%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT122^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.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 : Wed Feb 25 08:44:50 AM UTC 2026
% Result : Theorem 3.27s 1.95s
% Output : Refutation 3.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : DAT122^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.08 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.27 % Computer : n024.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Tue Feb 24 01:07:11 EST 2026
% 0.09/0.28 % CPUTime :
% 0.09/0.28 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.37 ---- Original DTF file ---
% 0.17/0.37 thf(spec,logic,$$dhol).
% 0.17/0.37 %------------------------------------------------------------------------------
% 0.17/0.37 % File : DAT122^1 : TPTP v9.2.1. Released v7.0.0.
% 0.17/0.37 % Domain : Data Structures
% 0.17/0.37 % Problem : Coinductive list 1876
% 0.17/0.37 % Version : [Bla16] axioms : Especial.
% 0.17/0.37 % English :
% 0.17/0.37
% 0.17/0.37 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.17/0.37 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.17/0.37 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.17/0.37 % Source : [Bla16]
% 0.17/0.37 % Names : coinductive_list__1876.p [Bla16]
% 0.17/0.37
% 0.17/0.37 % Status : Theorem
% 0.17/0.37 % Rating : 0.00 v7.1.0
% 0.17/0.37 % Syntax : Number of formulae : 402 ( 206 unt; 73 typ; 0 def)
% 0.17/0.37 % Number of atoms : 717 ( 340 equ; 0 cnn)
% 0.17/0.37 % Maximal formula atoms : 8 ( 2 avg)
% 0.17/0.37 % Number of connectives : 4016 ( 156 ~; 40 |; 81 &;3506 @)
% 0.17/0.37 % ( 0 <=>; 233 =>; 0 <=; 0 <~>)
% 0.17/0.37 % Maximal formula depth : 28 ( 7 avg)
% 0.17/0.37 % Number of types : 9 ( 8 usr)
% 0.17/0.37 % Number of type conns : 303 ( 303 >; 0 *; 0 +; 0 <<)
% 0.17/0.37 % Number of symbols : 68 ( 65 usr; 4 con; 0-6 aty)
% 0.17/0.37 % Number of variables : 1090 ( 36 ^; 955 !; 39 ?;1090 :)
% 0.17/0.37 % ( 60 !>; 0 ?*; 0 @-; 0 @+)
% 0.17/0.37 % SPC : TH1_THM_EQU_NAR
% 0.17/0.37
% 0.17/0.37 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.17/0.37 % 2016-07-13 14:53:07.332
% 0.17/0.37 %------------------------------------------------------------------------------
% 0.17/0.37 %----Could-be-implicit typings (15)
% 0.17/0.37 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.17/0.37 coindu1593790203_llist: $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Record_Otuple__isomorphism,type,
% 0.17/0.37 tuple_isomorphism: $tType > $tType > $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Code__Numeral_Onatural,type,
% 0.17/0.37 code_natural: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Code__Evaluation_Oterm,type,
% 0.17/0.37 code_term: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Product__Type_Ounit,type,
% 0.17/0.37 product_unit: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Product__Type_Oprod,type,
% 0.17/0.37 product_prod: $tType > $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Extended__Nat_Oenat,type,
% 0.17/0.37 extended_enat: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Typerep_Otyperep,type,
% 0.17/0.37 typerep: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_String_Oliteral,type,
% 0.17/0.37 literal: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Sum__Type_Osum,type,
% 0.17/0.37 sum_sum: $tType > $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Option_Ooption,type,
% 0.17/0.37 option: $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Set_Oset,type,
% 0.17/0.37 set: $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_Nat_Onat,type,
% 0.17/0.37 nat: $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_t_itself,type,
% 0.17/0.37 itself: $tType > $tType ).
% 0.17/0.37
% 0.17/0.37 thf(ty_tf_a,type,
% 0.17/0.37 a: $tType ).
% 0.17/0.37
% 0.17/0.37 %----Explicit typings (58)
% 0.17/0.37 thf(sy_cl_Enum_Oenum,type,
% 0.17/0.37 enum:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Typerep_Otyperep,type,
% 0.17/0.37 typerep2:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_HOL_Otype,type,
% 0.17/0.37 type:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_HOL_Oequal,type,
% 0.17/0.37 cl_HOL_Oequal:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Code__Evaluation_Oterm__of,type,
% 0.17/0.37 code_term_of:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Nat_Osize,type,
% 0.17/0.37 size:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Groups_Ozero,type,
% 0.17/0.37 zero:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Rings_Osemiring__1,type,
% 0.17/0.37 semiring_1:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Quickcheck__Random_Orandom,type,
% 0.17/0.37 quickcheck_random:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_cl_Divides_Osemiring__numeral__div,type,
% 0.17/0.37 semiring_numeral_div:
% 0.17/0.37 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Code__Numeral_OSuc,type,
% 0.17/0.37 code_Suc: code_natural > code_natural ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
% 0.17/0.37 code_case_natural:
% 0.17/0.37 !>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
% 0.17/0.37 code_rec_natural:
% 0.17/0.37 !>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
% 0.17/0.37 code_size_natural: code_natural > nat ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oiterates,type,
% 0.17/0.37 coindu1529956631erates:
% 0.17/0.37 !>[A: $tType] : ( ( A > A ) > A > ( coindu1593790203_llist @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.17/0.37 coindu268472904append:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 0.17/0.37 coindu300403952lexord:
% 0.17/0.37 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.17/0.37 coindu1121789889_LCons:
% 0.17/0.37 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.17/0.37 coindu1598213697e_LNil:
% 0.17/0.37 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 0.17/0.37 coindu882539134_llist:
% 0.17/0.37 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.17/0.37 coindu1046438764le_lhd:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 0.17/0.37 coindu987187967t_all2:
% 0.17/0.37 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olmap,type,
% 0.17/0.37 coindu1062782156e_lmap:
% 0.17/0.37 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ Aa ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.17/0.37 coindu335574135_lnull:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.17/0.37 coindu1047225960le_ltl:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.17/0.37 coindu567634248member:
% 0.17/0.37 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olnth,type,
% 0.17/0.37 coindu749330388e_lnth:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > nat > A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.17/0.37 coindu1696667936prefix:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.17/0.37 coindu574146665prefix:
% 0.17/0.37 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake,type,
% 0.17/0.37 coindu1802687541_ltake:
% 0.17/0.37 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 0.17/0.37 coindu721411036eWhile:
% 0.17/0.37 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olzip,type,
% 0.17/0.37 coindu847746867e_lzip:
% 0.17/0.37 !>[A: $tType,B: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > ( coindu1593790203_llist @ ( product_prod @ A @ B ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.17/0.37 coindu1599971794_llist:
% 0.17/0.37 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__Nat_Oco_Oenat_Ocase__enat,type,
% 0.17/0.37 coindu440805660e_enat:
% 0.17/0.37 !>[A: $tType] : ( A > ( extended_enat > A ) > extended_enat > A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__Nat_Oco_Oenat_Oepred,type,
% 0.17/0.37 coinductive_epred: extended_enat > extended_enat ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Coinductive__Nat_Oenat__unfold,type,
% 0.17/0.37 coindu1491768222unfold:
% 0.17/0.37 !>[A: $tType] : ( ( A > $o ) > ( A > A ) > A > extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Divides_Osemiring__numeral__div__class_Odivides__aux,type,
% 0.17/0.37 semiri577515795es_aux:
% 0.17/0.37 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Extended__Nat_Oenat_Ocase__enat,type,
% 0.17/0.37 extended_case_enat:
% 0.17/0.37 !>[T: $tType] : ( ( nat > T ) > T > extended_enat > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Extended__Nat_Othe__enat,type,
% 0.17/0.37 extended_the_enat: extended_enat > nat ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.17/0.37 zero_zero:
% 0.17/0.37 !>[A: $tType] : A ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_HOL_Obool_Osize__bool,type,
% 0.17/0.37 size_bool: $o > nat ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 0.17/0.37 default_default:
% 0.17/0.37 !>[A: $tType] : A ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_If,type,
% 0.17/0.37 if:
% 0.17/0.37 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Nat_Oold_Onat_Orec__nat,type,
% 0.17/0.37 rec_nat:
% 0.17/0.37 !>[T: $tType] : ( T > ( nat > T > T ) > nat > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
% 0.17/0.37 semiri532925092at_aux:
% 0.17/0.37 !>[A: $tType] : ( ( A > A ) > nat > A > A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.17/0.37 size_size:
% 0.17/0.37 !>[A: $tType] : ( A > nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_OPair,type,
% 0.17/0.37 product_Pair:
% 0.17/0.37 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_OUnity,type,
% 0.17/0.37 product_Unity: product_unit ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.17/0.37 produc2004651681e_prod:
% 0.17/0.37 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 0.17/0.37 product_rec_bool:
% 0.17/0.37 !>[T: $tType] : ( T > T > $o > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.17/0.37 product_rec_prod:
% 0.17/0.37 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 0.17/0.37 product_rec_unit:
% 0.17/0.37 !>[T: $tType] : ( T > product_unit > T ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
% 0.17/0.37 product_case_unit:
% 0.17/0.37 !>[A: $tType] : ( A > product_unit > A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Product__Type_Ounit_Osize__unit,type,
% 0.17/0.37 product_size_unit: product_unit > nat ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Pure_Otype,type,
% 0.17/0.37 type2:
% 0.17/0.37 !>[A: $tType] : ( itself @ A ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_Set_OCollect,type,
% 0.17/0.37 collect:
% 0.17/0.37 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_c_member,type,
% 0.17/0.37 member:
% 0.17/0.37 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(sy_v_xs,type,
% 0.17/0.37 xs: coindu1593790203_llist @ a ).
% 0.17/0.37
% 0.17/0.37 %----Relevant facts (241)
% 0.17/0.37 thf(fact_0_lzip_Oexhaust,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.17/0.37 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.exhaust
% 0.17/0.37 thf(fact_1_lappend_Oexhaust,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend.exhaust
% 0.17/0.37 thf(fact_2_ltakeWhile_Oexhaust,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.17/0.37 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.exhaust
% 0.17/0.37 thf(fact_3_ltakeWhile_Odisc__iff_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 0.17/0.37 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 & ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.disc_iff(2)
% 0.17/0.37 thf(fact_4_ltakeWhile_Odisc__iff_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.17/0.37 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.disc_iff(1)
% 0.17/0.37 thf(fact_5_ltakeWhile_Odisc_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.disc(2)
% 0.17/0.37 thf(fact_6_ltakeWhile_Odisc_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.disc(1)
% 0.17/0.37 thf(fact_7_ltakeWhile_Osimps_I3_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.simps(3)
% 0.17/0.37 thf(fact_8_zero__natural_Orsp,axiom,
% 0.17/0.37 ( ( zero_zero @ nat )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % zero_natural.rsp
% 0.17/0.37 thf(fact_9_zero__reorient,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( zero @ A @ ( type2 @ A ) )
% 0.17/0.37 => ! [X: A] :
% 0.17/0.37 ( ( ( zero_zero @ A )
% 0.17/0.37 = X )
% 0.17/0.37 = ( X
% 0.17/0.37 = ( zero_zero @ A ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % zero_reorient
% 0.17/0.37 thf(fact_10_lzip_Odisc__iff_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) )
% 0.17/0.37 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 & ~ ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.disc_iff(2)
% 0.17/0.37 thf(fact_11_lzip_Odisc__iff_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 0.17/0.37 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.disc_iff(1)
% 0.17/0.37 thf(fact_12_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,F: A > A,X: A] :
% 0.17/0.37 ( ( coindu1046438764le_lhd @ A @ ( coindu1529956631erates @ A @ F @ X ) )
% 0.17/0.37 = X ) ).
