TSTP Solution File: ITP214^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP214^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:20:12 EDT 2023
% Result : Theorem 112.47s 112.91s
% Output : Proof 112.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 3.35/3.40 % Problem : ITP214^1 : TPTP v8.1.2. Released v8.1.0.
% 3.35/3.41 % Command : do_cvc5 %s %d
% 3.41/3.62 % Computer : n025.cluster.edu
% 3.41/3.62 % Model : x86_64 x86_64
% 3.41/3.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 3.41/3.62 % Memory : 8042.1875MB
% 3.41/3.62 % OS : Linux 3.10.0-693.el7.x86_64
% 3.41/3.62 % CPULimit : 300
% 3.41/3.62 % WCLimit : 300
% 3.41/3.62 % DateTime : Sun Aug 27 16:56:57 EDT 2023
% 3.41/3.62 % CPUTime :
% 6.88/7.08 %----Proving TH0
% 6.88/7.09 %------------------------------------------------------------------------------
% 6.88/7.09 % File : ITP214^1 : TPTP v8.1.2. Released v8.1.0.
% 6.88/7.09 % Domain : Interactive Theorem Proving
% 6.88/7.09 % Problem : Sledgehammer problem Hoare_Triple 00428_012651
% 6.88/7.09 % Version : [Des22] axioms.
% 6.88/7.09 % English :
% 6.88/7.09
% 6.88/7.09 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 6.88/7.09 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 6.88/7.09 % Source : [Des22]
% 6.88/7.09 % Names : 0025_Hoare_Triple_00428_012651 [Des22]
% 6.88/7.09
% 6.88/7.09 % Status : Theorem
% 6.88/7.09 % Rating : 0.23 v8.1.0
% 6.88/7.09 % Syntax : Number of formulae : 12112 (5171 unt;1845 typ; 0 def)
% 6.88/7.09 % Number of atoms : 29629 (11254 equ; 0 cnn)
% 6.88/7.09 % Maximal formula atoms : 48 ( 2 avg)
% 6.88/7.09 % Number of connectives : 111866 (2669 ~; 470 |;2086 &;95072 @)
% 6.88/7.09 % ( 0 <=>;11569 =>; 0 <=; 0 <~>)
% 6.88/7.09 % Maximal formula depth : 25 ( 6 avg)
% 6.88/7.09 % Number of types : 192 ( 191 usr)
% 6.88/7.09 % Number of type conns : 8544 (8544 >; 0 *; 0 +; 0 <<)
% 6.88/7.09 % Number of symbols : 1657 (1654 usr; 99 con; 0-8 aty)
% 6.88/7.09 % Number of variables : 29524 (3706 ^;25258 !; 560 ?;29524 :)
% 6.88/7.09 % SPC : TH0_THM_EQU_NAR
% 6.88/7.09
% 6.88/7.09 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 6.88/7.09 % from the van Emde Boas Trees session in the Archive of Formal
% 6.88/7.09 % proofs -
% 6.88/7.09 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 6.88/7.09 % 2022-02-17 15:41:40.043
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_t__Nat__Onat,type,
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_t__Int__Oint,type,
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_tf__b,type,
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% 6.88/7.09
% 6.88/7.09 thf(ty_n_tf__a,type,
% 6.88/7.09 a: $tType ).
% 6.88/7.09
% 6.88/7.09 % Explicit typings (1654)
% 6.88/7.09 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 6.88/7.09 archim2889992004027027881ng_rat: rat > int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 6.88/7.09 archim3151403230148437115or_rat: rat > int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 6.88/7.09 archimedean_frac_rat: rat > rat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 6.88/7.09 archim7778729529865785530nd_rat: rat > int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oalloc_001_Eo,type,
% 6.88/7.09 array_alloc_o: list_o > heap_e7401611519738050253t_unit > produc5011041761010125393t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oalloc_001t__Int__Oint,type,
% 6.88/7.09 array_alloc_int: list_int > heap_e7401611519738050253t_unit > produc3407818250607552075t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oalloc_001t__Nat__Onat,type,
% 6.88/7.09 array_alloc_nat: list_nat > heap_e7401611519738050253t_unit > produc1730305018825802663t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Olen_001_Eo,type,
% 6.88/7.09 array_len_o: array_o > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Olen_001t__Int__Oint,type,
% 6.88/7.09 array_len_int: array_int > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Olen_001t__Nat__Onat,type,
% 6.88/7.09 array_len_nat: array_nat > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Omake_001_Eo,type,
% 6.88/7.09 array_make_o: nat > ( nat > $o ) > heap_T5660665574680485309rray_o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Omake_001t__Int__Oint,type,
% 6.88/7.09 array_make_int: nat > ( nat > int ) > heap_T1346037964561226099ay_int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Omake_001t__Nat__Onat,type,
% 6.88/7.09 array_make_nat: nat > ( nat > nat ) > heap_T3836121109492952855ay_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001_Eo,type,
% 6.88/7.09 array_nth_o: array_o > nat > heap_Time_Heap_o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001t__Int__Oint,type,
% 6.88/7.09 array_nth_int: array_int > nat > heap_Time_Heap_int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001t__Nat__Onat,type,
% 6.88/7.09 array_nth_nat: array_nat > nat > heap_Time_Heap_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Onth_001t__Product____Type__Ounit,type,
% 6.88/7.09 array_7872002506669749220t_unit: array_Product_unit > nat > heap_T5738788834812785303t_unit ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oof__list_001_Eo,type,
% 6.88/7.09 array_of_list_o: list_o > heap_T5660665574680485309rray_o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oof__list_001t__Int__Oint,type,
% 6.88/7.09 array_of_list_int: list_int > heap_T1346037964561226099ay_int ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Array__Time_Oof__list_001t__Nat__Onat,type,
% 6.88/7.09 array_of_list_nat: list_nat > heap_T3836121109492952855ay_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oassn_OAbs__assn,type,
% 6.88/7.09 abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oassn_ORep__assn,type,
% 6.88/7.09 rep_assn: assn > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oentails,type,
% 6.88/7.09 entails: assn > assn > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oin__range,type,
% 6.88/7.09 in_range: produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oin__range__rel,type,
% 6.88/7.09 in_range_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oone__assn__raw,type,
% 6.88/7.09 one_assn_raw: produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Oone__assn__raw__rel,type,
% 6.88/7.09 one_assn_raw_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Opure__assn,type,
% 6.88/7.09 pure_assn: $o > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Opure__assn__raw_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 6.88/7.09 pure_a825153325127701367it_nat: $o > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Opure__assn__raw__rel_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 6.88/7.09 pure_a6022498039421069578it_nat: produc6197004810343482825et_nat > produc6197004810343482825et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_OrelH,type,
% 6.88/7.09 relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001_Eo,type,
% 6.88/7.09 snga_assn_o: array_o > list_o > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001t__Int__Oint,type,
% 6.88/7.09 snga_assn_int: array_int > list_int > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001t__Nat__Onat,type,
% 6.88/7.09 snga_assn_nat: array_nat > list_nat > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osnga__assn_001t__Product____Type__Ounit,type,
% 6.88/7.09 snga_a4522542871529764173t_unit: array_Product_unit > list_Product_unit > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Osngr__assn_001t__Product____Type__Ounit,type,
% 6.88/7.09 sngr_a5825115052027484668t_unit: ref_Product_unit > product_unit > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Otimes__assn__raw,type,
% 6.88/7.09 times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Otimes__assn__raw__rel,type,
% 6.88/7.09 times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Owand__assn,type,
% 6.88/7.09 wand_assn: assn > assn > assn ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Owand__raw,type,
% 6.88/7.09 wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_Assertions_Owand__raw__rel,type,
% 6.88/7.09 wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
% 6.88/7.09 bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Nat__Onat,type,
% 6.88/7.09 bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 6.88/7.09 bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 6.88/7.09 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Int__Oint,type,
% 6.88/7.09 bNF_Ca1965613569405424510nt_int: set_Pr958786334691620121nt_int > ( int > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Nat__Onat,type,
% 6.88/7.09 bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > ( int > nat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Num__Onum,type,
% 6.88/7.09 bNF_Ca7748807862925029228nt_num: set_Pr958786334691620121nt_int > ( int > num ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Rat__Orat,type,
% 6.88/7.09 bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > ( int > rat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 6.88/7.09 bNF_Ca583493526879471924et_int: set_Pr958786334691620121nt_int > ( int > set_int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 6.88/7.09 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.88/7.09 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.88/7.09 bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 6.88/7.09 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 6.88/7.09 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 6.88/7.09 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.88/7.09 bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 6.88/7.09 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 6.88/7.09 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.88/7.09 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 6.88/7.09 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.88/7.09 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 6.88/7.09 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 6.88/7.09 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 6.88/7.09 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 6.88/7.09
% 6.88/7.09 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.88/7.09 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 6.88/7.10 bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.88/7.10 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 6.88/7.10 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
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% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 6.88/7.10 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 6.88/7.10 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.88/7.10 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
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% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
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% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 6.88/7.10 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 6.88/7.10 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.88/7.10 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 6.88/7.10 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.88/7.10 bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 6.88/7.10 bNF_re7934895593101944656at_int: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > $o ).
