give:
%%% H23: 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 H24 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H25 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H26 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H27 has been replaced by "true". (It is already present, as
H17).
--- Hypothesis H28 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H29 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H30 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H31 has been replaced by "true". (It is already present, as
H17).
%%% Simplified H33 on reading formula in, to give:
%%% H33: false
%%% Simplified C2 on reading formula in, to give:
%%% C2: 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 C3 on reading formula in, to give:
%%% C3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified C4 on reading formula in, to give:
%%% C4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified C8 on reading formula in, to give:
%%% C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified C9 on reading formula in, to give:
%%% C9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) <= rr_type__classtype__last))
%%% Simplified C10 on reading formula in, to give:
%%% C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified C11 on reading formula in, to give:
%%% C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(update(dns_table_type__ptrrecordkeys, [bucket],
update(element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i]
, lower_key)), [i___1]), [i___2]), [i___3]) and element(element(
element(update(dns_table_type__ptrrecordkeys, [bucket], update(
element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i],
lower_key)), [i___1]), [i___2]), [i___3]) <= character__last)))
*** Proved C1: true
*** Proved C2: 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 H2.
*** Proved C3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first
<= i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__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: fld_ttlinseconds(fld_inherit(therecord)) >=
unsigned_types__unsigned32__first
using hypothesis H6.
*** Proved C7: fld_ttlinseconds(fld_inherit(therecord)) <=
unsigned_types__unsigned32__last
using hypothesis H7.
*** Proved C12: loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
using hypothesis H12.
*** Proved C14: loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
using hypothesis H12.
-S- Applied substitution rule insertptrrec_rules(60).
This was achieved by replacing all occurrences of
rr_type__returnedrecordsindextype__last by:
64.
<S> New H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New H9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
<S> New H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
<S> New H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
<S> New H13: loop__1__i <= 64
<S> New H34: not loop__1__i = 64
<S> New C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New C9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) <= rr_type__classtype__last))
<S> New C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
<S> New C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(update(dns_table_type__ptrrecordkeys, [bucket],
update(element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i]
, lower_key)), [i___1]), [i___2]), [i___3]) and element(element(
element(update(dns_table_type__ptrrecordkeys, [bucket], update(
element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i],
lower_key)), [i___1]), [i___2]), [i___3]) <= character__last)))
<S> New C13: loop__1__i <= 63
<S> New C15: loop__1__i <= 63
*** Proved C13: loop__1__i <= 63
using hypotheses H13 & H34.
*** Proved C15: loop__1__i <= 63
using hypotheses H13 & H34.
>>> Restructured hypothesis H34 into:
>>> H34: loop__1__i <> 64
-S- Applied substitution rule insertptrrec_rules(9).
This was achieved by replacing all occurrences of character__first by:
0.
<S> New H2: 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 H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
fld_domainname(therecord), [i___1]) and element(fld_domainname(
therecord), [i___1]) <= character__last)
<S> New H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])), [
i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [i___3]) and
element(element(element(dns_table_type__ptrrecordkeys, [i___1]), [
i___2]), [i___3]) <= character__last)))
<S> New H23: 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 C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
update(dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) and element(element(element(update(
dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) <= character__last)))
-S- Applied substitution rule insertptrrec_rules(10).
This was achieved by replacing all occurrences of character__last by:
255.
<S> New H2: 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 H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last -> 0 <= element(
fld_domainname(therecord), [i___1]) and element(fld_domainname(
therecord), [i___1]) <= 255)
<S> New H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])), [
i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <= 255))
)
<S> New H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [i___3]) and
element(element(element(dns_table_type__ptrrecordkeys, [i___1]), [
i___2]), [i___3]) <= 255)))
<S> New H23: 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 C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S> New C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
update(dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) and element(element(element(update(
dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) <= 255)))
-S- Applied substitution rule insertptrrec_rules(19).
This was achieved by replacing all occurrences of
unsigned_types__unsigned32__first by:
0.