% 0.17/0.37
% 0.17/0.37 % Coinductive_List_Mirabelle_kmikjhschf.iterates.simps(2)
% 0.17/0.37 thf(fact_13_ltake_Oexhaust,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ~ ( ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 | ( coindu335574135_lnull @ A @ Xs ) )
% 0.17/0.37 => ~ ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.exhaust
% 0.17/0.37 thf(fact_14_lzip_Odisc_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.17/0.37 => ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.disc(1)
% 0.17/0.37 thf(fact_15_lzip_Odisc_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.disc(2)
% 0.17/0.37 thf(fact_16_iterates_Odisc__iff,axiom,
% 0.17/0.37 ! [A: $tType,F: A > A,X: A] :
% 0.17/0.37 ~ ( coindu335574135_lnull @ A @ ( coindu1529956631erates @ A @ F @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % iterates.disc_iff
% 0.17/0.37 thf(fact_17_natural_Osize_I1_J,axiom,
% 0.17/0.37 ( ( code_size_natural @ ( zero_zero @ code_natural ) )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.size(1)
% 0.17/0.37 thf(fact_18_natural_Osize_I3_J,axiom,
% 0.17/0.37 ( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.size(3)
% 0.17/0.37 thf(fact_19_lzip_Osimps_I3_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 0.17/0.37 = ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ B @ Ys ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.simps(3)
% 0.17/0.37 thf(fact_20_ltakeWhile_Octr_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.17/0.37 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.ctr(1)
% 0.17/0.37 thf(fact_21_ltakeWhile_Osimps_I4_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.17/0.37 = ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.simps(4)
% 0.17/0.37 thf(fact_22_of__nat__aux_Osimps_I1_J,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( semiring_1 @ A @ ( type2 @ A ) )
% 0.17/0.37 => ! [Inc: A > A,I: A] :
% 0.17/0.37 ( ( semiri532925092at_aux @ A @ Inc @ ( zero_zero @ nat ) @ I )
% 0.17/0.37 = I ) ) ).
% 0.17/0.37
% 0.17/0.37 % of_nat_aux.simps(1)
% 0.17/0.37 thf(fact_23_lnth__0,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu749330388e_lnth @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( zero_zero @ nat ) )
% 0.17/0.37 = X ) ).
% 0.17/0.37
% 0.17/0.37 % lnth_0
% 0.17/0.37 thf(fact_24_llist_Omap__sel_I1_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,A2: coindu1593790203_llist @ A,F: A > B] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 0.17/0.37 = ( F @ ( coindu1046438764le_lhd @ A @ A2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.map_sel(1)
% 0.17/0.37 thf(fact_25_lhd__lappend,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lhd_lappend
% 0.17/0.37 thf(fact_26_old_Onat_Osimps_I6_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: nat > T > T] :
% 0.17/0.37 ( ( rec_nat @ T @ F1 @ F2 @ ( zero_zero @ nat ) )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % old.nat.simps(6)
% 0.17/0.37 thf(fact_27_llist_Oinject,axiom,
% 0.17/0.37 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.17/0.37 = ( ( X21 = Y21 )
% 0.17/0.37 & ( X22 = Y22 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.inject
% 0.17/0.37 thf(fact_28_lappend_Odisc__iff_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.17/0.37 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend.disc_iff(2)
% 0.17/0.37 thf(fact_29_lnull__lappend,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.17/0.37 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lnull_lappend
% 0.17/0.37 thf(fact_30_lappend__code_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_code(2)
% 0.17/0.37 thf(fact_31_llist_Omap__disc__iff,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,F: A > B,A2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 0.17/0.37 = ( coindu335574135_lnull @ A @ A2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.map_disc_iff
% 0.17/0.37 thf(fact_32_lappend__LNil2,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = Xs ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_LNil2
% 0.17/0.37 thf(fact_33_lappend__code_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.17/0.37 = Ys ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_code(1)
% 0.17/0.37 thf(fact_34_ltl__lmap,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( coindu1047225960le_ltl @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.17/0.37 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1047225960le_ltl @ B @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltl_lmap
% 0.17/0.37 thf(fact_35_ltl__lappend,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.17/0.37 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.17/0.37 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltl_lappend
% 0.17/0.37 thf(fact_36_lhd__LCons__ltl,axiom,
% 0.17/0.37 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.17/0.37 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 0.17/0.37 = Llist ) ) ).
% 0.17/0.37
% 0.17/0.37 % lhd_LCons_ltl
% 0.17/0.37 thf(fact_37_eq__LConsD,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Xs
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.17/0.37 => ( ( Xs
% 0.17/0.37 != ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.17/0.37 = Y )
% 0.17/0.37 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 0.17/0.37 = Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % eq_LConsD
% 0.17/0.37 thf(fact_38_llist_Oexhaust__sel,axiom,
% 0.17/0.37 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Llist
% 0.17/0.37 != ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ( Llist
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.exhaust_sel
% 0.17/0.37 thf(fact_39_lappend__ltl,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys )
% 0.17/0.37 = ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_ltl
% 0.17/0.37 thf(fact_40_llist_Omap__sel_I2_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,A2: coindu1593790203_llist @ A,F: A > B] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 0.17/0.37 = ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1047225960le_ltl @ A @ A2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.map_sel(2)
% 0.17/0.37 thf(fact_41_mem__Collect__eq,axiom,
% 0.17/0.37 ! [A: $tType,A2: A,P: A > $o] :
% 0.17/0.37 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.17/0.37 = ( P @ A2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % mem_Collect_eq
% 0.17/0.37 thf(fact_42_Collect__mem__eq,axiom,
% 0.17/0.37 ! [A: $tType,A3: set @ A] :
% 0.17/0.37 ( ( collect @ A
% 0.17/0.37 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.17/0.37 = A3 ) ).
% 0.17/0.37
% 0.17/0.37 % Collect_mem_eq
% 0.17/0.37 thf(fact_43_Collect__cong,axiom,
% 0.17/0.37 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.17/0.37 ( ! [X3: A] :
% 0.17/0.37 ( ( P @ X3 )
% 0.17/0.37 = ( Q @ X3 ) )
% 0.17/0.37 => ( ( collect @ A @ P )
% 0.17/0.37 = ( collect @ A @ Q ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % Collect_cong
% 0.17/0.37 thf(fact_44_ext,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.17/0.37 ( ! [X3: A] :
% 0.17/0.37 ( ( F @ X3 )
% 0.17/0.37 = ( G @ X3 ) )
% 0.17/0.37 => ( F = G ) ) ).
% 0.17/0.37
% 0.17/0.37 % ext
% 0.17/0.37 thf(fact_45_lappend__snocL1__conv__LCons2,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.17/0.37 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_snocL1_conv_LCons2
% 0.17/0.37 thf(fact_46_lmap__lappend__distrib,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu268472904append @ B @ Xs @ Ys ) )
% 0.17/0.37 = ( coindu268472904append @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) @ ( coindu1062782156e_lmap @ B @ A @ F @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lmap_lappend_distrib
% 0.17/0.37 thf(fact_47_lappend__eq__LNil__iff,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( Ys
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_eq_LNil_iff
% 0.17/0.37 thf(fact_48_LNil__eq__lappend__iff,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu1598213697e_LNil @ A )
% 0.17/0.37 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.17/0.37 = ( ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( Ys
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % LNil_eq_lappend_iff
% 0.17/0.37 thf(fact_49_lmap__eq__LCons__conv,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.17/0.37 = ( ? [X2: B,Xs2: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( Xs
% 0.17/0.37 = ( coindu1121789889_LCons @ B @ X2 @ Xs2 ) )
% 0.17/0.37 & ( Y
% 0.17/0.37 = ( F @ X2 ) )
% 0.17/0.37 & ( Ys
% 0.17/0.37 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lmap_eq_LCons_conv
% 0.17/0.37 thf(fact_50_lappend__LNil__LNil,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_LNil_LNil
% 0.17/0.37 thf(fact_51_neq__LNil__conv,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Xs
% 0.17/0.37 != ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( ? [X2: A,Xs2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( Xs
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % neq_LNil_conv
% 0.17/0.37 thf(fact_52_llist_Oexhaust,axiom,
% 0.17/0.37 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Y
% 0.17/0.37 != ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.exhaust
% 0.17/0.37 thf(fact_53_lappend__assoc,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.17/0.37 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_assoc
% 0.17/0.37 thf(fact_54_lmap__eq__LNil,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lmap_eq_LNil
% 0.17/0.37 thf(fact_55_LNil__eq__lmap,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( ( coindu1598213697e_LNil @ A )
% 0.17/0.37 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.17/0.37 = ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % LNil_eq_lmap
% 0.17/0.37 thf(fact_56_llist_Odistinct_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1598213697e_LNil @ A )
% 0.17/0.37 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.distinct(1)
% 0.17/0.37 thf(fact_57_llist_Osimps_I12_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F: A > B] :
% 0.17/0.37 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( coindu1598213697e_LNil @ B ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.simps(12)
% 0.17/0.37 thf(fact_58_llist_Osimps_I13_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.17/0.37 = ( coindu1121789889_LCons @ B @ ( F @ X21 ) @ ( coindu1062782156e_lmap @ A @ B @ F @ X22 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.simps(13)
% 0.17/0.37 thf(fact_59_ltl__simps_I1_J,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltl_simps(1)
% 0.17/0.37 thf(fact_60_ltl__simps_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.17/0.37 = X22 ) ).
% 0.17/0.37
% 0.17/0.37 % ltl_simps(2)
% 0.17/0.37 thf(fact_61_lappend_Octr_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.17/0.37 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend.ctr(1)
% 0.17/0.37 thf(fact_62_lzip_Ocode,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType] :
% 0.17/0.37 ( ( coindu847746867e_lzip @ A @ B )
% 0.17/0.37 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ B] :
% 0.17/0.37 ( if @ ( coindu1593790203_llist @ ( product_prod @ A @ B ) )
% 0.17/0.37 @ ( ( coindu335574135_lnull @ A @ Xs3 )
% 0.17/0.37 | ( coindu335574135_lnull @ B @ Ys2 ) )
% 0.17/0.37 @ ( coindu1598213697e_LNil @ ( product_prod @ A @ B ) )
% 0.17/0.37 @ ( coindu1121789889_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs3 ) @ ( coindu1046438764le_lhd @ B @ Ys2 ) ) @ ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs3 ) @ ( coindu1047225960le_ltl @ B @ Ys2 ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.code
% 0.17/0.37 thf(fact_63_ltakeWhile_Ocode,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu721411036eWhile @ A )
% 0.17/0.37 = ( ^ [P2: A > $o,Xs3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( if @ ( coindu1593790203_llist @ A )
% 0.17/0.37 @ ( ( coindu335574135_lnull @ A @ Xs3 )
% 0.17/0.37 | ~ ( P2 @ ( coindu1046438764le_lhd @ A @ Xs3 ) ) )
% 0.17/0.37 @ ( coindu1598213697e_LNil @ A )
% 0.17/0.37 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs3 ) @ ( coindu721411036eWhile @ A @ P2 @ ( coindu1047225960le_ltl @ A @ Xs3 ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.code
% 0.17/0.37 thf(fact_64_lzip_Octr_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.17/0.37 => ( ( coindu847746867e_lzip @ A @ B @ Xs @ Ys )
% 0.17/0.37 = ( coindu1121789889_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ B @ Ys ) ) @ ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ B @ Ys ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.ctr(2)
% 0.17/0.37 thf(fact_65_lzip_Osimps_I4_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 0.17/0.37 = ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ B @ Ys ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.simps(4)
% 0.17/0.37 thf(fact_66_lnull__ltlI,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lnull_ltlI
% 0.17/0.37 thf(fact_67_llist_Odisc_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.disc(2)
% 0.17/0.37 thf(fact_68_llist_OdiscI_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Llist
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.discI(2)
% 0.17/0.37 thf(fact_69_not__lnull__conv,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.17/0.37 = ( ? [X2: A,Xs2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( Xs
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % not_lnull_conv
% 0.17/0.37 thf(fact_70_lappend_Odisc_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend.disc(2)
% 0.17/0.37 thf(fact_71_lappend_Odisc_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend.disc(1)
% 0.17/0.37 thf(fact_72_lappend__lnull1,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.17/0.37 = Ys ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_lnull1
% 0.17/0.37 thf(fact_73_lappend__lnull2,axiom,
% 0.17/0.37 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Ys )
% 0.17/0.37 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.17/0.37 = Xs ) ) ).
% 0.17/0.37
% 0.17/0.37 % lappend_lnull2
% 0.17/0.37 thf(fact_74_lhd__LCons,axiom,
% 0.17/0.37 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.17/0.37 = X21 ) ).