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% 6.88/7.10
% 6.88/7.10 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
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% 6.88/7.10 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 comp_C95226695241045696nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_C4049556595663050210at_nat: ( code_integer > nat ) > ( nat > code_integer ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 6.92/7.10 comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Rat__Orat_001t__Int__Oint,type,
% 6.92/7.10 comp_int_rat_int: ( int > rat ) > ( int > int ) > int > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 6.92/7.10 comp_n3898172953802868194er_nat: ( nat > code_integer ) > ( nat > nat ) > nat > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.10 comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Nat__Onat,type,
% 6.92/7.10 comp_n8698576032424989604at_nat: ( nat > multis2468970476368604999at_nat ) > ( nat > nat ) > nat > multis2468970476368604999at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Rat__Orat_001t__Nat__Onat,type,
% 6.92/7.10 comp_nat_rat_nat: ( nat > rat ) > ( nat > nat ) > nat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Int__Oint_001t__Num__Onum,type,
% 6.92/7.10 comp_num_int_num: ( num > int ) > ( num > num ) > num > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Nat__Onat_001t__Num__Onum,type,
% 6.92/7.10 comp_num_nat_num: ( num > nat ) > ( num > num ) > num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Num__Onum_001t__Num__Onum,type,
% 6.92/7.10 comp_num_num_num: ( num > num ) > ( num > num ) > num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 6.92/7.10 comp_n6731957995704128387um_num: ( num > option_num ) > ( num > num ) > num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 comp_o7188567781464924208nteger: ( option8057788054806935849nteger > option7428179582072448501nteger ) > ( option_Code_integer > option8057788054806935849nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Code____Numeral__Ointeger_J_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Option__Ooption_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 comp_o9011007105448239796nteger: ( option_Code_integer > option7428179582072448501nteger ) > ( option_Code_integer > option_Code_integer ) > option_Code_integer > option7428179582072448501nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Nat__Onat_001t__Option__Ooption_It__Int__Oint_J,type,
% 6.92/7.10 comp_o5073597352248849069on_int: ( option_int > nat ) > ( option_int > option_int ) > option_int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Int__Oint_J_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Int__Oint_J,type,
% 6.92/7.10 comp_o4824269118391204861on_int: ( option_int > option_nat ) > ( option_int > option_int ) > option_int > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Nat__Onat_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 comp_o6878144249584144265on_num: ( option_num > nat ) > ( option_num > option_num ) > option_num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 comp_o8931257242830428707on_num: ( option_num > option_num ) > ( option_num > option_num ) > option_num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 6.92/7.10 comp_P3118722334806803912t_unit: ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > ( heap_e7401611519738050253t_unit > produc8664842809031399944it_nat ) > heap_e7401611519738050253t_unit > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 6.92/7.10 comp_P8552900652980440422t_unit: ( produc3260487557148687353it_nat > option3562590408128118217it_nat ) > ( heap_e7401611519738050253t_unit > produc3260487557148687353it_nat ) > heap_e7401611519738050253t_unit > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 6.92/7.10 comp_P6401406225962756324t_unit: ( produc7388388658123137530it_nat > option4065278094766928714it_nat ) > ( heap_e7401611519738050253t_unit > produc7388388658123137530it_nat ) > heap_e7401611519738050253t_unit > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ocomp_001t__Rat__Orat_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 comp_rat_nat_nat: ( rat > nat ) > ( nat > rat ) > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001_Eo,type,
% 6.92/7.10 id_o: $o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001t__Int__Oint,type,
% 6.92/7.10 id_int: int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 6.92/7.10 id_nat: nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oid_001t__Num__Onum,type,
% 6.92/7.10 id_num: num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 6.92/7.10 map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo_001_Eo,type,
% 6.92/7.10 map_fu6957801986076833569nt_o_o: ( code_integer > int ) > ( $o > $o ) > ( int > $o ) > code_integer > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
% 6.92/7.10 map_fu6256889081107267320ural_o: ( code_natural > nat ) > ( ( nat > $o ) > code_natural > $o ) > ( nat > nat > $o ) > code_natural > code_natural > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 6.92/7.10 map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_Eo_001_Eo,type,
% 6.92/7.10 map_fu4892316939951275536at_o_o: ( code_natural > nat ) > ( $o > $o ) > ( nat > $o ) > code_natural > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 6.92/7.10 map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 6.92/7.10 map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 6.92/7.10 map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 6.92/7.10 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 6.92/7.10 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 6.92/7.10 map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 6.92/7.10 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 6.92/7.10 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun__Def_Omax__strict,type,
% 6.92/7.10 fun_max_strict: set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun__Def_Omax__weak,type,
% 6.92/7.10 fun_max_weak: set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Fun__Def_Omin__strict,type,
% 6.92/7.10 fun_min_strict: set_Pr4329608150637261639at_nat ).
% 6.92/7.10
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 6.92/7.10 ring_1_Ints_int: set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 6.92/7.10 ring_1_Ints_rat: set_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 ring_18347121197199848620nteger: int > code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 6.92/7.10 ring_1_of_int_int: int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 6.92/7.10 ring_1_of_int_rat: int > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 6.92/7.10 inf_in2641120393918057659_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 6.92/7.10 inf_in3295504058751909687_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_Eo_M_Eo_J,type,
% 6.92/7.10 inf_inf_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 6.92/7.10 inf_inf_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 inf_inf_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 inf_inf_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 6.92/7.10 inf_inf_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
% 6.92/7.10 inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 inf_in5163264567034779214_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 inf_inf_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 6.92/7.10 inf_in5102985939729578038_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__a_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 6.92/7.10 inf_in8051596381320575356_nat_o: ( a > produc6653097349344004940it_nat > $o ) > ( a > produc6653097349344004940it_nat > $o ) > a > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__b_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 6.92/7.10 inf_in844129575377303227_nat_o: ( b > produc6653097349344004940it_nat > $o ) > ( b > produc6653097349344004940it_nat > $o ) > b > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
% 6.92/7.10 inf_inf_assn: assn > assn > assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 6.92/7.10 inf_inf_int: int > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 6.92/7.10 inf_inf_nat: nat > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 6.92/7.10 inf_in7104746047340619750_int_o: option1893999432384633940_int_o > option1893999432384633940_int_o > option1893999432384633940_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Assertions__Oassn_J,type,
% 6.92/7.10 inf_inf_option_assn: option_assn > option_assn > option_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Nat__Onat_J,type,
% 6.92/7.10 inf_inf_option_nat: option_nat > option_nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 inf_in7812914138253463912et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 inf_in777885744494410645at_nat: option8963830502488799655at_nat > option8963830502488799655at_nat > option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
% 6.92/7.10 inf_inf_Product_unit: product_unit > product_unit > product_unit ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
% 6.92/7.10 inf_inf_rat: rat > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 inf_inf_set_o: set_o > set_o > set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Assertions__Oassn_J,type,
% 6.92/7.10 inf_inf_set_assn: set_assn > set_assn > set_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 inf_inf_set_int: set_int > set_int > set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 6.92/7.10 inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Num__Onum_J,type,
% 6.92/7.10 inf_inf_set_num: set_num > set_num > set_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
% 6.92/7.10 inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.92/7.10 inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 inf_in3493107508024165057it_nat: set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 inf_in3995795194662975554it_nat: set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
% 6.92/7.10 inf_inf_set_rat: set_rat > set_rat > set_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 inf_inf_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 6.92/7.10 inf_in8396524679539076455nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Assertions__Oassn,type,
% 6.92/7.10 semila8603258263270017530r_assn: ( assn > assn > assn ) > assn > ( assn > assn > $o ) > ( assn > assn > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 6.92/7.10 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 semila2554085542299052326_set_o: ( set_o > set_o > set_o ) > set_o > ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 semila6712789903965657268et_int: ( set_int > set_int > set_int ) > set_int > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 semila1667268886620078168et_nat: ( set_nat > set_nat > set_nat ) > set_nat > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 semila5207306265035627125at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 semila4918476307565957903at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 semila6534579987270727413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_Eo_M_Eo_J,type,
% 6.92/7.10 sup_sup_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 6.92/7.10 sup_sup_int_int_o: ( int > int > $o ) > ( int > int > $o ) > int > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 sup_sup_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 sup_sup_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su2200014604384089602_nat_o: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 6.92/7.10 sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 6.92/7.10 sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 sup_su8463660629351352368_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 6.92/7.10 sup_su6256023009775730178_nat_o: ( produc4166570645942440679at_nat > $o ) > ( produc4166570645942440679at_nat > $o ) > produc4166570645942440679at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su362511073950362882_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 6.92/7.10 sup_su2080679670758317954_nat_o: ( produc3843707927480180839at_nat > $o ) > ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 6.92/7.10 sup_sup_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 6.92/7.10 sup_su1852724690005176016_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su7519161239522478338_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su2191776239474528790_nat_o: ( a > produc6653097349344004940it_nat > $o ) > ( a > produc6653097349344004940it_nat > $o ) > a > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__b_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 6.92/7.10 sup_su4207681470386032469_nat_o: ( b > produc6653097349344004940it_nat > $o ) > ( b > produc6653097349344004940it_nat > $o ) > b > produc6653097349344004940it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 6.92/7.10 sup_sup_assn: assn > assn > assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 6.92/7.10 sup_sup_int: int > int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 6.92/7.10 sup_sup_nat: nat > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Int__Oint_J,type,