<S> New H6: fld_ttlinseconds(fld_inherit(therecord)) >= 0
<S> New H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <=
fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) and
fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
<S> New C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <=
fld_ttlinseconds(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
update(dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) <= unsigned_types__unsigned32__last))
-S- Applied substitution rule insertptrrec_rules(20).
This was achieved by replacing all occurrences of
unsigned_types__unsigned32__last by:
4294967295.
<S> New H7: fld_ttlinseconds(fld_inherit(therecord)) <= 4294967295
<S> New H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <=
fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) and
fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S> New C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <=
fld_ttlinseconds(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
update(dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) <= 4294967295))
-S- Applied substitution rule insertptrrec_rules(25).
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 H9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__internet <= fld_class(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
<S> New C9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__internet <= fld_class(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) and fld_class(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) <=
rr_type__classtype__last))
-S- Applied substitution rule insertptrrec_rules(26).
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 H9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__internet <= fld_class(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= rr_type__hs))
<S> New C9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__internet <= fld_class(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) and fld_class(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) <= rr_type__hs))
-S- Applied substitution rule insertptrrec_rules(52).
This was achieved by replacing all occurrences of
rr_type__wirestringtypeindex__first by:
1.
<S> New H2: 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 H3: for_all(i___1 : integer, 1 <= i___1 and i___1 <=
rr_type__wirestringtypeindex__last -> 0 <= element(fld_domainname(
therecord), [i___1]) and element(fld_domainname(therecord), [i___1])
<= 255)
<S> New H8: for_all(i___3 : integer, 1 <= i___3 and i___3 <=
rr_type__wirestringtypeindex__last -> for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <= 255))
)
<S> New H11: for_all(i___3 : integer, 1 <= i___3 and i___3 <=
rr_type__wirestringtypeindex__last -> for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= 255)))
<S> New H23: 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 C8: for_all(i___3 : integer, 1 <= i___3 and i___3 <=
rr_type__wirestringtypeindex__last -> for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <= element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S> New C11: for_all(i___3 : integer, 1 <= i___3 and i___3 <=
rr_type__wirestringtypeindex__last -> for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last -> 0 <= element(
element(element(update(dns_table_type__ptrrecordkeys, [bucket],
update(element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i]
, lower_key)), [i___1]), [i___2]), [i___3]) and element(element(
element(update(dns_table_type__ptrrecordkeys, [bucket], update(
element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i],
lower_key)), [i___1]), [i___2]), [i___3]) <= 255)))
-S- Applied substitution rule insertptrrec_rules(53).
This was achieved by replacing all occurrences of
rr_type__wirestringtypeindex__last by:
129.
<S> New H2: 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 H3: for_all(i___1 : integer, 1 <= i___1 and i___1 <= 129 -> 0 <=
element(fld_domainname(therecord), [i___1]) and element(
fld_domainname(therecord), [i___1]) <= 255)
<S> New H8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])), [
i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <= 255))
)
<S> New H11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [i___3]) and
element(element(element(dns_table_type__ptrrecordkeys, [i___1]), [
i___2]), [i___3]) <= 255)))
<S> New H23: 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 C8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S> New C11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
update(dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) and element(element(element(update(
dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) <= 255)))
-S- Applied substitution rule insertptrrec_rules(59).
This was achieved by replacing all occurrences of
rr_type__returnedrecordsindextype__first by:
1.
<S> New H12: loop__1__i >= 1
<S> New H10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, rr_type__numbucketsindextype__first <= i___1 and
i___1 <= rr_type__numbucketsindextype__last -> 0 <= fld_ttlinseconds(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S> New H9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, rr_type__numbucketsindextype__first <= i___1 and
i___1 <= rr_type__numbucketsindextype__last -> rr_type__internet <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= rr_type__hs))
<S> New H8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])), [
i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <= 255))
)
<S> New H11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [i___3]) and
element(element(element(dns_table_type__ptrrecordkeys, [i___1]), [
i___2]), [i___3]) <= 255)))
<S> New C10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, rr_type__numbucketsindextype__first <= i___1 and
i___1 <= rr_type__numbucketsindextype__last -> 0 <= fld_ttlinseconds(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) <= 4294967295))
<S> New C9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, rr_type__numbucketsindextype__first <= i___1 and
i___1 <= rr_type__numbucketsindextype__last -> rr_type__internet <=
fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) <= rr_type__hs))
<S> New C8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(fld_domainname(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S> New C11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= element(element(element(
update(dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) and element(element(element(update(
dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) <= 255)))
-S- Applied substitution rule insertptrrec_rules(64).