% 0.17/0.37
% 0.17/0.37 % lhd_LCons
% 0.17/0.37 thf(fact_75_llist_Odisc_I1_J,axiom,
% 0.17/0.37 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.disc(1)
% 0.17/0.37 thf(fact_76_llist_OdiscI_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Llist
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.discI(1)
% 0.17/0.37 thf(fact_77_llist_Ocollapse_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Llist )
% 0.17/0.37 => ( Llist
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.collapse(1)
% 0.17/0.37 thf(fact_78_lnull__def,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A )
% 0.17/0.37 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( Llist2
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lnull_def
% 0.17/0.37 thf(fact_79_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I3_J,axiom,
% 0.17/0.37 ! [A: $tType,F: A > A,X: A] :
% 0.17/0.37 ( ( coindu1047225960le_ltl @ A @ ( coindu1529956631erates @ A @ F @ X ) )
% 0.17/0.37 = ( coindu1529956631erates @ A @ F @ ( F @ X ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % Coinductive_List_Mirabelle_kmikjhschf.iterates.simps(3)
% 0.17/0.37 thf(fact_80_iterates_Ocode,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu1529956631erates @ A )
% 0.17/0.37 = ( ^ [F3: A > A,X2: A] : ( coindu1121789889_LCons @ A @ X2 @ ( coindu1529956631erates @ A @ F3 @ ( F3 @ X2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % iterates.code
% 0.17/0.37 thf(fact_81_ltakeWhile_Octr_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.17/0.37 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.17/0.37 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltakeWhile.ctr(2)
% 0.17/0.37 thf(fact_82_llist_Oexpand,axiom,
% 0.17/0.37 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Llist )
% 0.17/0.37 = ( coindu335574135_lnull @ A @ Llist3 ) )
% 0.17/0.37 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.17/0.37 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Llist3 ) )
% 0.17/0.37 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 0.17/0.37 = ( coindu1047225960le_ltl @ A @ Llist3 ) ) ) ) )
% 0.17/0.37 => ( Llist = Llist3 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.expand
% 0.17/0.37 thf(fact_83_llist_Ocoinduct,axiom,
% 0.17/0.37 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( R @ Llist @ Llist3 )
% 0.17/0.37 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( R @ Llist4 @ Llist5 )
% 0.17/0.37 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.17/0.37 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.17/0.37 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.17/0.37 & ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 0.17/0.37 => ( Llist = Llist3 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.coinduct
% 0.17/0.37 thf(fact_84_llist_Ocoinduct__strong,axiom,
% 0.17/0.37 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( R @ Llist @ Llist3 )
% 0.17/0.37 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( R @ Llist4 @ Llist5 )
% 0.17/0.37 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.17/0.37 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.17/0.37 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.17/0.37 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) )
% 0.17/0.37 | ( ( coindu1047225960le_ltl @ A @ Llist4 )
% 0.17/0.37 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 0.17/0.37 => ( Llist = Llist3 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.coinduct_strong
% 0.17/0.37 thf(fact_85_lzip_Octr_I1_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.17/0.37 => ( ( coindu847746867e_lzip @ A @ B @ Xs @ Ys )
% 0.17/0.37 = ( coindu1598213697e_LNil @ ( product_prod @ A @ B ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lzip.ctr(1)
% 0.17/0.37 thf(fact_86_old_Oprod_Oinject,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,A2: A,B2: B,A4: A,B3: B] :
% 0.17/0.37 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.17/0.37 = ( product_Pair @ A @ B @ A4 @ B3 ) )
% 0.17/0.37 = ( ( A2 = A4 )
% 0.17/0.37 & ( B2 = B3 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % old.prod.inject
% 0.17/0.37 thf(fact_87_prod_Oinject,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y2: B] :
% 0.17/0.37 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 0.17/0.37 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.17/0.37 = ( ( X1 = Y1 )
% 0.17/0.37 & ( X23 = Y2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod.inject
% 0.17/0.37 thf(fact_88_natural_Osimps_I4_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: code_natural > T] :
% 0.17/0.37 ( ( code_case_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % natural.simps(4)
% 0.17/0.37 thf(fact_89_llist_Osplit__sel,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.17/0.37 = ( ( ( Llist
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ( P @ F1 ) )
% 0.17/0.37 & ( ( Llist
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.17/0.37 => ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.split_sel
% 0.17/0.37 thf(fact_90_llist_Osplit__sel__asm,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.17/0.37 = ( ~ ( ( ( Llist
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ~ ( P @ F1 ) )
% 0.17/0.37 | ( ( Llist
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.17/0.37 & ~ ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.split_sel_asm
% 0.17/0.37 thf(fact_91_unfold__llist__id,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 0.17/0.37 = Xs ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist_id
% 0.17/0.37 thf(fact_92_natural_Osimps_I6_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: code_natural > T > T] :
% 0.17/0.37 ( ( code_rec_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % natural.simps(6)
% 0.17/0.37 thf(fact_93_llist_Ocase__eq__if,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType] :
% 0.17/0.37 ( ( coindu882539134_llist @ B @ A )
% 0.17/0.37 = ( ^ [F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist2: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist2 ) @ F12 @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.case_eq_if
% 0.17/0.37 thf(fact_94_divides__aux__eq,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( semiring_numeral_div @ A @ ( type2 @ A ) )
% 0.17/0.37 => ! [Q2: A,R2: A] :
% 0.17/0.37 ( ( semiri577515795es_aux @ A @ ( product_Pair @ A @ A @ Q2 @ R2 ) )
% 0.17/0.37 = ( R2
% 0.17/0.37 = ( zero_zero @ A ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % divides_aux_eq
% 0.17/0.37 thf(fact_95_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 0.17/0.37 = ( P3 @ A2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.disc_iff(1)
% 0.17/0.37 thf(fact_96_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) )
% 0.17/0.37 = ( ~ ( P3 @ A2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.disc_iff(2)
% 0.17/0.37 thf(fact_97_unfold__llist__eq__LCons,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.17/0.37 = ( ~ ( IS_LNIL @ B2 )
% 0.17/0.37 & ( X
% 0.17/0.37 = ( LHD @ B2 ) )
% 0.17/0.37 & ( Xs
% 0.17/0.37 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist_eq_LCons
% 0.17/0.37 thf(fact_98_unfold__llist_Odisc_I1_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.17/0.37 ( ( P3 @ A2 )
% 0.17/0.37 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.disc(1)
% 0.17/0.37 thf(fact_99_unfold__llist_Odisc_I2_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.17/0.37 ( ~ ( P3 @ A2 )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.disc(2)
% 0.17/0.37 thf(fact_100_unfold__llist_Octr_I2_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.17/0.37 ( ~ ( P3 @ A2 )
% 0.17/0.37 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 0.17/0.37 = ( coindu1121789889_LCons @ B @ ( G21 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.ctr(2)
% 0.17/0.37 thf(fact_101_unfold__llist_Octr_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.17/0.37 ( ( P3 @ A2 )
% 0.17/0.37 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 0.17/0.37 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.ctr(1)
% 0.17/0.37 thf(fact_102_unfold__llist_Osimps_I4_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.17/0.37 ( ~ ( P3 @ A2 )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 0.17/0.37 = ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.simps(4)
% 0.17/0.37 thf(fact_103_unfold__llist_Osimps_I3_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.17/0.37 ( ~ ( P3 @ A2 )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 0.17/0.37 = ( G21 @ A2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.simps(3)
% 0.17/0.37 thf(fact_104_llist_Osimps_I5_J,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.17/0.37 = ( F2 @ X21 @ X22 ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.simps(5)
% 0.17/0.37 thf(fact_105_llist_Osimps_I4_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B] :
% 0.17/0.37 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % llist.simps(4)
% 0.17/0.37 thf(fact_106_unfold__llist_Ocode,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType] :
% 0.17/0.37 ( ( coindu1599971794_llist @ A @ B )
% 0.17/0.37 = ( ^ [P4: A > $o,G212: A > B,G222: A > A,A5: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P4 @ A5 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A5 ) @ ( coindu1599971794_llist @ A @ B @ P4 @ G212 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % unfold_llist.code
% 0.17/0.37 thf(fact_107_ltl__unfold__llist,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.17/0.37 ( ( ( IS_LNIL @ A2 )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) )
% 0.17/0.37 & ( ~ ( IS_LNIL @ A2 )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.17/0.37 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltl_unfold_llist
% 0.17/0.37 thf(fact_108_surj__pair,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.17/0.37 ? [X3: A,Y3: B] :
% 0.17/0.37 ( P3
% 0.17/0.37 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 0.17/0.37
% 0.17/0.37 % surj_pair
% 0.17/0.37 thf(fact_109_prod__cases,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.17/0.37 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.17/0.37 => ( P @ P3 ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_cases
% 0.17/0.37 thf(fact_110_Pair__inject,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,A2: A,B2: B,A4: A,B3: B] :
% 0.17/0.37 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.17/0.37 = ( product_Pair @ A @ B @ A4 @ B3 ) )
% 0.17/0.37 => ~ ( ( A2 = A4 )
% 0.17/0.37 => ( B2 != B3 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % Pair_inject
% 0.17/0.37 thf(fact_111_prod__cases3,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.17/0.37 ~ ! [A6: A,B4: B,C2: C] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_cases3
% 0.17/0.37 thf(fact_112_prod__cases4,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.17/0.37 ~ ! [A6: A,B4: B,C2: C,D2: D] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_cases4
% 0.17/0.37 thf(fact_113_prod__cases5,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.17/0.37 ~ ! [A6: A,B4: B,C2: C,D2: D,E2: E] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_cases5
% 0.17/0.37 thf(fact_114_prod__cases6,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.17/0.37 ~ ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_cases6
% 0.17/0.37 thf(fact_115_prod__cases7,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.17/0.37 ~ ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4,G3: G2] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_cases7
% 0.17/0.37 thf(fact_116_prod__induct3,axiom,
% 0.17/0.37 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.17/0.37 ( ! [A6: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.17/0.37 => ( P @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_induct3
% 0.17/0.37 thf(fact_117_prod__induct4,axiom,
% 0.17/0.37 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.17/0.37 ( ! [A6: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.17/0.37 => ( P @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_induct4
% 0.17/0.37 thf(fact_118_prod__induct5,axiom,
% 0.17/0.37 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.17/0.37 ( ! [A6: A,B4: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.17/0.37 => ( P @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_induct5
% 0.17/0.37 thf(fact_119_prod__induct6,axiom,
% 0.17/0.37 ! [F4: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 0.17/0.37 ( ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) )
% 0.17/0.37 => ( P @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_induct6
% 0.17/0.37 thf(fact_120_prod__induct7,axiom,
% 0.17/0.37 ! [G2: $tType,F4: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 0.17/0.37 ( ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) )
% 0.17/0.37 => ( P @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod_induct7
% 0.17/0.37 thf(fact_121_old_Oprod_Oexhaust,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.17/0.37 ~ ! [A6: A,B4: B] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( product_Pair @ A @ B @ A6 @ B4 ) ) ).
% 0.17/0.37
% 0.17/0.37 % old.prod.exhaust
% 0.17/0.37 thf(fact_122_old_Oprod_Oinducts,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.17/0.37 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.17/0.37 => ( P @ Prod ) ) ).