% 6.92/7.10 sup_sup_option_int: option_int > option_int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Nat__Onat_J,type,
% 6.92/7.10 sup_sup_option_nat: option_nat > option_nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 sup_su3598758113090618626et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 6.92/7.10 sup_su5873096292857799009at_nat: option2498585697089621389at_nat > option2498585697089621389at_nat > option2498585697089621389at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 6.92/7.10 sup_su2273273666271716065at_nat: option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 6.92/7.10 sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 6.92/7.10 sup_sup_rat: rat > rat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 sup_sup_set_o: set_o > set_o > set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 sup_sup_set_int: set_int > set_int > set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 6.92/7.10 sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Num__Onum_J,type,
% 6.92/7.10 sup_sup_set_num: set_num > set_num > set_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
% 6.92/7.10 sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.92/7.10 sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 sup_su3035147773818789531at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 sup_su3211442154794319707it_nat: set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.10 sup_su3714129841433130204it_nat: set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat > set_Pr7600907837789447088it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
% 6.92/7.10 sup_sup_set_rat: set_rat > set_rat > set_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 6.92/7.10 sup_su2047564715030645325nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 6.92/7.10 lattic8263393255366662781ax_int: set_int > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 6.92/7.10 lattic8265883725875713057ax_nat: set_nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 lattic8660852769118194346_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Assertions__Oassn,type,
% 6.92/7.10 lattic5623431474481994958t_assn: ( assn > assn > assn ) > ( assn > assn > $o ) > ( assn > assn > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Int__Oint,type,
% 6.92/7.10 lattic6006661108824415698et_int: ( int > int > int ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Nat__Onat,type,
% 6.92/7.10 lattic6009151579333465974et_nat: ( nat > nat > nat ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Num__Onum,type,
% 6.92/7.10 lattic2566483365489244608et_num: ( num > num > num ) > ( num > num > $o ) > ( num > num > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Rat__Orat,type,
% 6.92/7.10 lattic5374021519246970238et_rat: ( rat > rat > rat ) > ( rat > rat > $o ) > ( rat > rat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 lattic8154731777541915528et_int: ( set_int > set_int > set_int ) > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 lattic3109210760196336428et_nat: ( set_nat > set_nat > set_nat ) > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 lattic5174734335190411425at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 lattic6529551498584149819at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 lattic6976360593897529633at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 6.92/7.10 append_int: list_int > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 6.92/7.10 append_nat: list_nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 6.92/7.10 butlast_nat: list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 6.92/7.10 drop_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oenumerate_001_Eo,type,
% 6.92/7.10 enumerate_o: nat > list_o > list_P7333126701944960589_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
% 6.92/7.10 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 6.92/7.10 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 6.92/7.10 filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001_Eo,type,
% 6.92/7.10 find_o: ( $o > $o ) > list_o > option_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Int__Oint,type,
% 6.92/7.10 find_int: ( int > $o ) > list_int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Nat__Onat,type,
% 6.92/7.10 find_nat: ( nat > $o ) > list_nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Num__Onum,type,
% 6.92/7.10 find_num: ( num > $o ) > list_num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 find_P5317947125398478060it_nat: ( produc8664842809031399944it_nat > $o ) > list_P626663023886443800it_nat > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 find_P4815471733760996061it_nat: ( produc3260487557148687353it_nat > $o ) > list_P6935614879863011209it_nat > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ofind_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 find_P8943372834735446238it_nat: ( produc7388388658123137530it_nat > $o ) > list_P7438302566501821706it_nat > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 6.92/7.10 last_nat: list_nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 6.92/7.10 linord2614967742042102400et_nat: set_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 6.92/7.10 cons_P6219271836124797827_nat_o: ( produc3658429121746597890et_nat > $o ) > list_P7985473006766602707_nat_o > list_P7985473006766602707_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 6.92/7.10 cons_o: $o > list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 6.92/7.10 cons_int: int > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 6.92/7.10 cons_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 6.92/7.10 cons_num: num > list_num > list_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 cons_option_num: option_num > list_option_num > list_option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 cons_P6329468272379687876et_nat: produc2732055786443039994et_nat > list_P362550909693114634et_nat > list_P362550909693114634et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 cons_P3419706843779801160et_nat: produc3925858234332021118et_nat > list_P2321686559999237006et_nat > list_P2321686559999237006et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 cons_P7873165156130251286it_nat: produc6653097349344004940it_nat > list_P131111800688179804it_nat > list_P131111800688179804it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 cons_P2869003950965171916et_nat: produc3658429121746597890et_nat > list_P9062070895058802706et_nat > list_P9062070895058802706et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 6.92/7.10 cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 6.92/7.10 cons_P2335045147070616083at_int: product_prod_nat_int > list_P3521021558325789923at_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 cons_P4136552807766418642it_nat: produc8664842809031399944it_nat > list_P626663023886443800it_nat > list_P626663023886443800it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 cons_P2339423585217329347it_nat: produc3260487557148687353it_nat > list_P6935614879863011209it_nat > list_P6935614879863011209it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 cons_P6467324686191779524it_nat: produc7388388658123137530it_nat > list_P7438302566501821706it_nat > list_P7438302566501821706it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001t__Rat__Orat,type,
% 6.92/7.10 cons_rat: rat > list_rat > list_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001tf__a,type,
% 6.92/7.10 cons_a: a > list_a > list_a ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_OCons_001tf__b,type,
% 6.92/7.10 cons_b: b > list_b > list_b ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 6.92/7.10 nil_int: list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 6.92/7.10 nil_nat: list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 6.92/7.10 hd_nat: list_nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 6.92/7.10 set_int2: list_int > set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001_Eo,type,
% 6.92/7.10 nth_o: list_o > nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 6.92/7.10 nth_int: list_int > nat > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 6.92/7.10 nth_nat: list_nat > nat > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 6.92/7.10 nth_num: list_num > nat > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Option__Ooption_It__Num__Onum_J,type,
% 6.92/7.10 nth_option_num: list_option_num > nat > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 6.92/7.10 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 6.92/7.10 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr4561283279332054789it_nat: list_P131111800688179804it_nat > nat > produc6653097349344004940it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
% 6.92/7.10 nth_Pr7514405829937366042_int_o: list_P5087981734274514673_int_o > nat > product_prod_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr8617346907841251940nt_nat: list_P8198026277950538467nt_nat > nat > product_prod_int_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 6.92/7.10 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 6.92/7.10 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 nth_Pr2956344619228612545it_nat: list_P626663023886443800it_nat > nat > produc8664842809031399944it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 nth_Pr8687047199098054322it_nat: list_P6935614879863011209it_nat > nat > produc3260487557148687353it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 nth_Pr3591576263217728691it_nat: list_P7438302566501821706it_nat > nat > produc7388388658123137530it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Product____Type__Ounit,type,
% 6.92/7.10 nth_Product_unit: list_Product_unit > nat > product_unit ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001t__Rat__Orat,type,
% 6.92/7.10 nth_rat: list_rat > nat > rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Onth_001tf__b,type,
% 6.92/7.10 nth_b: list_b > nat > b ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 6.92/7.10 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 6.92/7.10 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 6.92/7.10 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Int__Oint_001_Eo,type,
% 6.92/7.10 product_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.10 product_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 6.92/7.10 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 product_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oproduct_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 produc1870533552098665926it_nat: list_b > list_P131111800688179804it_nat > list_P7438302566501821706it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate1_001_Eo,type,
% 6.92/7.10 rotate1_o: list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 6.92/7.10 rotate1_int: list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 6.92/7.10 rotate1_nat: list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate_001_Eo,type,
% 6.92/7.10 rotate_o: nat > list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate_001t__Int__Oint,type,
% 6.92/7.10 rotate_int: nat > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Orotate_001t__Nat__Onat,type,
% 6.92/7.10 rotate_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001_Eo,type,
% 6.92/7.10 sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 6.92/7.10 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 6.92/7.10 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Num__Onum,type,
% 6.92/7.10 sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Osorted__wrt_001t__Rat__Orat,type,
% 6.92/7.10 sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 6.92/7.10 take_nat: nat > list_nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupt,type,
% 6.92/7.10 upt: nat > nat > list_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupto,type,
% 6.92/7.10 upto: int > int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupto__aux,type,
% 6.92/7.10 upto_aux: int > int > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Oupto__rel,type,
% 6.92/7.10 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 zip_Pr8136144321567152340et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 zip_Pr7134870689397686104et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 6.92/7.10 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 6.92/7.10 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 6.92/7.10 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Int__Oint_001_Eo,type,