This was achieved by replacing all occurrences of
rr_type__numbucketsindextype__first by:
1.
<S> New H16: bucket >= 1
<S> New H10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= fld_ttlinseconds(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S> New H9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__internet <= fld_class(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= rr_type__hs))
<S> New H8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= rr_type__numbucketsindextype__last
-> 0 <= element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) and
element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <= 255))
)
<S> New H11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= rr_type__numbucketsindextype__last
-> 0 <= element(element(element(dns_table_type__ptrrecordkeys, [i___1]
), [i___2]), [i___3]) and element(element(element(
dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [i___3]) <= 255)))
<S> New C10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> 0 <= fld_ttlinseconds(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) <= 4294967295))
<S> New C9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__internet <= fld_class(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) and fld_class(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) <= rr_type__hs))
<S> New C8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= rr_type__numbucketsindextype__last
-> 0 <= element(fld_domainname(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2])), [i___3]) and element(fld_domainname(element(
element(update(dns_table_type__ptrrecordtable, [bucket], update(
element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i],
therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S> New C11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= rr_type__numbucketsindextype__last
-> 0 <= element(element(element(update(dns_table_type__ptrrecordkeys,
[bucket], update(element(dns_table_type__ptrrecordkeys, [bucket]), [
loop__1__i], lower_key)), [i___1]), [i___2]), [i___3]) and element(
element(element(update(dns_table_type__ptrrecordkeys, [bucket],
update(element(dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i]
, lower_key)), [i___1]), [i___2]), [i___3]) <= 255)))
-S- Applied substitution rule insertptrrec_rules(65).
This was achieved by replacing all occurrences of
rr_type__numbucketsindextype__last by:
64.
<S> New H17: bucket <= 64
<S> New H10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= fld_ttlinseconds(
fld_inherit(element(element(dns_table_type__ptrrecordtable, [i___1]),
[i___2]))) and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= 4294967295))
<S> New H9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <= 64 -> rr_type__internet <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <= rr_type__hs))
<S> New H8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= 64 -> 0 <= element(fld_domainname(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])), [
i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <= 255))
)
<S> New H11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= 64 -> 0 <= element(element(element(
dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [i___3]) and
element(element(element(dns_table_type__ptrrecordkeys, [i___1]), [
i___2]), [i___3]) <= 255)))
<S> New C10: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <= 64 -> 0 <= fld_ttlinseconds(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) and fld_ttlinseconds(
fld_inherit(element(element(update(dns_table_type__ptrrecordtable, [
bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2]))) <= 4294967295))
<S> New C9: for_all(i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(
i___1 : integer, 1 <= i___1 and i___1 <= 64 -> rr_type__internet <=
fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(update(
dns_table_type__ptrrecordtable, [bucket], update(element(
dns_table_type__ptrrecordtable, [bucket]), [loop__1__i], therecord)),
[i___1]), [i___2]))) <= rr_type__hs))
<S> New C8: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= 64 -> 0 <= element(fld_domainname(
element(element(update(dns_table_type__ptrrecordtable, [bucket],
update(element(dns_table_type__ptrrecordtable, [bucket]), [loop__1__i]
, therecord)), [i___1]), [i___2])), [i___3]) and element(
fld_domainname(element(element(update(dns_table_type__ptrrecordtable,
[bucket], update(element(dns_table_type__ptrrecordtable, [bucket]), [
loop__1__i], therecord)), [i___1]), [i___2])), [i___3]) <= 255)))
<S> New C11: for_all(i___3 : integer, 1 <= i___3 and i___3 <= 129 -> for_all(
i___2 : integer, 1 <= i___2 and i___2 <= 64 -> for_all(i___1 :
integer, 1 <= i___1 and i___1 <= 64 -> 0 <= element(element(element(
update(dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) and element(element(element(update(
dns_table_type__ptrrecordkeys, [bucket], update(element(
dns_table_type__ptrrecordkeys, [bucket]), [loop__1__i], lower_key)), [
i___1]), [i___2]), [i___3]) <= 255)))
%%% Hypotheses H13 & H34 together imply that
loop__1__i < 64.