% 0.17/0.37
% 0.17/0.37 % old.prod.inducts
% 0.17/0.37 thf(fact_123_old_Oprod_Orec,axiom,
% 0.17/0.37 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.17/0.37 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.17/0.37 = ( F1 @ A2 @ B2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % old.prod.rec
% 0.17/0.37 thf(fact_124_internal__case__prod__conv,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.17/0.37 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.17/0.37 = ( C3 @ A2 @ B2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % internal_case_prod_conv
% 0.17/0.37 thf(fact_125_llexord_Ocases,axiom,
% 0.17/0.37 ! [A: $tType,R2: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu300403952lexord @ A @ R2 @ A1 @ A22 )
% 0.17/0.37 => ( ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X3: A] :
% 0.17/0.37 ( ( A1
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) )
% 0.17/0.37 => ( ( A22
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X3 @ Ys3 ) )
% 0.17/0.37 => ~ ( coindu300403952lexord @ A @ R2 @ Xs4 @ Ys3 ) ) )
% 0.17/0.37 => ( ! [X3: A] :
% 0.17/0.37 ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.17/0.37 ( A1
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) )
% 0.17/0.37 => ! [Y3: A] :
% 0.17/0.37 ( ? [Ys3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( A22
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y3 @ Ys3 ) )
% 0.17/0.37 => ~ ( R2 @ X3 @ Y3 ) ) )
% 0.17/0.37 => ~ ( ( A1
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ! [Ys3: coindu1593790203_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llexord.cases
% 0.17/0.37 thf(fact_126_llexord_Osimps,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu300403952lexord @ A )
% 0.17/0.37 = ( ^ [R3: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ? [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 0.17/0.37 ( ( A12
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 0.17/0.37 & ( A23
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 0.17/0.37 & ( coindu300403952lexord @ A @ R3 @ Xs3 @ Ys2 ) )
% 0.17/0.37 | ? [X2: A,Y4: A,Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( A12
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 0.17/0.37 & ( A23
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y4 @ Ys2 ) )
% 0.17/0.37 & ( R3 @ X2 @ Y4 ) )
% 0.17/0.37 | ? [Ys2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( A12
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( A23 = Ys2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llexord.simps
% 0.17/0.37 thf(fact_127_llexord_Ocoinduct,axiom,
% 0.17/0.37 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R2: A > A > $o] :
% 0.17/0.37 ( ( X4 @ X @ Xa )
% 0.17/0.37 => ( ! [X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( X4 @ X3 @ Xa2 )
% 0.17/0.37 => ( ? [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 0.17/0.37 ( ( X3
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 0.17/0.37 & ( Xa2
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 0.17/0.37 & ( ( X4 @ Xs5 @ Ys4 )
% 0.17/0.37 | ( coindu300403952lexord @ A @ R2 @ Xs5 @ Ys4 ) ) )
% 0.17/0.37 | ? [Xb: A,Y5: A,Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( X3
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 0.17/0.37 & ( Xa2
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y5 @ Ys4 ) )
% 0.17/0.37 & ( R2 @ Xb @ Y5 ) )
% 0.17/0.37 | ? [Ys4: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( X3
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( Xa2 = Ys4 ) ) ) )
% 0.17/0.37 => ( coindu300403952lexord @ A @ R2 @ X @ Xa ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llexord.coinduct
% 0.17/0.37 thf(fact_128_llexord__LCons__less,axiom,
% 0.17/0.37 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( R2 @ X @ Y )
% 0.17/0.37 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llexord_LCons_less
% 0.17/0.37 thf(fact_129_llexord__LCons__eq,axiom,
% 0.17/0.37 ! [A: $tType,R2: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.17/0.37 ( ( coindu300403952lexord @ A @ R2 @ Xs @ Ys )
% 0.17/0.37 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llexord_LCons_eq
% 0.17/0.37 thf(fact_130_llexord__LNil,axiom,
% 0.17/0.37 ! [A: $tType,R2: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R2 @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.17/0.37
% 0.17/0.37 % llexord_LNil
% 0.17/0.37 thf(fact_131_natural_Osimps_I5_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: code_natural > T,Natural: code_natural] :
% 0.17/0.37 ( ( code_case_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 0.17/0.37 = ( F2 @ Natural ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.simps(5)
% 0.17/0.37 thf(fact_132_lmember__code_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,X: A] :
% 0.17/0.37 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % lmember_code(1)
% 0.17/0.37 thf(fact_133_lmember__code_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.17/0.37 = ( ( X = Y )
% 0.17/0.37 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lmember_code(2)
% 0.17/0.37 thf(fact_134_natural_Oinject,axiom,
% 0.17/0.37 ! [Natural: code_natural,Natural2: code_natural] :
% 0.17/0.37 ( ( ( code_Suc @ Natural )
% 0.17/0.37 = ( code_Suc @ Natural2 ) )
% 0.17/0.37 = ( Natural = Natural2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.inject
% 0.17/0.37 thf(fact_135_natural_Osimps_I7_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: code_natural > T > T,Natural: code_natural] :
% 0.17/0.37 ( ( code_rec_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 0.17/0.37 = ( F2 @ Natural @ ( code_rec_natural @ T @ F1 @ F2 @ Natural ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.simps(7)
% 0.17/0.37 thf(fact_136_natural_Oinducts,axiom,
% 0.17/0.37 ! [P: code_natural > $o,Natural: code_natural] :
% 0.17/0.37 ( ( P @ ( zero_zero @ code_natural ) )
% 0.17/0.37 => ( ! [Natural3: code_natural] :
% 0.17/0.37 ( ( P @ Natural3 )
% 0.17/0.37 => ( P @ ( code_Suc @ Natural3 ) ) )
% 0.17/0.37 => ( P @ Natural ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.inducts
% 0.17/0.37 thf(fact_137_natural_Oexhaust,axiom,
% 0.17/0.37 ! [Y: code_natural] :
% 0.17/0.37 ( ( Y
% 0.17/0.37 != ( zero_zero @ code_natural ) )
% 0.17/0.37 => ~ ! [Natural3: code_natural] :
% 0.17/0.37 ( Y
% 0.17/0.37 != ( code_Suc @ Natural3 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.exhaust
% 0.17/0.37 thf(fact_138_natural_Odistinct_I1_J,axiom,
% 0.17/0.37 ! [Natural2: code_natural] :
% 0.17/0.37 ( ( zero_zero @ code_natural )
% 0.17/0.37 != ( code_Suc @ Natural2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.distinct(1)
% 0.17/0.37 thf(fact_139_natural_Odistinct_I2_J,axiom,
% 0.17/0.37 ! [Natural4: code_natural] :
% 0.17/0.37 ( ( code_Suc @ Natural4 )
% 0.17/0.37 != ( zero_zero @ code_natural ) ) ).
% 0.17/0.37
% 0.17/0.37 % natural.distinct(2)
% 0.17/0.37 thf(fact_140_random__aux__set_Ocases,axiom,
% 0.17/0.37 ! [X: product_prod @ code_natural @ code_natural] :
% 0.17/0.37 ( ! [J: code_natural] :
% 0.17/0.37 ( X
% 0.17/0.37 != ( product_Pair @ code_natural @ code_natural @ ( zero_zero @ code_natural ) @ J ) )
% 0.17/0.37 => ~ ! [I2: code_natural,J: code_natural] :
% 0.17/0.37 ( X
% 0.17/0.37 != ( product_Pair @ code_natural @ code_natural @ ( code_Suc @ I2 ) @ J ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % random_aux_set.cases
% 0.17/0.37 thf(fact_141_random__aux__rec,axiom,
% 0.17/0.37 ! [A: $tType,Random_aux: code_natural > A,Rhs: code_natural > A,K: code_natural] :
% 0.17/0.37 ( ( ( Random_aux @ ( zero_zero @ code_natural ) )
% 0.17/0.37 = ( Rhs @ ( zero_zero @ code_natural ) ) )
% 0.17/0.37 => ( ! [K2: code_natural] :
% 0.17/0.37 ( ( Random_aux @ ( code_Suc @ K2 ) )
% 0.17/0.37 = ( Rhs @ ( code_Suc @ K2 ) ) )
% 0.17/0.37 => ( ( Random_aux @ K )
% 0.17/0.37 = ( Rhs @ K ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % random_aux_rec
% 0.17/0.37 thf(fact_142_random__aux__set_Oinduct,axiom,
% 0.17/0.37 ! [B: $tType] :
% 0.17/0.37 ( ( quickcheck_random @ B @ ( type2 @ B ) )
% 0.17/0.37 => ! [P: code_natural > code_natural > $o,A0: code_natural,A1: code_natural] :
% 0.17/0.37 ( ! [X12: code_natural] : ( P @ ( zero_zero @ code_natural ) @ X12 )
% 0.17/0.37 => ( ! [I2: code_natural,J: code_natural] :
% 0.17/0.37 ( ! [X5: product_prod @ B @ ( product_unit > code_term )] : ( P @ I2 @ J )
% 0.17/0.37 => ( P @ ( code_Suc @ I2 ) @ J ) )
% 0.17/0.37 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % random_aux_set.induct
% 0.17/0.37 thf(fact_143_case__enat__0,axiom,
% 0.17/0.37 ! [A: $tType,F: nat > A,I: A] :
% 0.17/0.37 ( ( extended_case_enat @ A @ F @ I @ ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( F @ ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % case_enat_0
% 0.17/0.37 thf(fact_144_the__enat__0,axiom,
% 0.17/0.37 ( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % the_enat_0
% 0.17/0.37 thf(fact_145_size__ne__size__imp__ne,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( size @ A @ ( type2 @ A ) )
% 0.17/0.37 => ! [X: A,Y: A] :
% 0.17/0.37 ( ( ( size_size @ A @ X )
% 0.17/0.37 != ( size_size @ A @ Y ) )
% 0.17/0.37 => ( X != Y ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_ne_size_imp_ne
% 0.17/0.37 thf(fact_146_lprefix__expand,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.17/0.37 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.17/0.37 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_expand
% 0.17/0.37 thf(fact_147_lprefix__refl,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_refl
% 0.17/0.37 thf(fact_148_llist_Oleq__refl,axiom,
% 0.17/0.37 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 0.17/0.37
% 0.17/0.37 % llist.leq_refl
% 0.17/0.37 thf(fact_149_LCons__lprefix__LCons,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.17/0.37 = ( ( X = Y )
% 0.17/0.37 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % LCons_lprefix_LCons
% 0.17/0.37 thf(fact_150_lprefix__code_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_code(1)
% 0.17/0.37 thf(fact_151_lprefix__LNil,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_LNil
% 0.17/0.37 thf(fact_152_lnull__lprefix,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.17/0.37
% 0.17/0.37 % lnull_lprefix
% 0.17/0.37 thf(fact_153_lprefix__lnull,axiom,
% 0.17/0.37 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ Ys )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_lnull
% 0.17/0.37 thf(fact_154_lprefix__lnullD,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_lnullD
% 0.17/0.37 thf(fact_155_lprefix__not__lnullD,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_not_lnullD
% 0.17/0.37 thf(fact_156_LCons__lprefix__conv,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.17/0.37 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Ys
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X @ Ys5 ) )
% 0.17/0.37 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % LCons_lprefix_conv
% 0.17/0.37 thf(fact_157_Le__LCons,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % Le_LCons
% 0.17/0.37 thf(fact_158_LNil__lprefix,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.17/0.37
% 0.17/0.37 % LNil_lprefix
% 0.17/0.37 thf(fact_159_lprefix__ltlI,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_ltlI
% 0.17/0.37 thf(fact_160_lprefix__lappend__sameI,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_lappend_sameI
% 0.17/0.37 thf(fact_161_lprefix__lappend,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_lappend
% 0.17/0.37 thf(fact_162_lprefix__trans,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_trans
% 0.17/0.37 thf(fact_163_llist_Oleq__trans,axiom,
% 0.17/0.37 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.leq_trans
% 0.17/0.37 thf(fact_164_lprefix__antisym,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.17/0.37 => ( Xs = Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_antisym
% 0.17/0.37 thf(fact_165_llist_Oleq__antisym,axiom,
% 0.17/0.37 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 0.17/0.37 => ( X = Y ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.leq_antisym
% 0.17/0.37 thf(fact_166_lprefix__down__linear,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.17/0.37 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_down_linear
% 0.17/0.37 thf(fact_167_lprefixI,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 0.17/0.37 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 0.17/0.37 => ( ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs4 @ Ys3 ) @ X4 )
% 0.17/0.37 => ( ( coindu335574135_lnull @ A @ Xs4 )
% 0.17/0.37 | ? [X5: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Xs4
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X5 @ Xs6 ) )
% 0.17/0.37 & ( Ys3
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X5 @ Ys6 ) )
% 0.17/0.37 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 0.17/0.37 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefixI
% 0.17/0.37 thf(fact_168_lprefix__code_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_code(2)
% 0.17/0.37 thf(fact_169_lprefix_Ocases,axiom,
% 0.17/0.37 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 0.17/0.37 => ( ( ( A1
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ! [Xs4: coindu1593790203_llist @ A] : ( A22 != Xs4 ) )
% 0.17/0.37 => ~ ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X3: A] :
% 0.17/0.37 ( ( A1
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) )
% 0.17/0.37 => ( ( A22
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X3 @ Ys3 ) )
% 0.17/0.37 => ~ ( coindu1696667936prefix @ A @ Xs4 @ Ys3 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix.cases
% 0.17/0.37 thf(fact_170_lprefix_Osimps,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A )
% 0.17/0.37 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( A12
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( A23 = Xs3 ) )
% 0.17/0.37 | ? [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 0.17/0.37 ( ( A12
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 0.17/0.37 & ( A23
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 0.17/0.37 & ( coindu1696667936prefix @ A @ Xs3 @ Ys2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix.simps
% 0.17/0.37 thf(fact_171_lprefix_Ocoinduct,axiom,
% 0.17/0.37 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( X4 @ X @ Xa )
% 0.17/0.37 => ( ! [X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( X4 @ X3 @ Xa2 )
% 0.17/0.37 => ( ? [Xs5: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( X3
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 & ( Xa2 = Xs5 ) )
% 0.17/0.37 | ? [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 0.17/0.37 ( ( X3
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 0.17/0.37 & ( Xa2
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 0.17/0.37 & ( ( X4 @ Xs5 @ Ys4 )
% 0.17/0.37 | ( coindu1696667936prefix @ A @ Xs5 @ Ys4 ) ) ) ) )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix.coinduct