% 6.92/7.10 zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.10 zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Nat__Onat_001_Eo,type,
% 6.92/7.10 zip_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 zip_a_1859587264247984595it_nat: list_a > list_P131111800688179804it_nat > list_P6935614879863011209it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_List_Ozip_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 zip_b_5987488365222434772it_nat: list_b > list_P131111800688179804it_nat > list_P7438302566501821706it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Int__Oint,type,
% 6.92/7.10 eps_Opt_int: ( int > $o ) > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Num__Onum,type,
% 6.92/7.10 eps_Opt_num: ( num > $o ) > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 eps_Op6423059015816587746et_nat: ( produc3925858234332021118et_nat > $o ) > option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 eps_Op8301357815426737072it_nat: ( produc6653097349344004940it_nat > $o ) > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 eps_Op2013419657081471078et_nat: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 eps_Op3393321821070424684it_nat: ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 eps_Op1741419982095519837it_nat: ( produc3260487557148687353it_nat > $o ) > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_OEps__Opt_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 eps_Op5869321083069970014it_nat: ( produc7388388658123137530it_nat > $o ) > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 bijective_int_int: set_Pr958786334691620121nt_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 biject5714339216877808333at_nat: set_Pr8551490117392284871at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 biject3503750217840948301at_nat: set_Pr8693737435421807431at_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 biject8592306251674886141it_nat: set_Pr7098220151150636591it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Obijective_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 biject3496835315794560510it_nat: set_Pr7600907837789447088it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001_Eo,type,
% 6.92/7.10 dflt_None_set_o: set_o > option_set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001t__Int__Oint,type,
% 6.92/7.10 dflt_None_set_int: set_int > option_set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001t__Nat__Onat,type,
% 6.92/7.10 dflt_None_set_nat: set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Odflt__None__set_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 6.92/7.10 dflt_N6592383573632408824at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Omap__to__set_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 map_to_set_int_int: ( int > option_int ) > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Omap__to__set_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 map_to_set_nat_nat: ( nat > option_nat ) > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 rel_of7774016450764239315et_nat: ( ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat ) > ( produc2732055786443039994et_nat > $o ) > set_Pr8536935166611901872et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 rel_of4838799251197538391et_nat: ( ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ) > ( produc3925858234332021118et_nat > $o ) > set_Pr3286484037609594932et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 rel_of_int_int: ( int > option_int ) > ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 rel_of_nat_nat: ( nat > option_nat ) > ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 rel_of2761222537318653906it_nat: ( a > option233860712434008220it_nat ) > ( produc3260487557148687353it_nat > $o ) > set_Pr7098220151150636591it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Orel__of_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 rel_of6889123638293104083it_nat: ( b > option233860712434008220it_nat ) > ( produc7388388658123137530it_nat > $o ) > set_Pr7600907837789447088it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 set_to2047380710992656148et_nat: set_Pr8536935166611901872et_nat > ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 set_to6040779677306527128et_nat: set_Pr3286484037609594932et_nat > ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.10 set_to_map_int_int: set_Pr958786334691620121nt_int > int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001t__Nat__Onat_001t__Nat__Onat,type,
% 6.92/7.10 set_to_map_nat_nat: set_Pr1261947904930325089at_nat > nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001tf__a_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 set_to2008915276733485075it_nat: set_Pr7098220151150636591it_nat > a > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oset__to__map_001tf__b_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 set_to6136816377707935252it_nat: set_Pr7600907837789447088it_nat > b > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oslice_001_Eo,type,
% 6.92/7.10 slice_o: nat > nat > list_o > list_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 6.92/7.10 slice_int: nat > nat > list_int > list_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Num_Opred__numeral,type,
% 6.92/7.10 pred_numeral: num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Num_Osqr,type,
% 6.92/7.10 sqr: num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__Num__Onum,type,
% 6.92/7.10 combine_options_num: ( num > num > num ) > option_num > option_num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 combin4318129983670048329it_nat: ( produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 combin5819755802923621690it_nat: ( produc3260487557148687353it_nat > produc3260487557148687353it_nat > produc3260487557148687353it_nat ) > option3562590408128118217it_nat > option3562590408128118217it_nat > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ocombine__options_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 combin724284867043296059it_nat: ( produc7388388658123137530it_nat > produc7388388658123137530it_nat > produc7388388658123137530it_nat ) > option4065278094766928714it_nat > option4065278094766928714it_nat > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 none_P2320557853698873699_int_o: option1893999432384633940_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Assertions__Oassn,type,
% 6.92/7.10 none_assn: option_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 6.92/7.10 none_nat: option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 6.92/7.10 none_num: option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 none_P199884684680593241et_nat: option2860828798490689354et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 none_P4972525538344268765et_nat: option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 none_P2377608414092835994nt_int: option4624381673175914239nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 none_P9117596204409417319it_nat: option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 none_P2651198173097904984it_nat: option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 none_P6779099274072355161it_nat: option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 none_set_o: option_set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 none_set_int: option_set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 none_set_nat: option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_ONone_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 none_s625347054029921090at_nat: option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.10 some_P180497116919641311_int_o: ( product_prod_int_int > $o ) > option1893999432384633940_int_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001_Eo,type,
% 6.92/7.10 some_o: $o > option_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Assertions__Oassn,type,
% 6.92/7.10 some_assn: assn > option_assn ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Int__Oint,type,
% 6.92/7.10 some_int: int > option_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 6.92/7.10 some_nat: nat > option_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 6.92/7.10 some_num: num > option_num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 some_P1630309045189364437et_nat: produc2732055786443039994et_nat > option2860828798490689354et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 6.92/7.10 some_P750831030444334937et_nat: produc3925858234332021118et_nat > option5190343406534369742et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_I_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P3509045262911171395it_nat: produc8032495849646651230it_nat > option1013472963438093988it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_It__Int__Oint_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P8650484732927216191it_nat: produc7196121022310644452it_nat > option2555668343544256180it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oarray_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P8206036975937309155it_nat: produc6751673265320737416it_nat > option4277301481530639448it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J,type,
% 6.92/7.10 some_P1054239925786823975it_nat: produc6653097349344004940it_nat > option233860712434008220it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.10 some_P624177172695371229et_nat: produc3658429121746597890et_nat > option936205604648967762et_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 6.92/7.10 some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P1914260805536162275it_nat: produc8664842809031399944it_nat > option8956607266484857688it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P7913643980934408916it_nat: produc3260487557148687353it_nat > option3562590408128118217it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_P2818173045054083285it_nat: produc7388388658123137530it_nat > option4065278094766928714it_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Rat__Orat,type,
% 6.92/7.10 some_rat: rat > option_rat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_I_Eo_J,type,
% 6.92/7.10 some_set_o: set_o > option_set_o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 some_set_int: set_int > option_set_int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.10 some_set_nat: set_nat > option_set_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 some_s287724117700012716at_nat: set_Pr8551490117392284871at_nat > option2498585697089621389at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 some_s147305329494351046at_nat: set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.10 some_s5890477192898017836at_nat: set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.10 case_o1441893360019914891nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 6.92/7.10 case_o7134296353695833103nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Assertions__Oassn,type,
% 6.92/7.10 case_option_o_assn: $o > ( assn > $o ) > option_assn > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Int__Oint,type,
% 6.92/7.10 case_option_o_int: $o > ( int > $o ) > option_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Nat__Onat,type,
% 6.92/7.10 case_option_o_nat: $o > ( nat > $o ) > option_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Num__Onum,type,
% 6.92/7.10 case_option_o_num: $o > ( num > $o ) > option_num > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 case_o2686588417244861013it_nat: $o > ( produc8664842809031399944it_nat > $o ) > option8956607266484857688it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 case_o3267218206291580230it_nat: $o > ( produc3260487557148687353it_nat > $o ) > option3562590408128118217it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.10 case_o7395119307266030407it_nat: $o > ( produc7388388658123137530it_nat > $o ) > option4065278094766928714it_nat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Rat__Orat,type,
% 6.92/7.10 case_option_o_rat: $o > ( rat > $o ) > option_rat > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.10 case_o223999843215110191et_int: $o > ( set_int > $o ) > option_set_int > $o ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Code____Numeral__Onatural_001t__Num__Onum,type,
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% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 6.92/7.10 case_option_int_num: int > ( num > int ) > option_num > int ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.10 case_option_nat_int: nat > ( int > nat ) > option_int > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Num__Onum,type,
% 6.92/7.10 case_option_nat_num: nat > ( num > nat ) > option_num > nat ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 6.92/7.10 case_option_num_num: num > ( num > num ) > option_num > num ).