H13 & H34 have therefore been deleted and a new H35 added to this effect.
### Established a contradiction [false-hypothesis] using hypothesis H33.
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_4. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
--- Hypothesis H14 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H15 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H18 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H19 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H20 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H21 has been replaced by "true". (It is already present, as
H17).
%%% Simplified C2 on reading formula in, to give:
%%% C2: 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 C3 on reading formula in, to give:
%%% C3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified C4 on reading formula in, to give:
%%% C4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified C8 on reading formula in, to give:
%%% C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified C9 on reading formula in, to give:
%%% C9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified C10 on reading formula in, to give:
%%% C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified C11 on reading formula in, to give:
%%% C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
*** Proved C1: true
*** Proved C2: 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 H2.
*** Proved C3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first
<= i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__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: fld_ttlinseconds(fld_inherit(therecord)) >=
unsigned_types__unsigned32__first
using hypothesis H6.
*** Proved C7: fld_ttlinseconds(fld_inherit(therecord)) <=
unsigned_types__unsigned32__last
using hypothesis H7.
*** Proved C8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first
<= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
using hypothesis H8.
*** Proved C9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
using hypothesis H9.
*** Proved C10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
using hypothesis H10.
*** Proved C11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first
<= i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
using hypothesis H11.
*** Proved C12: loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
using hypothesis H12.
*** Proved C14: loop__1__i + 1 >= rr_type__returnedrecordsindextype__first
using hypothesis H12.
-S- Applied substitution rule insertptrrec_rules(60).
This was achieved by replacing all occurrences of
rr_type__returnedrecordsindextype__last by:
64.
<S> New H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
<S> New H9: for_all(i___2 : integer, rr_type__returnedrecordsindextype__first
<= i___2 and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
<S> New H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <= 64 ->
for_all(i___1 : integer, rr_type__numbucketsindextype__first <= i___1
and i___1 <= rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
<S> New H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= 64 -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
<S> New H13: loop__1__i <= 64
<S> New H25: not loop__1__i = 64
<S> New C13: loop__1__i <= 63
<S> New C15: loop__1__i <= 63
*** Proved C13: loop__1__i <= 63
using hypotheses H13 & H25.
*** Proved C15: loop__1__i <= 63
using hypotheses H13 & H25.
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_5. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
--- Hypothesis H14 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H15 has been replaced by "true". (It is already present, as
H13).
*** Proved C1: loop__1__i >= rr_type__returnedrecordsindextype__first
using hypothesis H12.
*** Proved C2: loop__1__i <= rr_type__returnedrecordsindextype__last
using hypothesis H13.
*** Proved C3: bucket >= rr_type__numbucketsindextype__first
using hypothesis H16.
*** Proved C4: bucket <= rr_type__numbucketsindextype__last
using hypothesis H17.
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_6. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
--- Hypothesis H14 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H15 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H18 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H19 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H20 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H21 has been replaced by "true". (It is already present, as
H17).
%%% Simplified H23 on reading formula in, to give:
%%% H23: 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 H12.
*** Proved C2: loop__1__i <= rr_type__returnedrecordsindextype__last
using hypothesis H13.
*** Proved C3: bucket >= rr_type__numbucketsindextype__first
using hypothesis H16.
*** Proved C4: bucket <= rr_type__numbucketsindextype__last
using hypothesis H17.