% 0.17/0.37 thf(fact_172_lprefix__LCons__conv,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.17/0.37 = ( ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 | ? [Xs2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( Xs
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ Y @ Xs2 ) )
% 0.17/0.37 & ( coindu1696667936prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_LCons_conv
% 0.17/0.37 thf(fact_173_lprefix__lhdD,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_lhdD
% 0.17/0.37 thf(fact_174_lprefix__coinduct,axiom,
% 0.17/0.37 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( P @ Xs @ Ys )
% 0.17/0.37 => ( ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( P @ Xs4 @ Ys3 )
% 0.17/0.37 => ( ( ( coindu335574135_lnull @ A @ Ys3 )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ Xs4 ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ Xs4 )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Ys3 )
% 0.17/0.37 => ( ( ( coindu1046438764le_lhd @ A @ Xs4 )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Ys3 ) )
% 0.17/0.37 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs4 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) )
% 0.17/0.37 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs4 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) ) ) ) ) ) ) )
% 0.17/0.37 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lprefix_coinduct
% 0.17/0.37 thf(fact_175_bool_Osize_I4_J,axiom,
% 0.17/0.37 ( ( size_size @ $o @ $false )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % bool.size(4)
% 0.17/0.37 thf(fact_176_bool_Osize_I3_J,axiom,
% 0.17/0.37 ( ( size_size @ $o @ $true )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % bool.size(3)
% 0.17/0.37 thf(fact_177_lstrict__prefix__def,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu574146665prefix @ A )
% 0.17/0.37 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1696667936prefix @ A @ Xs3 @ Ys2 )
% 0.17/0.37 & ( Xs3 != Ys2 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lstrict_prefix_def
% 0.17/0.37 thf(fact_178_size__bool,axiom,
% 0.17/0.37 ( ( size_size @ $o )
% 0.17/0.37 = ( ^ [B5: $o] : ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_bool
% 0.17/0.37 thf(fact_179_sum_Osize__neq,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,X: sum_sum @ A @ B] :
% 0.17/0.37 ( ( size_size @ ( sum_sum @ A @ B ) @ X )
% 0.17/0.37 != ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % sum.size_neq
% 0.17/0.37 thf(fact_180_prod_Osize__neq,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,X: product_prod @ A @ B] :
% 0.17/0.37 ( ( size_size @ ( product_prod @ A @ B ) @ X )
% 0.17/0.37 != ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % prod.size_neq
% 0.17/0.37 thf(fact_181_bool_Osize_I2_J,axiom,
% 0.17/0.37 ( ( size_bool @ $false )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % bool.size(2)
% 0.17/0.37 thf(fact_182_bool_Osize_I1_J,axiom,
% 0.17/0.37 ( ( size_bool @ $true )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % bool.size(1)
% 0.17/0.37 thf(fact_183_size__bool__overloaded__def,axiom,
% 0.17/0.37 ( ( size_size @ $o )
% 0.17/0.37 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_bool_overloaded_def
% 0.17/0.37 thf(fact_184_old_Obool_Osimps_I5_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: T] :
% 0.17/0.37 ( ( product_rec_bool @ T @ F1 @ F2 @ $true )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % old.bool.simps(5)
% 0.17/0.37 thf(fact_185_old_Obool_Osimps_I6_J,axiom,
% 0.17/0.37 ! [T: $tType,F1: T,F2: T] :
% 0.17/0.37 ( ( product_rec_bool @ T @ F1 @ F2 @ $false )
% 0.17/0.37 = F2 ) ).
% 0.17/0.37
% 0.17/0.37 % old.bool.simps(6)
% 0.17/0.37 thf(fact_186_size__bool__def,axiom,
% 0.17/0.37 ( size_bool
% 0.17/0.37 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_bool_def
% 0.17/0.37 thf(fact_187_tuple__isomorphism_Osize__neq,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,C: $tType,X: tuple_isomorphism @ A @ B @ C] :
% 0.17/0.37 ( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ X )
% 0.17/0.37 != ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % tuple_isomorphism.size_neq
% 0.17/0.37 thf(fact_188_size__literal__def,axiom,
% 0.17/0.37 ( ( size_size @ literal )
% 0.17/0.37 = ( ^ [S: literal] : ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_literal_def
% 0.17/0.37 thf(fact_189_typerep_Osize__neq,axiom,
% 0.17/0.37 ! [X: typerep] :
% 0.17/0.37 ( ( size_size @ typerep @ X )
% 0.17/0.37 != ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % typerep.size_neq
% 0.17/0.37 thf(fact_190_option_Osize__neq,axiom,
% 0.17/0.37 ! [A: $tType,X: option @ A] :
% 0.17/0.37 ( ( size_size @ ( option @ A ) @ X )
% 0.17/0.37 != ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % option.size_neq
% 0.17/0.37 thf(fact_191_size__unit__overloaded__def,axiom,
% 0.17/0.37 ( ( size_size @ product_unit )
% 0.17/0.37 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_unit_overloaded_def
% 0.17/0.37 thf(fact_192_ssubst__Pair__rhs,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType,R2: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 0.17/0.37 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S2 ) @ R )
% 0.17/0.37 => ( ( S3 = S2 )
% 0.17/0.37 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S3 ) @ R ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ssubst_Pair_rhs
% 0.17/0.37 thf(fact_193_size__unit__def,axiom,
% 0.17/0.37 ( product_size_unit
% 0.17/0.37 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % size_unit_def
% 0.17/0.37 thf(fact_194_unit_Osize_I2_J,axiom,
% 0.17/0.37 ( ( size_size @ product_unit @ product_Unity )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % unit.size(2)
% 0.17/0.37 thf(fact_195_old_Ounit_Orec,axiom,
% 0.17/0.37 ! [T: $tType,F1: T] :
% 0.17/0.37 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % old.unit.rec
% 0.17/0.37 thf(fact_196_unit_Osize_I1_J,axiom,
% 0.17/0.37 ( ( product_size_unit @ product_Unity )
% 0.17/0.37 = ( zero_zero @ nat ) ) ).
% 0.17/0.37
% 0.17/0.37 % unit.size(1)
% 0.17/0.37 thf(fact_197_old_Ounit_Oinducts,axiom,
% 0.17/0.37 ! [P: product_unit > $o,Unit: product_unit] :
% 0.17/0.37 ( ( P @ product_Unity )
% 0.17/0.37 => ( P @ Unit ) ) ).
% 0.17/0.37
% 0.17/0.37 % old.unit.inducts
% 0.17/0.37 thf(fact_198_old_Ounit_Oexhaust,axiom,
% 0.17/0.37 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 0.17/0.37
% 0.17/0.37 % old.unit.exhaust
% 0.17/0.37 thf(fact_199_default__unit__def,axiom,
% 0.17/0.37 ( ( default_default @ product_unit )
% 0.17/0.37 = product_Unity ) ).
% 0.17/0.37
% 0.17/0.37 % default_unit_def
% 0.17/0.37 thf(fact_200_old_Ounit_Ocase,axiom,
% 0.17/0.37 ! [A: $tType,F: A] :
% 0.17/0.37 ( ( product_case_unit @ A @ F @ product_Unity )
% 0.17/0.37 = F ) ).
% 0.17/0.37
% 0.17/0.37 % old.unit.case
% 0.17/0.37 thf(fact_201_unit_Ocase__distrib,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,H: A > B,F: A,Unit: product_unit] :
% 0.17/0.37 ( ( H @ ( product_case_unit @ A @ F @ Unit ) )
% 0.17/0.37 = ( product_case_unit @ B @ ( H @ F ) @ Unit ) ) ).
% 0.17/0.37
% 0.17/0.37 % unit.case_distrib
% 0.17/0.37 thf(fact_202_ltake_Osimps_I3_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.simps(3)
% 0.17/0.37 thf(fact_203_llist_Orel__sel,axiom,
% 0.17/0.37 ! [B: $tType,A: $tType] :
% 0.17/0.37 ( ( coindu987187967t_all2 @ A @ B )
% 0.17/0.37 = ( ^ [R4: A > B > $o,A5: coindu1593790203_llist @ A,B5: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( ( coindu335574135_lnull @ A @ A5 )
% 0.17/0.37 = ( coindu335574135_lnull @ B @ B5 ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ A5 )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ B @ B5 )
% 0.17/0.37 => ( ( R4 @ ( coindu1046438764le_lhd @ A @ A5 ) @ ( coindu1046438764le_lhd @ B @ B5 ) )
% 0.17/0.37 & ( coindu987187967t_all2 @ A @ B @ R4 @ ( coindu1047225960le_ltl @ A @ A5 ) @ ( coindu1047225960le_ltl @ B @ B5 ) ) ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_sel
% 0.17/0.37 thf(fact_204_ltake__is__lprefix,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ Xs ) ).
% 0.17/0.37
% 0.17/0.37 % ltake_is_lprefix
% 0.17/0.37 thf(fact_205_ltake__LNil,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat] :
% 0.17/0.37 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake_LNil
% 0.17/0.37 thf(fact_206_llist_Orel__inject_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 0.17/0.37 = ( ( R @ X21 @ Y21 )
% 0.17/0.37 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_inject(2)
% 0.17/0.37 thf(fact_207_ltake__lmap,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,N: extended_enat,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.17/0.37 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1802687541_ltake @ B @ N @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake_lmap
% 0.17/0.37 thf(fact_208_lnull__ltake,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.17/0.37 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 | ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lnull_ltake
% 0.17/0.37 thf(fact_209_ltake_Odisc__iff_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.17/0.37 = ( ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 | ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.disc_iff(1)
% 0.17/0.37 thf(fact_210_ltake_Odisc__iff_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) )
% 0.17/0.37 = ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 & ~ ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.disc_iff(2)
% 0.17/0.37 thf(fact_211_LNil__eq__ltake__iff,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu1598213697e_LNil @ A )
% 0.17/0.37 = ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.17/0.37 = ( ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 | ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % LNil_eq_ltake_iff
% 0.17/0.37 thf(fact_212_ltake__0,axiom,
% 0.17/0.37 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1802687541_ltake @ A @ ( zero_zero @ extended_enat ) @ Xs )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake_0
% 0.17/0.37 thf(fact_213_lhd__ltake,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.17/0.37 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % lhd_ltake
% 0.17/0.37 thf(fact_214_llist_Orel__cases,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 0.17/0.37 => ( ( ( A2
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 => ( B2
% 0.17/0.37 != ( coindu1598213697e_LNil @ B ) ) )
% 0.17/0.37 => ~ ! [X12: A,X24: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( A2
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ X12 @ X24 ) )
% 0.17/0.37 => ! [Y12: B,Y23: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( B2
% 0.17/0.37 = ( coindu1121789889_LCons @ B @ Y12 @ Y23 ) )
% 0.17/0.37 => ( ( R @ X12 @ Y12 )
% 0.17/0.37 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X24 @ Y23 ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_cases
% 0.17/0.37 thf(fact_215_llist_Orel__distinct_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.17/0.37 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_distinct(1)
% 0.17/0.37 thf(fact_216_llist_Orel__distinct_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.17/0.37 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_distinct(2)
% 0.17/0.37 thf(fact_217_ltake_Odisc_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.disc(2)
% 0.17/0.37 thf(fact_218_ltake_Odisc_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 | ( coindu335574135_lnull @ A @ Xs ) )
% 0.17/0.37 => ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.disc(1)
% 0.17/0.37 thf(fact_219_ltake__eq__LNil__iff,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 = ( ( Xs
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) )
% 0.17/0.37 | ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake_eq_LNil_iff
% 0.17/0.37 thf(fact_220_llist_Orel__intros_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( R @ X21 @ Y21 )
% 0.17/0.37 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 0.17/0.37 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_intros(2)
% 0.17/0.37 thf(fact_221_llist_Octr__transfer_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.ctr_transfer(1)
% 0.17/0.37 thf(fact_222_llist_Orel__eq,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu987187967t_all2 @ A @ A
% 0.17/0.37 @ ^ [Y6: A,Z2: A] : ( Y6 = Z2 ) )
% 0.17/0.37 = ( ^ [Y6: coindu1593790203_llist @ A,Z2: coindu1593790203_llist @ A] : ( Y6 = Z2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_eq
% 0.17/0.37 thf(fact_223_llist_Orel__refl,axiom,
% 0.17/0.37 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 0.17/0.37 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_refl
% 0.17/0.37 thf(fact_224_ltake_Octr_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( ( N
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 | ( coindu335574135_lnull @ A @ Xs ) )
% 0.17/0.37 => ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.17/0.37 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.ctr(1)
% 0.17/0.37 thf(fact_225_llist_Orel__coinduct,axiom,
% 0.17/0.37 ! [A: $tType,B: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,R: A > B > $o] :
% 0.17/0.37 ( ( P @ X @ Y )
% 0.17/0.37 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ B] :
% 0.17/0.37 ( ( P @ Llist4 @ Llist5 )
% 0.17/0.37 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.17/0.37 = ( coindu335574135_lnull @ B @ Llist5 ) )
% 0.17/0.37 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ B @ Llist5 )
% 0.17/0.37 => ( ( R @ ( coindu1046438764le_lhd @ A @ Llist4 ) @ ( coindu1046438764le_lhd @ B @ Llist5 ) )
% 0.17/0.37 & ( P @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ B @ Llist5 ) ) ) ) ) ) )
% 0.17/0.37 => ( coindu987187967t_all2 @ A @ B @ R @ X @ Y ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % llist.rel_coinduct
% 0.17/0.37 thf(fact_226_ltake_Ocode,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu1802687541_ltake @ A )
% 0.17/0.37 = ( ^ [N2: extended_enat,Xs3: coindu1593790203_llist @ A] :
% 0.17/0.37 ( if @ ( coindu1593790203_llist @ A )
% 0.17/0.37 @ ( ( N2
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 | ( coindu335574135_lnull @ A @ Xs3 ) )
% 0.17/0.37 @ ( coindu1598213697e_LNil @ A )
% 0.17/0.37 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs3 ) @ ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N2 ) @ ( coindu1047225960le_ltl @ A @ Xs3 ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.code
% 0.17/0.37 thf(fact_227_ltake_Octr_I2_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.17/0.37 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N ) @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.ctr(2)
% 0.17/0.37 thf(fact_228_ltake__epred__ltl,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N ) @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.17/0.37 = ( coindu1047225960le_ltl @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake_epred_ltl
% 0.17/0.37 thf(fact_229_epred__0,axiom,
% 0.17/0.37 ( ( coinductive_epred @ ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) ).