% 6.92/7.10
% 6.92/7.10 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_I_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.11 case_o670596351732880613_int_o: option1893999432384633940_int_o > ( ( product_prod_int_int > $o ) > option1893999432384633940_int_o ) > option1893999432384633940_int_o > option1893999432384633940_int_o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Assertions__Oassn_J_001t__Assertions__Oassn,type,
% 6.92/7.11 case_o4484465799723439917n_assn: option_assn > ( assn > option_assn ) > option_assn > option_assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Int__Oint_J_001t__Int__Oint,type,
% 6.92/7.11 case_o390784466056649525nt_int: option_int > ( int > option_int ) > option_int > option_int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat,type,
% 6.92/7.11 case_o7429725398727453821at_nat: option_nat > ( nat > option_nat ) > option_nat > option_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 6.92/7.11 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o2963978774867076333it_nat: option8956607266484857688it_nat > ( produc8664842809031399944it_nat > option8956607266484857688it_nat ) > option8956607266484857688it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o7727800614283616222it_nat: option8956607266484857688it_nat > ( produc3260487557148687353it_nat > option8956607266484857688it_nat ) > option3562590408128118217it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o2632329678403290591it_nat: option8956607266484857688it_nat > ( produc7388388658123137530it_nat > option8956607266484857688it_nat ) > option4065278094766928714it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o6061097939050036047it_nat: option3562590408128118217it_nat > ( produc3260487557148687353it_nat > option3562590408128118217it_nat ) > option3562590408128118217it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o965627003169710416it_nat: option3562590408128118217it_nat > ( produc7388388658123137530it_nat > option3562590408128118217it_nat ) > option4065278094766928714it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o1773283271472524752it_nat: option4065278094766928714it_nat > ( produc3260487557148687353it_nat > option4065278094766928714it_nat ) > option3562590408128118217it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o5901184372446974929it_nat: option4065278094766928714it_nat > ( produc7388388658123137530it_nat > option4065278094766928714it_nat ) > option4065278094766928714it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.11 case_o4054078431260844265et_nat: option_set_nat > ( set_nat > option_set_nat ) > option_set_nat > option_set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.11 case_o8757249484648823045at_nat: option2498585697089621389at_nat > ( set_Pr8551490117392284871at_nat > option2498585697089621389at_nat ) > option2498585697089621389at_nat > option2498585697089621389at_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 case_o311359030874850053at_nat: option8963830502488799655at_nat > ( set_Pr1261947904930325089at_nat > option8963830502488799655at_nat ) > option8963830502488799655at_nat > option8963830502488799655at_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 6.92/7.11 case_o9080059180780454917at_nat: option1583680563626158861at_nat > ( set_Pr4329608150637261639at_nat > option1583680563626158861at_nat ) > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 6.92/7.11 map_op3563471509957180299nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option8057788054806935849nteger > option7428179582072448501nteger ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 6.92/7.11 map_op370346339404370627nteger: ( code_integer > code_integer > code_integer ) > option_Code_integer > option8057788054806935849nteger ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 6.92/7.11 map_op9146685272036663823nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > option_Code_integer > option7428179582072448501nteger ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 6.92/7.11 map_op3669829223712506439nteger: ( code_integer > code_integer ) > option_Code_integer > option_Code_integer ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Int__Oint,type,
% 6.92/7.11 map_option_int_int: ( int > int ) > option_int > option_int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Int__Oint_001t__Nat__Onat,type,
% 6.92/7.11 map_option_int_nat: ( int > nat ) > option_int > option_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 6.92/7.11 map_option_num_num: ( num > num ) > option_num > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op8118133509425879471it_nat: ( num > produc8664842809031399944it_nat ) > option_num > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op7586128837645442720it_nat: ( num > produc3260487557148687353it_nat ) > option_num > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op2490657901765117089it_nat: ( num > produc7388388658123137530it_nat ) > option_num > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 6.92/7.11 map_op2731889312448867759at_num: ( produc8664842809031399944it_nat > num ) > option8956607266484857688it_nat > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op604423251913076367it_nat: ( produc8664842809031399944it_nat > produc7388388658123137530it_nat ) > option8956607266484857688it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 6.92/7.11 map_op5165227558541518752at_num: ( produc3260487557148687353it_nat > num ) > option3562590408128118217it_nat > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op7599720869725723008it_nat: ( produc3260487557148687353it_nat > produc7388388658123137530it_nat ) > option3562590408128118217it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Num__Onum,type,
% 6.92/7.11 map_op6233829773304596897at_num: ( produc7388388658123137530it_nat > num ) > option4065278094766928714it_nat > option_num ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op8924890681001947535it_nat: ( produc7388388658123137530it_nat > produc8664842809031399944it_nat ) > option4065278094766928714it_nat > option8956607266484857688it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op4453737856117102208it_nat: ( produc7388388658123137530it_nat > produc3260487557148687353it_nat ) > option4065278094766928714it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Omap__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 map_op8581638957091552385it_nat: ( produc7388388658123137530it_nat > produc7388388658123137530it_nat ) > option4065278094766928714it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Int__Oint,type,
% 6.92/7.11 size_option_int: ( int > nat ) > option_int > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 6.92/7.11 size_option_num: ( num > nat ) > option_num > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 size_o29782932136985253it_nat: ( produc8664842809031399944it_nat > nat ) > option8956607266484857688it_nat > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 size_o1731029420616209814it_nat: ( produc3260487557148687353it_nat > nat ) > option3562590408128118217it_nat > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 6.92/7.11 size_o5858930521590659991it_nat: ( produc7388388658123137530it_nat > nat ) > option4065278094766928714it_nat > nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Olinear__order__on_001t__Nat__Onat,type,
% 6.92/7.11 order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Opartial__order__on_001t__Nat__Onat,type,
% 6.92/7.11 order_5251275573222108571on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Opreorder__on_001t__Nat__Onat,type,
% 6.92/7.11 order_4861654808422542329on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
% 6.92/7.11 order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Order__Relation_Owell__order__on_001t__Nat__Onat,type,
% 6.92/7.11 order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 6.92/7.11 bot_bo3790638025767943357_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 6.92/7.11 bot_bo5580076615179976505_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_M_Eo_J,type,
% 6.92/7.11 bot_bot_o_o: $o > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 6.92/7.11 bot_bot_int_int_o: int > int > $o ).
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% 6.92/7.11 thf(sy_c_Product__Type_OPair_001tf__b_001tf__b,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oarray_It__Nat__Onat_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Product____Type__Oprod_It__Heap__Oarray_It__Nat__Onat_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11 produc5645566021302314940it_nat: ( heap_e7401611519738050253t_unit > nat > option3562590408128118217it_nat ) > produc6653097349344004940it_nat > option3562590408128118217it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 6.92/7.11 produc6148253707941125437it_nat: ( heap_e7401611519738050253t_unit > nat > option4065278094766928714it_nat ) > produc6653097349344004940it_nat > option4065278094766928714it_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 6.92/7.11 produc1459180154077124618_int_o: ( int > int > product_prod_int_int > $o ) > product_prod_int_int > product_prod_int_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 6.92/7.11 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_I_Eo_J,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.11 produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.11 produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 6.92/7.11 produc5233655623923918146et_nat: ( int > int > set_set_nat ) > product_prod_int_int > set_set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 6.92/7.11 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 6.92/7.11 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 6.92/7.11 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Ounit_OAbs__unit,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Product__Type_Ounit_ORep__unit,type,
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% 6.92/7.11
% 6.92/7.11 thf(sy_c_Random_Oinc__shift,type,
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11
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% 6.92/7.11 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 6.92/7.11 member_set_int: set_int > set_set_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 6.92/7.11 member_set_nat: set_nat > set_set_nat > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 6.92/7.11 member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_P,type,
% 6.92/7.11 p: assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_Q,type,
% 6.92/7.11 q: b > assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_R,type,
% 6.92/7.11 r: a > assn ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_as____,type,
% 6.92/7.11 as: set_nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_f,type,
% 6.92/7.11 f: heap_Time_Heap_a ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_g,type,
% 6.92/7.11 g: a > heap_Time_Heap_b ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_h_H_H____,type,
% 6.92/7.11 h: heap_e7401611519738050253t_unit ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_h_H____,type,
% 6.92/7.11 h2: heap_e7401611519738050253t_unit ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_h____,type,
% 6.92/7.11 h3: heap_e7401611519738050253t_unit ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_rf____,type,
% 6.92/7.11 rf: a ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_rg____,type,
% 6.92/7.11 rg: b ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_t_H_H____,type,
% 6.92/7.11 t: nat ).
% 6.92/7.11
% 6.92/7.11 thf(sy_v_t_H____,type,
% 6.92/7.11 t2: nat ).
% 6.92/7.11
% 6.92/7.11 % Relevant facts (10207)
% 6.92/7.11 thf(fact_0__092_060open_062new__addrs_Ah_H_A_Inew__addrs_Ah_Aas_Ah_H_J_Ah_H_H_A_061_Anew__addrs_Ah_Aas_Ah_H_H_092_060close_062,axiom,
% 6.92/7.11 ( ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h )
% 6.92/7.11 = ( hoare_new_addrs @ h3 @ as @ h ) ) ).
% 6.92/7.11
% 6.92/7.11 % \<open>new_addrs h' (new_addrs h as h') h'' = new_addrs h as h''\<close>
% 6.92/7.11 thf(fact_1__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_092_060close_062,axiom,
% 6.92/7.11 rep_assn @ p @ ( produc7507926704131184380et_nat @ h3 @ as ) ).
% 6.92/7.11
% 6.92/7.11 % \<open>(h, as) \<Turnstile> P\<close>
% 6.92/7.11 thf(fact_2_new__addr__refl,axiom,
% 6.92/7.11 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 6.92/7.11 ( ( hoare_new_addrs @ H @ As @ H )
% 6.92/7.11 = As ) ).
% 6.92/7.11
% 6.92/7.11 % new_addr_refl
% 6.92/7.11 thf(fact_3_POST__G,axiom,
% 6.92/7.11 rep_assn @ ( q @ rg ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ h ) ) ).
% 6.92/7.11
% 6.92/7.11 % POST_G
% 6.92/7.11 thf(fact_4_POST__F,axiom,
% 6.92/7.11 rep_assn @ ( r @ rf ) @ ( produc7507926704131184380et_nat @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % POST_F
% 6.92/7.11 thf(fact_5_Rep__assn__inject,axiom,
% 6.92/7.11 ! [X: assn,Y: assn] :
% 6.92/7.11 ( ( ( rep_assn @ X )
% 6.92/7.11 = ( rep_assn @ Y ) )
% 6.92/7.11 = ( X = Y ) ) ).