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_7. @@@@@@@@@@
%%% Simplified H2 on reading formula in, to give:
%%% H2: 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 H3 on reading formula in, to give:
%%% H3: for_all(i___1 : integer, rr_type__wirestringtypeindex__first <=
i___1 and i___1 <= rr_type__wirestringtypeindex__last ->
character__first <= element(fld_domainname(therecord), [i___1]) and
element(fld_domainname(therecord), [i___1]) <= character__last)
%%% Simplified H4 on reading formula in, to give:
%%% H4: rr_type__classtype__first <= fld_class(fld_inherit(therecord))
%%% Simplified H8 on reading formula in, to give:
%%% H8: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
fld_domainname(element(element(dns_table_type__ptrrecordtable, [i___1]
), [i___2])), [i___3]) and element(fld_domainname(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2])), [i___3]) <=
character__last)))
%%% Simplified H9 on reading formula in, to give:
%%% H9: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> rr_type__classtype__first <=
fld_class(fld_inherit(element(element(dns_table_type__ptrrecordtable,
[i___1]), [i___2]))) and fld_class(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
rr_type__classtype__last))
%%% Simplified H10 on reading formula in, to give:
%%% H10: for_all(i___2 : integer,
rr_type__returnedrecordsindextype__first <= i___2 and i___2 <=
rr_type__returnedrecordsindextype__last -> for_all(i___1 : integer,
rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last ->
unsigned_types__unsigned32__first <= fld_ttlinseconds(fld_inherit(
element(element(dns_table_type__ptrrecordtable, [i___1]), [i___2])))
and fld_ttlinseconds(fld_inherit(element(element(
dns_table_type__ptrrecordtable, [i___1]), [i___2]))) <=
unsigned_types__unsigned32__last))
%%% Simplified H11 on reading formula in, to give:
%%% H11: for_all(i___3 : integer, rr_type__wirestringtypeindex__first <=
i___3 and i___3 <= rr_type__wirestringtypeindex__last -> for_all(
i___2 : integer, rr_type__returnedrecordsindextype__first <= i___2
and i___2 <= rr_type__returnedrecordsindextype__last -> for_all(i___1
: integer, rr_type__numbucketsindextype__first <= i___1 and i___1 <=
rr_type__numbucketsindextype__last -> character__first <= element(
element(element(dns_table_type__ptrrecordkeys, [i___1]), [i___2]), [
i___3]) and element(element(element(dns_table_type__ptrrecordkeys, [
i___1]), [i___2]), [i___3]) <= character__last)))
--- Hypothesis H14 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H15 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H18 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H19 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H20 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H21 has been replaced by "true". (It is already present, as
H17).
%%% Simplified H23 on reading formula in, to give:
%%% H23: 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 H24 has been replaced by "true". (It is already present, as
H12).
--- Hypothesis H25 has been replaced by "true". (It is already present, as
H13).
--- Hypothesis H26 has been replaced by "true". (It is already present, as
H16).
--- Hypothesis H27 has been replaced by "true". (It is already present, as
H17).
*** Proved C1: loop__1__i >= rr_type__returnedrecordsindextype__first
using hypothesis H12.
*** Proved C2: loop__1__i <= rr_type__returnedrecordsindextype__last
using hypothesis H13.
*** Proved C3: bucket >= rr_type__numbucketsindextype__first
using hypothesis H16.
*** Proved C4: bucket <= rr_type__numbucketsindextype__last
using hypothesis H17.
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_8. @@@@@@@@@@
*** Proved C1: true
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_9. @@@@@@@@@@
*** Proved C1: true
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_10. @@@@@@@@@@
*** Proved C1: true
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_11. @@@@@@@@@@
*** Proved C1: true
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_12. @@@@@@@@@@
*** Proved C1: true
*** PROVED VC.
@@@@@@@@@@ VC: procedure_insertptrrecord_13. @@@@@@@@@@
*** Proved C1: true
*** PROVED VC.