% 0.17/0.37
% 0.17/0.37 % epred_0
% 0.17/0.37 thf(fact_230_epred__inject,axiom,
% 0.17/0.37 ! [X: extended_enat,Y: extended_enat] :
% 0.17/0.37 ( ( X
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( Y
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( ( coinductive_epred @ X )
% 0.17/0.37 = ( coinductive_epred @ Y ) )
% 0.17/0.37 = ( X = Y ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % epred_inject
% 0.17/0.37 thf(fact_231_enat__coinduct,axiom,
% 0.17/0.37 ! [P: extended_enat > extended_enat > $o,M: extended_enat,N: extended_enat] :
% 0.17/0.37 ( ( P @ M @ N )
% 0.17/0.37 => ( ! [M2: extended_enat,N3: extended_enat] :
% 0.17/0.37 ( ( P @ M2 @ N3 )
% 0.17/0.37 => ( ( ( M2
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( N3
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) )
% 0.17/0.37 & ( ( M2
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( N3
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( P @ ( coinductive_epred @ M2 ) @ ( coinductive_epred @ N3 ) )
% 0.17/0.37 | ( ( coinductive_epred @ M2 )
% 0.17/0.37 = ( coinductive_epred @ N3 ) ) ) ) ) ) )
% 0.17/0.37 => ( M = N ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % enat_coinduct
% 0.17/0.37 thf(fact_232_co_Oenat_Oexpand,axiom,
% 0.17/0.37 ! [Enat: extended_enat,Enat2: extended_enat] :
% 0.17/0.37 ( ( ( Enat
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( Enat2
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) )
% 0.17/0.37 => ( ( ( Enat
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( Enat2
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( coinductive_epred @ Enat )
% 0.17/0.37 = ( coinductive_epred @ Enat2 ) ) ) )
% 0.17/0.37 => ( Enat = Enat2 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % co.enat.expand
% 0.17/0.37 thf(fact_233_enat__coinduct2,axiom,
% 0.17/0.37 ! [P: extended_enat > extended_enat > $o,M: extended_enat,N: extended_enat] :
% 0.17/0.37 ( ( P @ M @ N )
% 0.17/0.37 => ( ! [M2: extended_enat,N3: extended_enat] :
% 0.17/0.37 ( ( P @ M2 @ N3 )
% 0.17/0.37 => ( ( M2
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( N3
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) ) )
% 0.17/0.37 => ( ! [M2: extended_enat,N3: extended_enat] :
% 0.17/0.37 ( ( P @ M2 @ N3 )
% 0.17/0.37 => ( ( M2
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( N3
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ( P @ ( coinductive_epred @ M2 ) @ ( coinductive_epred @ N3 ) )
% 0.17/0.37 | ( ( coinductive_epred @ M2 )
% 0.17/0.37 = ( coinductive_epred @ N3 ) ) ) ) ) )
% 0.17/0.37 => ( M = N ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % enat_coinduct2
% 0.17/0.37 thf(fact_234_ltake_Osimps_I4_J,axiom,
% 0.17/0.37 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.17/0.37 ( ( N
% 0.17/0.37 != ( zero_zero @ extended_enat ) )
% 0.17/0.37 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.17/0.37 => ( ( coindu1047225960le_ltl @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.17/0.37 = ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N ) @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % ltake.simps(4)
% 0.17/0.37 thf(fact_235_epred__enat__unfold,axiom,
% 0.17/0.37 ! [A: $tType,Stop: A > $o,A2: A,Next: A > A] :
% 0.17/0.37 ( ( ( Stop @ A2 )
% 0.17/0.37 => ( ( coinductive_epred @ ( coindu1491768222unfold @ A @ Stop @ Next @ A2 ) )
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) )
% 0.17/0.37 & ( ~ ( Stop @ A2 )
% 0.17/0.37 => ( ( coinductive_epred @ ( coindu1491768222unfold @ A @ Stop @ Next @ A2 ) )
% 0.17/0.37 = ( coindu1491768222unfold @ A @ Stop @ Next @ ( Next @ A2 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % epred_enat_unfold
% 0.17/0.37 thf(fact_236_co_Oenat_Ocase__eq__if,axiom,
% 0.17/0.37 ! [A: $tType] :
% 0.17/0.37 ( ( coindu440805660e_enat @ A )
% 0.17/0.37 = ( ^ [F12: A,F22: extended_enat > A,Enat3: extended_enat] :
% 0.17/0.37 ( if @ A
% 0.17/0.37 @ ( Enat3
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 @ F12
% 0.17/0.37 @ ( F22 @ ( coinductive_epred @ Enat3 ) ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % co.enat.case_eq_if
% 0.17/0.37 thf(fact_237_enat__unfold__stop,axiom,
% 0.17/0.37 ! [A: $tType,Stop: A > $o,A2: A,Next: A > A] :
% 0.17/0.37 ( ( Stop @ A2 )
% 0.17/0.37 => ( ( coindu1491768222unfold @ A @ Stop @ Next @ A2 )
% 0.17/0.37 = ( zero_zero @ extended_enat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 % enat_unfold_stop
% 0.17/0.37 thf(fact_238_enat__unfold__eq__0,axiom,
% 0.17/0.37 ! [A: $tType,Stop: A > $o,Next: A > A,A2: A] :
% 0.17/0.37 ( ( ( coindu1491768222unfold @ A @ Stop @ Next @ A2 )
% 0.17/0.37 = ( zero_zero @ extended_enat ) )
% 0.17/0.37 = ( Stop @ A2 ) ) ).
% 0.17/0.37
% 0.17/0.37 % enat_unfold_eq_0
% 0.17/0.37 thf(fact_239_enat__cocase__0,axiom,
% 0.17/0.37 ! [A: $tType,Z: A,S2: extended_enat > A] :
% 0.17/0.37 ( ( coindu440805660e_enat @ A @ Z @ S2 @ ( zero_zero @ extended_enat ) )
% 0.17/0.37 = Z ) ).
% 0.17/0.37
% 0.17/0.37 % enat_cocase_0
% 0.17/0.37 thf(fact_240_co_Oenat_Ocase_I1_J,axiom,
% 0.17/0.37 ! [A: $tType,F1: A,F2: extended_enat > A] :
% 0.17/0.37 ( ( coindu440805660e_enat @ A @ F1 @ F2 @ ( zero_zero @ extended_enat ) )
% 0.17/0.37 = F1 ) ).