% 6.92/7.11
% 6.92/7.11 % Rep_assn_inject
% 6.92/7.11 thf(fact_6_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 6.92/7.11 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 6.92/7.11 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_7_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_8_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_9_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: b,X2: produc6653097349344004940it_nat,Y1: b,Y2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc4082563078715348724it_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc4082563078715348724it_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_10_prod_Oinject,axiom,
% 6.92/7.11 ! [X1: a,X2: produc6653097349344004940it_nat,Y1: a,Y2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc9178034014595674355it_nat @ X1 @ X2 )
% 6.92/7.11 = ( produc9178034014595674355it_nat @ Y1 @ Y2 ) )
% 6.92/7.11 = ( ( X1 = Y1 )
% 6.92/7.11 & ( X2 = Y2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod.inject
% 6.92/7.11 thf(fact_11_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: int,B: int,A2: int,B2: int] :
% 6.92/7.11 ( ( ( product_Pair_int_int @ A @ B )
% 6.92/7.11 = ( product_Pair_int_int @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_12_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 6.92/7.11 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_13_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 6.92/7.11 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_14_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: b,B: produc6653097349344004940it_nat,A2: b,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc4082563078715348724it_nat @ A @ B )
% 6.92/7.11 = ( produc4082563078715348724it_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_15_old_Oprod_Oinject,axiom,
% 6.92/7.11 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc9178034014595674355it_nat @ A @ B )
% 6.92/7.11 = ( produc9178034014595674355it_nat @ A2 @ B2 ) )
% 6.92/7.11 = ( ( A = A2 )
% 6.92/7.11 & ( B = B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.inject
% 6.92/7.11 thf(fact_16_one__assn__raw_Ocases,axiom,
% 6.92/7.11 ! [X: produc3658429121746597890et_nat] :
% 6.92/7.11 ~ ! [H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.11 ( X
% 6.92/7.11 != ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % one_assn_raw.cases
% 6.92/7.11 thf(fact_17_times__assn__raw_Ocases,axiom,
% 6.92/7.11 ! [X: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As2: set_nat] :
% 6.92/7.11 ( X
% 6.92/7.11 != ( produc2245416461498447860et_nat @ P @ ( produc5001842942810119800et_nat @ Q @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % times_assn_raw.cases
% 6.92/7.11 thf(fact_18_prod__induct4,axiom,
% 6.92/7.11 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D: set_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D ) ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct4
% 6.92/7.11 thf(fact_19_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_20_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_21_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc7388388658123137530it_nat > $o,X: produc7388388658123137530it_nat] :
% 6.92/7.11 ( ! [A3: b,B3: heap_e7401611519738050253t_unit,C: nat] : ( P2 @ ( produc4082563078715348724it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_22_prod__induct3,axiom,
% 6.92/7.11 ! [P2: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 6.92/7.11 ( ! [A3: a,B3: heap_e7401611519738050253t_unit,C: nat] : ( P2 @ ( produc9178034014595674355it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) )
% 6.92/7.11 => ( P2 @ X ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_induct3
% 6.92/7.11 thf(fact_23_prod__cases4,axiom,
% 6.92/7.11 ! [Y: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D: set_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases4
% 6.92/7.11 thf(fact_24_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc3925858234332021118et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_25_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_26_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc7388388658123137530it_nat] :
% 6.92/7.11 ~ ! [A3: b,B3: heap_e7401611519738050253t_unit,C: nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc4082563078715348724it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_27_prod__cases3,axiom,
% 6.92/7.11 ! [Y: produc3260487557148687353it_nat] :
% 6.92/7.11 ~ ! [A3: a,B3: heap_e7401611519738050253t_unit,C: nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc9178034014595674355it_nat @ A3 @ ( produc584006145561248582it_nat @ B3 @ C ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases3
% 6.92/7.11 thf(fact_28_Pair__inject,axiom,
% 6.92/7.11 ! [A: int,B: int,A2: int,B2: int] :
% 6.92/7.11 ( ( ( product_Pair_int_int @ A @ B )
% 6.92/7.11 = ( product_Pair_int_int @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_29_Pair__inject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 6.92/7.11 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_30_Pair__inject,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 6.92/7.11 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_31_Pair__inject,axiom,
% 6.92/7.11 ! [A: b,B: produc6653097349344004940it_nat,A2: b,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc4082563078715348724it_nat @ A @ B )
% 6.92/7.11 = ( produc4082563078715348724it_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_32_Pair__inject,axiom,
% 6.92/7.11 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( produc9178034014595674355it_nat @ A @ B )
% 6.92/7.11 = ( produc9178034014595674355it_nat @ A2 @ B2 ) )
% 6.92/7.11 => ~ ( ( A = A2 )
% 6.92/7.11 => ( B != B2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Pair_inject
% 6.92/7.11 thf(fact_33_prod__cases,axiom,
% 6.92/7.11 ! [P2: product_prod_int_int > $o,P3: product_prod_int_int] :
% 6.92/7.11 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_34_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc3925858234332021118et_nat > $o,P3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_35_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc2732055786443039994et_nat > $o,P3: produc2732055786443039994et_nat] :
% 6.92/7.11 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_36_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc7388388658123137530it_nat > $o,P3: produc7388388658123137530it_nat] :
% 6.92/7.11 ( ! [A3: b,B3: produc6653097349344004940it_nat] : ( P2 @ ( produc4082563078715348724it_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_37_prod__cases,axiom,
% 6.92/7.11 ! [P2: produc3260487557148687353it_nat > $o,P3: produc3260487557148687353it_nat] :
% 6.92/7.11 ( ! [A3: a,B3: produc6653097349344004940it_nat] : ( P2 @ ( produc9178034014595674355it_nat @ A3 @ B3 ) )
% 6.92/7.11 => ( P2 @ P3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % prod_cases
% 6.92/7.11 thf(fact_38_surj__pair,axiom,
% 6.92/7.11 ! [P3: product_prod_int_int] :
% 6.92/7.11 ? [X3: int,Y3: int] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_39_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc3925858234332021118et_nat] :
% 6.92/7.11 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_40_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc2732055786443039994et_nat] :
% 6.92/7.11 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_41_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc7388388658123137530it_nat] :
% 6.92/7.11 ? [X3: b,Y3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc4082563078715348724it_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_42_surj__pair,axiom,
% 6.92/7.11 ! [P3: produc3260487557148687353it_nat] :
% 6.92/7.11 ? [X3: a,Y3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( P3
% 6.92/7.11 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % surj_pair
% 6.92/7.11 thf(fact_43_bex2I,axiom,
% 6.92/7.11 ! [A: int,B: int,S: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 6.92/7.11 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: int,B3: int] :
% 6.92/7.11 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_44_bex2I,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 6.92/7.11 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_45_bex2I,axiom,
% 6.92/7.11 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 6.92/7.11 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_46_bex2I,axiom,
% 6.92/7.11 ! [A: b,B: produc6653097349344004940it_nat,S: set_Pr7600907837789447088it_nat,P2: b > produc6653097349344004940it_nat > $o] :
% 6.92/7.11 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_47_bex2I,axiom,
% 6.92/7.11 ! [A: a,B: produc6653097349344004940it_nat,S: set_Pr7098220151150636591it_nat,P2: a > produc6653097349344004940it_nat > $o] :
% 6.92/7.11 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ S )
% 6.92/7.11 => ( P2 @ A @ B ) )
% 6.92/7.11 => ? [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A3 @ B3 ) @ S )
% 6.92/7.11 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bex2I
% 6.92/7.11 thf(fact_48_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: product_prod_int_int] :
% 6.92/7.11 ~ ! [A3: int,B3: int] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_49_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc3925858234332021118et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc5001842942810119800et_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc2732055786443039994et_nat] :
% 6.92/7.11 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc2245416461498447860et_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc7388388658123137530it_nat] :
% 6.92/7.11 ~ ! [A3: b,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc4082563078715348724it_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 6.92/7.11 ! [Y: produc3260487557148687353it_nat] :
% 6.92/7.11 ~ ! [A3: a,B3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( Y
% 6.92/7.11 != ( produc9178034014595674355it_nat @ A3 @ B3 ) ) ).
% 6.92/7.11
% 6.92/7.11 % old.prod.exhaust
% 6.92/7.11 thf(fact_53_T1,axiom,
% 6.92/7.11 hoare_hoare_triple_a @ p @ f @ r ).
% 6.92/7.11
% 6.92/7.11 % T1
% 6.92/7.11 thf(fact_54_T2,axiom,
% 6.92/7.11 ! [X: a] : ( hoare_hoare_triple_b @ ( r @ X ) @ ( g @ X ) @ q ) ).
% 6.92/7.11
% 6.92/7.11 % T2
% 6.92/7.11 thf(fact_55_EX__G,axiom,
% 6.92/7.11 ( ( heap_Time_execute_b @ ( g @ rf ) @ h2 )
% 6.92/7.11 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ rg @ ( produc584006145561248582it_nat @ h @ t ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % EX_G
% 6.92/7.11 thf(fact_56_LIM__G,axiom,
% 6.92/7.11 ord_less_eq_nat @ ( lim_Product_unit @ h2 ) @ ( lim_Product_unit @ h ) ).
% 6.92/7.11
% 6.92/7.11 % LIM_G
% 6.92/7.11 thf(fact_57_LIM__F,axiom,
% 6.92/7.11 ord_less_eq_nat @ ( lim_Product_unit @ h3 ) @ ( lim_Product_unit @ h2 ) ).