% 0.17/0.37
% 0.17/0.37 % co.enat.case(1)
% 0.17/0.37
% 0.17/0.37 %----Type constructors (83)
% 0.17/0.37 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Code__Evaluation_Oterm__of,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( code_term_of @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___HOL_Oequal,axiom,
% 0.17/0.37 ! [A7: $tType] : ( cl_HOL_Oequal @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType,A9: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) )
% 0.17/0.37 & ( typerep2 @ A9 @ ( type2 @ A9 ) ) )
% 0.17/0.37 => ( code_term_of @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType,A9: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3,axiom,
% 0.17/0.37 code_term_of @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4,axiom,
% 0.17/0.37 cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5,axiom,
% 0.17/0.37 code_term_of @ code_term @ ( type2 @ code_term ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6,axiom,
% 0.17/0.37 cl_HOL_Oequal @ code_term @ ( type2 @ code_term ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7,axiom,
% 0.17/0.37 code_term_of @ product_unit @ ( type2 @ product_unit ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Ounit___HOL_Oequal_8,axiom,
% 0.17/0.37 cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( code_term_of @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Oprod___HOL_Oequal_10,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___Code__Evaluation_Oterm__of_11,axiom,
% 0.17/0.37 code_term_of @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___HOL_Oequal_12,axiom,
% 0.17/0.37 cl_HOL_Oequal @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_13,axiom,
% 0.17/0.37 code_term_of @ typerep @ ( type2 @ typerep ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Typerep_Otyperep___HOL_Oequal_14,axiom,
% 0.17/0.37 cl_HOL_Oequal @ typerep @ ( type2 @ typerep ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_15,axiom,
% 0.17/0.37 code_term_of @ literal @ ( type2 @ literal ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_String_Oliteral___HOL_Oequal_16,axiom,
% 0.17/0.37 cl_HOL_Oequal @ literal @ ( type2 @ literal ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_17,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( code_term_of @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Option_Ooption___HOL_Oequal_18,axiom,
% 0.17/0.37 ! [A7: $tType] : ( cl_HOL_Oequal @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_19,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( code_term_of @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Sum__Type_Osum___HOL_Oequal_20,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_21,axiom,
% 0.17/0.37 code_term_of @ $o @ ( type2 @ $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_HOL_Obool___HOL_Oequal_22,axiom,
% 0.17/0.37 cl_HOL_Oequal @ $o @ ( type2 @ $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_23,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( code_term_of @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Set_Oset___HOL_Oequal_24,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( cl_HOL_Oequal @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_25,axiom,
% 0.17/0.37 code_term_of @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___HOL_Oequal_26,axiom,
% 0.17/0.37 cl_HOL_Oequal @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_fun___Code__Evaluation_Oterm__of_27,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( code_term_of @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_fun___HOL_Oequal_28,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( cl_HOL_Oequal @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( cl_HOL_Oequal @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_fun___Typerep_Otyperep,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( typerep2 @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_fun___Enum_Oenum,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( enum @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( enum @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Typerep_Otyperep_29,axiom,
% 0.17/0.37 typerep2 @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Set_Oset___Typerep_Otyperep_30,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( typerep2 @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Set_Oset___Enum_Oenum_31,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( enum @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( enum @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_HOL_Obool___Typerep_Otyperep_32,axiom,
% 0.17/0.37 typerep2 @ $o @ ( type2 @ $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_HOL_Obool___Enum_Oenum_33,axiom,
% 0.17/0.37 enum @ $o @ ( type2 @ $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Sum__Type_Osum___Typerep_Otyperep_34,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( typerep2 @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Sum__Type_Osum___Enum_Oenum_35,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( enum @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( enum @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Option_Ooption___Typerep_Otyperep_36,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( typerep2 @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Option_Ooption___Enum_Oenum_37,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( enum @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( enum @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_String_Oliteral___Typerep_Otyperep_38,axiom,
% 0.17/0.37 typerep2 @ literal @ ( type2 @ literal ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Typerep_Otyperep___Typerep_Otyperep_39,axiom,
% 0.17/0.37 typerep2 @ typerep @ ( type2 @ typerep ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___Typerep_Otyperep_40,axiom,
% 0.17/0.37 typerep2 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Oprod___Typerep_Otyperep_41,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( typerep2 @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Oprod___Enum_Oenum_42,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( enum @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( enum @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Ounit___Typerep_Otyperep_43,axiom,
% 0.17/0.37 typerep2 @ product_unit @ ( type2 @ product_unit ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Ounit___Enum_Oenum_44,axiom,
% 0.17/0.37 enum @ product_unit @ ( type2 @ product_unit ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_45,axiom,
% 0.17/0.37 typerep2 @ code_term @ ( type2 @ code_term ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_46,axiom,
% 0.17/0.37 typerep2 @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_47,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType,A9: $tType] :
% 0.17/0.37 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( typerep2 @ A8 @ ( type2 @ A8 ) )
% 0.17/0.37 & ( typerep2 @ A9 @ ( type2 @ A9 ) ) )
% 0.17/0.37 => ( typerep2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Typerep_Otyperep_48,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( typerep2 @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_fun___Quickcheck__Random_Orandom,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( code_term_of @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( quickcheck_random @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Divides_Osemiring__numeral__div,axiom,
% 0.17/0.37 semiring_numeral_div @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_49,axiom,
% 0.17/0.37 quickcheck_random @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Rings_Osemiring__1,axiom,
% 0.17/0.37 semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.17/0.37 zero @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.17/0.37 size @ nat @ ( type2 @ nat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Set_Oset___Quickcheck__Random_Orandom_50,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( quickcheck_random @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_51,axiom,
% 0.17/0.37 quickcheck_random @ $o @ ( type2 @ $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_HOL_Obool___Nat_Osize_52,axiom,
% 0.17/0.37 size @ $o @ ( type2 @ $o ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_53,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( quickcheck_random @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Sum__Type_Osum___Nat_Osize_54,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] : ( size @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_55,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( quickcheck_random @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Option_Ooption___Nat_Osize_56,axiom,
% 0.17/0.37 ! [A7: $tType] : ( size @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_57,axiom,
% 0.17/0.37 quickcheck_random @ literal @ ( type2 @ literal ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_String_Oliteral___Nat_Osize_58,axiom,
% 0.17/0.37 size @ literal @ ( type2 @ literal ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Typerep_Otyperep___Nat_Osize_59,axiom,
% 0.17/0.37 size @ typerep @ ( type2 @ typerep ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___Quickcheck__Random_Orandom_60,axiom,
% 0.17/0.37 quickcheck_random @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___Rings_Osemiring__1_61,axiom,
% 0.17/0.37 semiring_1 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___Groups_Ozero_62,axiom,
% 0.17/0.37 zero @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Extended__Nat_Oenat___Nat_Osize_63,axiom,
% 0.17/0.37 size @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_64,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] :
% 0.17/0.37 ( ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 0.17/0.37 => ( quickcheck_random @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Oprod___Nat_Osize_65,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType] : ( size @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_66,axiom,
% 0.17/0.37 quickcheck_random @ product_unit @ ( type2 @ product_unit ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Product__Type_Ounit___Nat_Osize_67,axiom,
% 0.17/0.37 size @ product_unit @ ( type2 @ product_unit ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_68,axiom,
% 0.17/0.37 quickcheck_random @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___Rings_Osemiring__1_69,axiom,
% 0.17/0.37 semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_70,axiom,
% 0.17/0.37 zero @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Code__Numeral_Onatural___Nat_Osize_71,axiom,
% 0.17/0.37 size @ code_natural @ ( type2 @ code_natural ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_72,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType,A9: $tType] :
% 0.17/0.37 ( ( ( code_term_of @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) )
% 0.17/0.37 & ( quickcheck_random @ A9 @ ( type2 @ A9 ) ) )
% 0.17/0.37 => ( quickcheck_random @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Record_Otuple__isomorphism___Nat_Osize_73,axiom,
% 0.17/0.37 ! [A7: $tType,A8: $tType,A9: $tType] : ( size @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Quickcheck__Random_Orandom_74,axiom,
% 0.17/0.37 ! [A7: $tType] :
% 0.17/0.37 ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 0.17/0.37 => ( quickcheck_random @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ) ).
% 0.17/0.37
% 0.17/0.37 %----Helper facts (3)
% 0.17/0.37 thf(help_If_3_1_T,axiom,
% 0.17/0.37 ! [P: $o] :
% 0.17/0.37 ( ( P = $true )
% 0.17/0.37 | ( P = $false ) ) ).
% 0.17/0.37
% 0.17/0.37 thf(help_If_2_1_T,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Y: A] :
% 0.17/0.37 ( ( if @ A @ $false @ X @ Y )
% 0.17/0.37 = Y ) ).
% 0.17/0.37
% 0.17/0.37 thf(help_If_1_1_T,axiom,
% 0.17/0.37 ! [A: $tType,X: A,Y: A] :
% 0.17/0.37 ( ( if @ A @ $true @ X @ Y )
% 0.17/0.37 = X ) ).
% 0.17/0.37
% 0.17/0.37 %----Conjectures (2)
% 0.17/0.37 thf(conj_0,hypothesis,
% 0.17/0.37 ~ ( coindu335574135_lnull @ a @ xs ) ).
% 0.17/0.37
% 0.17/0.37 thf(conj_1,conjecture,
% 0.17/0.37 ( ( coindu1046438764le_lhd @ a @ xs )
% 0.17/0.37 = ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ) ).
% 0.17/0.37
% 0.17/0.37 %------------------------------------------------------------------------------
% 0.17/0.37 ------------------------
% 3.17/1.63 ---- Embedded in THF ---
% 3.17/1.63 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.17/1.63 %%% Generated on Tue Feb 24 01:07:12 EST 2026
% 3.17/1.63 %%% using '$$dhol' embedding, version 1.3.0.
% 3.17/1.63 %%% Logic specification used:
% 3.17/1.63 %%% thf(spec, logic, $$dhol).
% 3.17/1.63
% 3.17/1.63 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2DTF7992.p
% 3.17/1.63 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 3.17/1.63 thf(ty_t_Record_Otuple__isomorphism, type, tuple_isomorphism: ($tType > ($tType > ($tType > $tType)))).
% 3.17/1.63 thf(ty_t_Code__Numeral_Onatural, type, code_natural: $tType).
% 3.17/1.63 thf(ty_t_Code__Evaluation_Oterm, type, code_term: $tType).
% 3.17/1.63 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 3.17/1.63 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.17/1.63 thf(ty_t_Extended__Nat_Oenat, type, extended_enat: $tType).
% 3.17/1.63 thf(ty_t_Typerep_Otyperep, type, typerep: $tType).
% 3.17/1.63 thf(ty_t_String_Oliteral, type, literal: $tType).
% 3.17/1.63 thf(ty_t_Sum__Type_Osum, type, sum_sum: ($tType > ($tType > $tType))).
% 3.17/1.63 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 3.17/1.63 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.17/1.63 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.17/1.63 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.17/1.63 thf(ty_tf_a, type, a: $tType).
% 3.17/1.63 thf(sy_cl_Enum_Oenum, type, enum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Typerep_Otyperep, type, typerep2: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_HOL_Oequal, type, cl_HOL_Oequal: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Code__Evaluation_Oterm__of, type, code_term_of: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Rings_Osemiring__1, type, semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Quickcheck__Random_Orandom, type, quickcheck_random: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_cl_Divides_Osemiring__numeral__div, type, semiring_numeral_div: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.17/1.63 thf(sy_c_Code__Numeral_OSuc, type, code_Suc: (code_natural > code_natural)).
% 3.17/1.63 thf(sy_c_Code__Numeral_Onatural_Ocase__natural, type, code_case_natural: (!> [T:$tType]: ((T > ((code_natural > T) > (code_natural > T)))))).
% 3.17/1.63 thf(sy_c_Code__Numeral_Onatural_Orec__natural, type, code_rec_natural: (!> [T:$tType]: ((T > ((code_natural > (T > T)) > (code_natural > T)))))).
% 3.17/1.63 thf(sy_c_Code__Numeral_Onatural_Osize__natural, type, code_size_natural: (code_natural > nat)).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oiterates, type, coindu1529956631erates: (!> [A:$tType]: (((A > A) > (A > (coindu1593790203_llist @ A)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord, type, coindu300403952lexord: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist, type, coindu882539134_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coindu1593790203_llist @ A) > B)) > ((coindu1593790203_llist @ A) > B)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd, type, coindu1046438764le_lhd: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2, type, coindu987187967t_all2: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > $o)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olmap, type, coindu1062782156e_lmap: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ Aa)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl, type, coindu1047225960le_ltl: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olnth, type, coindu749330388e_lnth: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (nat > A))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix, type, coindu574146665prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake, type, coindu1802687541_ltake: (!> [A:$tType]: ((extended_enat > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile, type, coindu721411036eWhile: (!> [A:$tType]: (((A > $o) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olzip, type, coindu847746867e_lzip: (!> [A:$tType,B:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > (coindu1593790203_llist @ ((product_prod @ A) @ B))))))).
% 3.17/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist, type, coindu1599971794_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coindu1593790203_llist @ B)))))))).
% 3.17/1.63 thf(sy_c_Coinductive__Nat_Oco_Oenat_Ocase__enat, type, coindu440805660e_enat: (!> [A:$tType]: ((A > ((extended_enat > A) > (extended_enat > A)))))).
% 3.17/1.63 thf(sy_c_Coinductive__Nat_Oco_Oenat_Oepred, type, coinductive_epred: (extended_enat > extended_enat)).
% 3.17/1.63 thf(sy_c_Coinductive__Nat_Oenat__unfold, type, coindu1491768222unfold: (!> [A:$tType]: (((A > $o) > ((A > A) > (A > extended_enat)))))).
% 3.17/1.63 thf(sy_c_Divides_Osemiring__numeral__div__class_Odivides__aux, type, semiri577515795es_aux: (!> [A:$tType]: ((((product_prod @ A) @ A) > $o)))).
% 3.17/1.63 thf(sy_c_Extended__Nat_Oenat_Ocase__enat, type, extended_case_enat: (!> [T:$tType]: (((nat > T) > (T > (extended_enat > T)))))).
% 3.17/1.63 thf(sy_c_Extended__Nat_Othe__enat, type, extended_the_enat: (extended_enat > nat)).
% 3.17/1.63 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 3.17/1.63 thf(sy_c_HOL_Obool_Osize__bool, type, size_bool: ($o > nat)).
% 3.17/1.63 thf(sy_c_HOL_Odefault__class_Odefault, type, default_default: (!> [A:$tType]: (A))).
% 3.17/1.63 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.17/1.63 thf(sy_c_Nat_Oold_Onat_Orec__nat, type, rec_nat: (!> [T:$tType]: ((T > ((nat > (T > T)) > (nat > T)))))).
% 3.17/1.63 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux, type, semiri532925092at_aux: (!> [A:$tType]: (((A > A) > (nat > (A > A)))))).
% 3.17/1.63 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 3.17/1.63 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.17/1.63 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 3.17/1.63 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 3.17/1.63 thf(sy_c_Product__Type_Oold_Obool_Orec__bool, type, product_rec_bool: (!> [T:$tType]: ((T > (T > ($o > T)))))).
% 3.17/1.63 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 3.17/1.63 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit, type, product_rec_unit: (!> [T:$tType]: ((T > (product_unit > T))))).
% 3.17/1.63 thf(sy_c_Product__Type_Ounit_Ocase__unit, type, product_case_unit: (!> [A:$tType]: ((A > (product_unit > A))))).
% 3.17/1.63 thf(sy_c_Product__Type_Ounit_Osize__unit, type, product_size_unit: (product_unit > nat)).