% 6.92/7.11
% 6.92/7.11 % LIM_F
% 6.92/7.11 thf(fact_58_EX__F,axiom,
% 6.92/7.11 ( ( heap_Time_execute_a @ f @ h3 )
% 6.92/7.11 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ rf @ ( produc584006145561248582it_nat @ h2 @ t2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % EX_F
% 6.92/7.11 thf(fact_59_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: $o,P2: $o > $o] :
% 6.92/7.11 ( ( member_o @ A @ ( collect_o @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_60_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: list_nat,P2: list_nat > $o] :
% 6.92/7.11 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_61_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: set_Pr958786334691620121nt_int,P2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.11 ( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_62_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: set_nat,P2: set_nat > $o] :
% 6.92/7.11 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_63_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: nat,P2: nat > $o] :
% 6.92/7.11 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_64_mem__Collect__eq,axiom,
% 6.92/7.11 ! [A: int,P2: int > $o] :
% 6.92/7.11 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 6.92/7.11 = ( P2 @ A ) ) ).
% 6.92/7.11
% 6.92/7.11 % mem_Collect_eq
% 6.92/7.11 thf(fact_65_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_o] :
% 6.92/7.11 ( ( collect_o
% 6.92/7.11 @ ^ [X4: $o] : ( member_o @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_66_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_list_nat] :
% 6.92/7.11 ( ( collect_list_nat
% 6.92/7.11 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_67_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_se6260736226359567993nt_int] :
% 6.92/7.11 ( ( collec5210948495886036740nt_int
% 6.92/7.11 @ ^ [X4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_68_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_set_nat] :
% 6.92/7.11 ( ( collect_set_nat
% 6.92/7.11 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_69_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_nat] :
% 6.92/7.11 ( ( collect_nat
% 6.92/7.11 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_70_Collect__mem__eq,axiom,
% 6.92/7.11 ! [A4: set_int] :
% 6.92/7.11 ( ( collect_int
% 6.92/7.11 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 6.92/7.11 = A4 ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_mem_eq
% 6.92/7.11 thf(fact_71_Collect__cong,axiom,
% 6.92/7.11 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 6.92/7.11 ( ! [X3: list_nat] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_list_nat @ P2 )
% 6.92/7.11 = ( collect_list_nat @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_72_Collect__cong,axiom,
% 6.92/7.11 ! [P2: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 6.92/7.11 ( ! [X3: set_Pr958786334691620121nt_int] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collec5210948495886036740nt_int @ P2 )
% 6.92/7.11 = ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_73_Collect__cong,axiom,
% 6.92/7.11 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 6.92/7.11 ( ! [X3: set_nat] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_set_nat @ P2 )
% 6.92/7.11 = ( collect_set_nat @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_74_Collect__cong,axiom,
% 6.92/7.11 ! [P2: nat > $o,Q2: nat > $o] :
% 6.92/7.11 ( ! [X3: nat] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_nat @ P2 )
% 6.92/7.11 = ( collect_nat @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_75_Collect__cong,axiom,
% 6.92/7.11 ! [P2: int > $o,Q2: int > $o] :
% 6.92/7.11 ( ! [X3: int] :
% 6.92/7.11 ( ( P2 @ X3 )
% 6.92/7.11 = ( Q2 @ X3 ) )
% 6.92/7.11 => ( ( collect_int @ P2 )
% 6.92/7.11 = ( collect_int @ Q2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % Collect_cong
% 6.92/7.11 thf(fact_76_bijective__def,axiom,
% 6.92/7.11 ( bijective_int_int
% 6.92/7.11 = ( ^ [R: set_Pr958786334691620121nt_int] :
% 6.92/7.11 ( ! [X4: int,Y4: int,Z: int] :
% 6.92/7.11 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: int,Y4: int,Z: int] :
% 6.92/7.11 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_77_bijective__def,axiom,
% 6.92/7.11 ( biject2615096655818420098et_nat
% 6.92/7.11 = ( ^ [R: set_Pr3286484037609594932et_nat] :
% 6.92/7.11 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat,Z: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_78_bijective__def,axiom,
% 6.92/7.11 ( biject1468766312547416318et_nat
% 6.92/7.11 = ( ^ [R: set_Pr8536935166611901872et_nat] :
% 6.92/7.11 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat,Z: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_79_bijective__def,axiom,
% 6.92/7.11 ( biject3496835315794560510it_nat
% 6.92/7.11 = ( ^ [R: set_Pr7600907837789447088it_nat] :
% 6.92/7.11 ( ! [X4: b,Y4: produc6653097349344004940it_nat,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: b,Y4: b,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_80_bijective__def,axiom,
% 6.92/7.11 ( biject8592306251674886141it_nat
% 6.92/7.11 = ( ^ [R: set_Pr7098220151150636591it_nat] :
% 6.92/7.11 ( ! [X4: a,Y4: produc6653097349344004940it_nat,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R )
% 6.92/7.11 & ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Z ) @ R ) )
% 6.92/7.11 => ( Y4 = Z ) )
% 6.92/7.11 & ! [X4: a,Y4: a,Z: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Z ) @ R )
% 6.92/7.11 & ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ Y4 @ Z ) @ R ) )
% 6.92/7.11 => ( X4 = Y4 ) ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % bijective_def
% 6.92/7.11 thf(fact_81_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: int,S2: int,R3: set_Pr958786334691620121nt_int,S3: int] :
% 6.92/7.11 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_82_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: produc3658429121746597890et_nat > $o,S2: produc3658429121746597890et_nat,R3: set_Pr3286484037609594932et_nat,S3: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_83_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: produc3658429121746597890et_nat > $o,S2: produc3925858234332021118et_nat,R3: set_Pr8536935166611901872et_nat,S3: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_84_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: b,S2: produc6653097349344004940it_nat,R3: set_Pr7600907837789447088it_nat,S3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member8682313912305727889it_nat @ ( produc4082563078715348724it_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_85_ssubst__Pair__rhs,axiom,
% 6.92/7.11 ! [R2: a,S2: produc6653097349344004940it_nat,R3: set_Pr7098220151150636591it_nat,S3: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ R2 @ S2 ) @ R3 )
% 6.92/7.11 => ( ( S3 = S2 )
% 6.92/7.11 => ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ssubst_Pair_rhs
% 6.92/7.11 thf(fact_86_curryI,axiom,
% 6.92/7.11 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 6.92/7.11 ( ( F @ ( product_Pair_int_int @ A @ B ) )
% 6.92/7.11 => ( produc175634133007206835_int_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_87_curryI,axiom,
% 6.92/7.11 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 6.92/7.11 => ( produc6216949301066131538_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_88_curryI,axiom,
% 6.92/7.11 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.11 ( ( F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 6.92/7.11 => ( produc5101573711933517782_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_89_curryI,axiom,
% 6.92/7.11 ! [F: produc7388388658123137530it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( F @ ( produc4082563078715348724it_nat @ A @ B ) )
% 6.92/7.11 => ( produc8043051624866120150_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_90_curryI,axiom,
% 6.92/7.11 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.11 ( ( F @ ( produc9178034014595674355it_nat @ A @ B ) )
% 6.92/7.11 => ( produc3709033845735585303_nat_o @ F @ A @ B ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryI
% 6.92/7.11 thf(fact_91_le__some__optE,axiom,
% 6.92/7.11 ! [M: set_int,X: option_set_int] :
% 6.92/7.11 ( ( ord_le353528952715127954et_int @ ( some_set_int @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: set_int] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_set_int @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_set_int @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_92_le__some__optE,axiom,
% 6.92/7.11 ! [M: rat,X: option_rat] :
% 6.92/7.11 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: rat] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_rat @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_rat @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_93_le__some__optE,axiom,
% 6.92/7.11 ! [M: num,X: option_num] :
% 6.92/7.11 ( ( ord_le6622620407824499402on_num @ ( some_num @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: num] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_num @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_num @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_94_le__some__optE,axiom,
% 6.92/7.11 ! [M: nat,X: option_nat] :
% 6.92/7.11 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: nat] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_nat @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_nat @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_95_le__some__optE,axiom,
% 6.92/7.11 ! [M: int,X: option_int] :
% 6.92/7.11 ( ( ord_le1736525451366464988on_int @ ( some_int @ M ) @ X )
% 6.92/7.11 => ~ ! [M2: int] :
% 6.92/7.11 ( ( X
% 6.92/7.11 = ( some_int @ M2 ) )
% 6.92/7.11 => ~ ( ord_less_eq_int @ M @ M2 ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % le_some_optE
% 6.92/7.11 thf(fact_96_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: set_int,B: set_int,C2: set_int,D2: set_int] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_set_int @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_set_int @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_97_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: rat,B: rat,C2: rat,D2: rat] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_rat @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_rat @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_98_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: num,B: num,C2: num,D2: num] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_num @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_num @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_99_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: nat,B: nat,C2: nat,D2: nat] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_nat @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_nat @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_100_ord__eq__le__eq__trans,axiom,
% 6.92/7.11 ! [A: int,B: int,C2: int,D2: int] :
% 6.92/7.11 ( ( A = B )
% 6.92/7.11 => ( ( ord_less_eq_int @ B @ C2 )
% 6.92/7.11 => ( ( C2 = D2 )
% 6.92/7.11 => ( ord_less_eq_int @ A @ D2 ) ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % ord_eq_le_eq_trans
% 6.92/7.11 thf(fact_101_hoare__triple__preI,axiom,
% 6.92/7.11 ! [P2: assn,C2: heap_Time_Heap_a,Q2: a > assn] :
% 6.92/7.11 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.11 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 ) )
% 6.92/7.11 => ( hoare_hoare_triple_a @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % hoare_triple_preI
% 6.92/7.11 thf(fact_102_hoare__triple__preI,axiom,
% 6.92/7.11 ! [P2: assn,C2: heap_Time_Heap_b,Q2: b > assn] :
% 6.92/7.11 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.11 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 ) )
% 6.92/7.11 => ( hoare_hoare_triple_b @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % hoare_triple_preI
% 6.92/7.11 thf(fact_103_hoare__triple__preI,axiom,
% 6.92/7.11 ! [P2: assn,C2: heap_T5738788834812785303t_unit,Q2: product_unit > assn] :
% 6.92/7.11 ( ! [H2: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( rep_assn @ P2 @ H2 )
% 6.92/7.11 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 ) )
% 6.92/7.11 => ( hoare_8945653483474564448t_unit @ P2 @ C2 @ Q2 ) ) ).
% 6.92/7.11
% 6.92/7.11 % hoare_triple_preI
% 6.92/7.11 thf(fact_104_curryD,axiom,
% 6.92/7.11 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 6.92/7.11 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 6.92/7.11 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryD
% 6.92/7.11 thf(fact_105_curryD,axiom,
% 6.92/7.11 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.11 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 6.92/7.11 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 6.92/7.11
% 6.92/7.11 % curryD
% 6.92/7.11 thf(fact_106_curryD,axiom,
% 6.92/7.11 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.12 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryD
% 6.92/7.12 thf(fact_107_curryD,axiom,
% 6.92/7.12 ! [F: produc7388388658123137530it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc8043051624866120150_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryD
% 6.92/7.12 thf(fact_108_curryD,axiom,
% 6.92/7.12 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc3709033845735585303_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryD
% 6.92/7.12 thf(fact_109_curryE,axiom,
% 6.92/7.12 ! [F: product_prod_int_int > $o,A: int,B: int] :
% 6.92/7.12 ( ( produc175634133007206835_int_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_110_curryE,axiom,
% 6.92/7.12 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 6.92/7.12 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_111_curryE,axiom,
% 6.92/7.12 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 6.92/7.12 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_112_curryE,axiom,
% 6.92/7.12 ! [F: produc7388388658123137530it_nat > $o,A: b,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc8043051624866120150_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc4082563078715348724it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_113_curryE,axiom,
% 6.92/7.12 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 6.92/7.12 ( ( produc3709033845735585303_nat_o @ F @ A @ B )
% 6.92/7.12 => ( F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % curryE
% 6.92/7.12 thf(fact_114_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: set_int,Y: set_int] :
% 6.92/7.12 ( ( ord_le353528952715127954et_int @ ( some_set_int @ X ) @ ( some_set_int @ Y ) )
% 6.92/7.12 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_115_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: rat,Y: rat] :
% 6.92/7.12 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 6.92/7.12 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_116_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: num,Y: num] :
% 6.92/7.12 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 6.92/7.12 = ( ord_less_eq_num @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_117_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: nat,Y: nat] :
% 6.92/7.12 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 6.92/7.12 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_118_less__eq__option__Some,axiom,
% 6.92/7.12 ! [X: int,Y: int] :
% 6.92/7.12 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 6.92/7.12 = ( ord_less_eq_int @ X @ Y ) ) ).
% 6.92/7.12
% 6.92/7.12 % less_eq_option_Some
% 6.92/7.12 thf(fact_119_option_Oinject,axiom,
% 6.92/7.12 ! [X2: produc7388388658123137530it_nat,Y2: produc7388388658123137530it_nat] :
% 6.92/7.12 ( ( ( some_P2818173045054083285it_nat @ X2 )
% 6.92/7.12 = ( some_P2818173045054083285it_nat @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_120_option_Oinject,axiom,
% 6.92/7.12 ! [X2: produc3260487557148687353it_nat,Y2: produc3260487557148687353it_nat] :
% 6.92/7.12 ( ( ( some_P7913643980934408916it_nat @ X2 )
% 6.92/7.12 = ( some_P7913643980934408916it_nat @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_121_option_Oinject,axiom,
% 6.92/7.12 ! [X2: produc8664842809031399944it_nat,Y2: produc8664842809031399944it_nat] :
% 6.92/7.12 ( ( ( some_P1914260805536162275it_nat @ X2 )
% 6.92/7.12 = ( some_P1914260805536162275it_nat @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_122_option_Oinject,axiom,
% 6.92/7.12 ! [X2: num,Y2: num] :
% 6.92/7.12 ( ( ( some_num @ X2 )
% 6.92/7.12 = ( some_num @ Y2 ) )
% 6.92/7.12 = ( X2 = Y2 ) ) ).
% 6.92/7.12
% 6.92/7.12 % option.inject
% 6.92/7.12 thf(fact_123_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_124_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_125_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_126_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_127_dual__order_Orefl,axiom,
% 6.92/7.12 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 6.92/7.12
% 6.92/7.12 % dual_order.refl
% 6.92/7.12 thf(fact_128_order__refl,axiom,
% 6.92/7.12 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_129_order__refl,axiom,
% 6.92/7.12 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_130_order__refl,axiom,
% 6.92/7.12 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_131_order__refl,axiom,
% 6.92/7.12 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_132_order__refl,axiom,
% 6.92/7.12 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 6.92/7.12
% 6.92/7.12 % order_refl
% 6.92/7.12 thf(fact_133__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rg_Ah_H_H_At_H_H_O_A_092_060lbrakk_062execute_A_Ig_Arf_J_Ah_H_A_061_ASome_A_Irg_M_Ah_H_H_M_At_H_H_J_059_A_Ih_H_H_M_Anew__addrs_Ah_H_A_Inew__addrs_Ah_Aas_Ah_H_J_Ah_H_H_J_A_092_060Turnstile_062_AQ_Arg_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_H_A_092_060and_062_Aa_A_092_060notin_062_Anew__addrs_Ah_Aas_Ah_H_125_Ah_H_Ah_H_H_059_Alim_Ah_H_A_092_060le_062_Alim_Ah_H_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 6.92/7.12 ~ ! [Rg: b,H3: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ? [T: nat] :
% 6.92/7.12 ( ( heap_Time_execute_b @ ( g @ rf ) @ h2 )
% 6.92/7.12 = ( some_P2818173045054083285it_nat @ ( produc4082563078715348724it_nat @ Rg @ ( produc584006145561248582it_nat @ H3 @ T ) ) ) )
% 6.92/7.12 => ( ( rep_assn @ ( q @ Rg ) @ ( produc7507926704131184380et_nat @ H3 @ ( hoare_new_addrs @ h2 @ ( hoare_new_addrs @ h3 @ as @ h2 ) @ H3 ) ) )
% 6.92/7.12 => ( ( relH
% 6.92/7.12 @ ( collect_nat
% 6.92/7.12 @ ^ [A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 6.92/7.12 & ~ ( member_nat @ A5 @ ( hoare_new_addrs @ h3 @ as @ h2 ) ) ) )
% 6.92/7.12 @ h2
% 6.92/7.12 @ H3 )
% 6.92/7.12 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ h2 ) @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % \<open>\<And>thesis. (\<And>rg h'' t''. \<lbrakk>execute (g rf) h' = Some (rg, h'', t''); (h'', new_addrs h' (new_addrs h as h') h'') \<Turnstile> Q rg; relH {a. a < lim h' \<and> a \<notin> new_addrs h as h'} h' h''; lim h' \<le> lim h''\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 6.92/7.12 thf(fact_134__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rf_Ah_H_At_H_O_A_092_060lbrakk_062execute_Af_Ah_A_061_ASome_A_Irf_M_Ah_H_M_At_H_J_059_A_Ih_H_M_Anew__addrs_Ah_Aas_Ah_H_J_A_092_060Turnstile_062_AR_Arf_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_Ah_Ah_H_059_Alim_Ah_A_092_060le_062_Alim_Ah_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 6.92/7.12 ~ ! [Rf: a,H4: heap_e7401611519738050253t_unit] :
% 6.92/7.12 ( ? [T2: nat] :
% 6.92/7.12 ( ( heap_Time_execute_a @ f @ h3 )
% 6.92/7.12 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Rf @ ( produc584006145561248582it_nat @ H4 @ T2 ) ) ) )
% 6.92/7.12 => ( ( rep_assn @ ( r @ Rf ) @ ( produc7507926704131184380et_nat @ H4 @ ( hoare_new_addrs @ h3 @ as @ H4 ) ) )
% 6.92/7.12 => ( ( relH
% 6.92/7.12 @ ( collect_nat
% 6.92/7.12 @ ^ [A5: nat] :
% 6.92/7.12 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h3 ) )
% 6.92/7.12 & ~ ( member_nat @ A5 @ as ) ) )
% 6.92/7.12 @ h3
% 6.92/7.12 @ H4 )
% 6.92/7.12 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ h3 ) @ ( lim_Product_unit @ H4 ) ) ) ) ) ).
% 6.92/7.12
% 6.92/7.12 % \<open>\<And>thesis. (\<And>rf h' t'. \<lbrakk>execute f h = Some (rf, h', t'); (h', new_addrs h as h') \<Turnstile> R rf; relH {a. a < lim h \<and> a \<notin> as} h h'; lim h \<le> lim h'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<