% 3.17/1.63 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 3.17/1.63 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.17/1.63 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.17/1.63 thf(sy_v_xs, type, xs: (coindu1593790203_llist @ a)).
% 3.17/1.63 thf(fact_0_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((coindu335574135_lnull @ B) @ Ys)))))))).
% 3.17/1.63 thf(fact_1_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.17/1.63 thf(fact_2_ltakeWhile_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))))).
% 3.17/1.63 thf(fact_3_ltakeWhile_Odisc__iff_I2_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) & (P @ ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.17/1.63 thf(fact_4_ltakeWhile_Odisc__iff_I1_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))).
% 3.17/1.63 thf(fact_5_ltakeWhile_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (~ (((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs))))))))).
% 3.17/1.63 thf(fact_6_ltakeWhile_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))) => ((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))))).
% 3.17/1.63 thf(fact_7_ltakeWhile_Osimps_I3_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (((coindu1046438764le_lhd @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.17/1.63 thf(fact_8_zero__natural_Orsp, axiom, ((zero_zero @ nat) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_9_zero__reorient, axiom, (! [A:$tType]: ((((zero @ A) @ (type2 @ A)) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 3.17/1.63 thf(fact_10_lzip_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) & (~ (((coindu335574135_lnull @ B) @ Ys)))))))).
% 3.17/1.63 thf(fact_11_lzip_Odisc__iff_I1_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: ((((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))))).
% 3.17/1.63 thf(fact_12_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I2_J, axiom, (! [A:$tType,F:(A > A),X:A]: ((((coindu1046438764le_lhd @ A) @ (((coindu1529956631erates @ A) @ F) @ X)) = X)))).
% 3.17/1.63 thf(fact_13_ltake_Oexhaust, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((~ (((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)))) => (~ (((N != (zero_zero @ extended_enat)) => ((coindu335574135_lnull @ A) @ Xs)))))))).
% 3.17/1.63 thf(fact_14_lzip_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)) => ((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)))))).
% 3.17/1.63 thf(fact_15_lzip_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (~ (((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys))))))))).
% 3.17/1.63 thf(fact_16_iterates_Odisc__iff, axiom, (! [A:$tType,F:(A > A),X:A]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1529956631erates @ A) @ F) @ X))))))).
% 3.17/1.63 thf(fact_17_natural_Osize_I1_J, axiom, ((code_size_natural @ (zero_zero @ code_natural)) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_18_natural_Osize_I3_J, axiom, (((size_size @ code_natural) @ (zero_zero @ code_natural)) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_19_lzip_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (((coindu1046438764le_lhd @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)) = ((((product_Pair @ A) @ B) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ ((coindu1046438764le_lhd @ B) @ Ys)))))))).
% 3.17/1.63 thf(fact_20_ltakeWhile_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 3.17/1.63 thf(fact_21_ltakeWhile_Osimps_I4_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (((coindu1047225960le_ltl @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu721411036eWhile @ A) @ P) @ ((coindu1047225960le_ltl @ A) @ Xs)))))))).
% 3.17/1.63 thf(fact_22_of__nat__aux_Osimps_I1_J, axiom, (! [A:$tType]: ((((semiring_1 @ A) @ (type2 @ A)) => (! [Inc:(A > A),I:A]: ((((((semiri532925092at_aux @ A) @ Inc) @ (zero_zero @ nat)) @ I) = I))))))).
% 3.17/1.63 thf(fact_23_lnth__0, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((coindu749330388e_lnth @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (zero_zero @ nat)) = X)))).
% 3.17/1.63 thf(fact_24_llist_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,A2:(coindu1593790203_llist @ A),F:(A > B)]: (((~ (((coindu335574135_lnull @ A) @ A2))) => (((coindu1046438764le_lhd @ B) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ A2)) = (F @ ((coindu1046438764le_lhd @ A) @ A2))))))).
% 3.17/1.63 thf(fact_25_lhd__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu1046438764le_lhd @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1046438764le_lhd @ A) @ Ys))) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.17/1.63 thf(fact_26_old_Onat_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F2:(nat > (T > T))]: ((((((rec_nat @ T) @ F1) @ F2) @ (zero_zero @ nat)) = F1)))).
% 3.17/1.63 thf(fact_27_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 3.17/1.63 thf(fact_28_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.17/1.63 thf(fact_29_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 3.17/1.63 thf(fact_30_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1121789889_LCons @ A) @ Xa) @ X)) @ Ys) = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu268472904append @ A) @ X) @ Ys)))))).
% 3.17/1.63 thf(fact_31_llist_Omap__disc__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ B) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ A2)) = ((coindu335574135_lnull @ A) @ A2))))).
% 3.17/1.63 thf(fact_32_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 3.17/1.63 thf(fact_33_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 3.17/1.63 thf(fact_34_ltl__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: ((((coindu1047225960le_ltl @ A) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ ((coindu1047225960le_ltl @ B) @ Xs)))))).
% 3.17/1.63 thf(fact_35_ltl__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1047225960le_ltl @ A) @ Ys))) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ Ys))))))).
% 3.17/1.63 thf(fact_36_lhd__LCons__ltl, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist)) = Llist))))).
% 3.17/1.63 thf(fact_37_eq__LConsD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) => ((Xs != (coindu1598213697e_LNil @ A)) & ((((coindu1046438764le_lhd @ A) @ Xs) = Y) & (((coindu1047225960le_ltl @ A) @ Xs) = Ys))))))).
% 3.17/1.63 thf(fact_38_llist_Oexhaust__sel, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist != (coindu1598213697e_LNil @ A)) => (Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))).
% 3.17/1.63 thf(fact_39_lappend__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((((coindu268472904append @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ Ys) = ((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 3.17/1.63 thf(fact_40_llist_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,A2:(coindu1593790203_llist @ A),F:(A > B)]: (((~ (((coindu335574135_lnull @ A) @ A2))) => (((coindu1047225960le_ltl @ B) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ A2)) = ((((coindu1062782156e_lmap @ A) @ B) @ F) @ ((coindu1047225960le_ltl @ A) @ A2))))))).
% 3.17/1.63 thf(fact_41_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.17/1.63 thf(fact_42_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 3.17/1.63 thf(fact_43_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.17/1.63 thf(fact_44_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 3.17/1.63 thf(fact_45_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ (coindu1598213697e_LNil @ A)))) @ Ys) = (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 3.17/1.63 thf(fact_46_lmap__lappend__distrib, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B),Ys:(coindu1593790203_llist @ B)]: ((((((coindu1062782156e_lmap @ B) @ A) @ F) @ (((coindu268472904append @ B) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Ys)))))).
% 3.17/1.63 thf(fact_47_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 3.17/1.63 thf(fact_48_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 3.17/1.63 thf(fact_49_lmap__eq__LCons__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs) = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (? [X2:B,Xs2:(coindu1593790203_llist @ B)]: (((Xs = (((coindu1121789889_LCons @ B) @ X2) @ Xs2)) & ((Y = (F @ X2)) & (Ys = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs2)))))))))).
% 3.17/1.63 thf(fact_50_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.17/1.63 thf(fact_51_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X2:A,Xs2:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))))).
% 3.17/1.63 thf(fact_52_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 3.17/1.63 thf(fact_53_lappend__assoc, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) = (((coindu268472904append @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs)))))).
% 3.17/1.63 thf(fact_54_lmap__eq__LNil, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: (((((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs) = (coindu1598213697e_LNil @ A)) = (Xs = (coindu1598213697e_LNil @ B)))))).
% 3.17/1.63 thf(fact_55_LNil__eq__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: ((((coindu1598213697e_LNil @ A) = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = (Xs = (coindu1598213697e_LNil @ B)))))).
% 3.17/1.63 thf(fact_56_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 3.17/1.63 thf(fact_57_llist_Osimps_I12_J, axiom, (! [A:$tType,B:$tType,F:(A > B)]: ((((((coindu1062782156e_lmap @ A) @ B) @ F) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ B))))).
% 3.17/1.63 thf(fact_58_llist_Osimps_I13_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:A,X22:(coindu1593790203_llist @ A)]: ((((((coindu1062782156e_lmap @ A) @ B) @ F) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = (((coindu1121789889_LCons @ B) @ (F @ X21)) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ X22)))))).
% 3.17/1.63 thf(fact_59_ltl__simps_I1_J, axiom, (! [A:$tType]: ((((coindu1047225960le_ltl @ A) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.17/1.63 thf(fact_60_ltl__simps_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1047225960le_ltl @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X22)))).
% 3.17/1.63 thf(fact_61_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 3.17/1.63 thf(fact_62_lzip_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu847746867e_lzip @ A) @ B) = (^ [Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ B)]: (((((if @ (coindu1593790203_llist @ ((product_prod @ A) @ B))) @ (((coindu335574135_lnull @ A) @ Xs3) | ((coindu335574135_lnull @ B) @ Ys2))) @ (coindu1598213697e_LNil @ ((product_prod @ A) @ B))) @ (((coindu1121789889_LCons @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ ((coindu1046438764le_lhd @ A) @ Xs3)) @ ((coindu1046438764le_lhd @ B) @ Ys2))) @ ((((coindu847746867e_lzip @ A) @ B) @ ((coindu1047225960le_ltl @ A) @ Xs3)) @ ((coindu1047225960le_ltl @ B) @ Ys2)))))))))).
% 3.17/1.63 thf(fact_63_ltakeWhile_Ocode, axiom, (! [A:$tType]: (((coindu721411036eWhile @ A) = (^ [P2:(A > $o),Xs3:(coindu1593790203_llist @ A)]: (((((if @ (coindu1593790203_llist @ A)) @ (((coindu335574135_lnull @ A) @ Xs3) | (~ ((P2 @ ((coindu1046438764le_lhd @ A) @ Xs3)))))) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs3)) @ (((coindu721411036eWhile @ A) @ P2) @ ((coindu1047225960le_ltl @ A) @ Xs3)))))))))).
% 3.17/1.63 thf(fact_64_lzip_Octr_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys) = (((coindu1121789889_LCons @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ ((coindu1046438764le_lhd @ B) @ Ys))) @ ((((coindu847746867e_lzip @ A) @ B) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ B) @ Ys))))))))).
% 3.17/1.63 thf(fact_65_lzip_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (((coindu1047225960le_ltl @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)) = ((((coindu847746867e_lzip @ A) @ B) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ B) @ Ys)))))))).
% 3.17/1.63 thf(fact_66_lnull__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu335574135_lnull @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))))).
% 3.17/1.63 thf(fact_67_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 3.17/1.63 thf(fact_68_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist))))))).
% 3.17/1.63 thf(fact_69_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X2:A,Xs2:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))))).
% 3.17/1.63 thf(fact_70_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 3.17/1.63 thf(fact_71_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 3.17/1.63 thf(fact_72_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 3.17/1.63 thf(fact_73_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 3.17/1.63 thf(fact_74_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1046438764le_lhd @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X21)))).
% 3.17/1.63 thf(fact_75_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 3.17/1.63 thf(fact_76_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 3.17/1.63 thf(fact_77_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 3.17/1.63 thf(fact_78_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist2:(coindu1593790203_llist @ A)]: ((Llist2 = (coindu1598213697e_LNil @ A)))))))).
% 3.17/1.63 thf(fact_79_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I3_J, axiom, (! [A:$tType,F:(A > A),X:A]: ((((coindu1047225960le_ltl @ A) @ (((coindu1529956631erates @ A) @ F) @ X)) = (((coindu1529956631erates @ A) @ F) @ (F @ X)))))).
% 3.17/1.63 thf(fact_80_iterates_Ocode, axiom, (! [A:$tType]: (((coindu1529956631erates @ A) = (^ [F3:(A > A),X2:A]: ((((coindu1121789889_LCons @ A) @ X2) @ (((coindu1529956631erates @ A) @ F3) @ (F3 @ X2))))))))).
% 3.17/1.63 thf(fact_81_ltakeWhile_Octr_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ (((coindu721411036eWhile @ A) @ P) @ ((coindu1047225960le_ltl @ A) @ Xs))))))))).
% 3.17/1.63 thf(fact_82_llist_Oexpand, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Llist) = ((coindu335574135_lnull @ A) @ Llist3)) => (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((((coindu1046438764le_lhd @ A) @ Llist) = ((coindu1046438764le_lhd @ A) @ Llist3)) & (((coindu1047225960le_ltl @ A) @ Llist) = ((coindu1047225960le_ltl @ A) @ Llist3))))) => (Llist = Llist3)))))).
% 3.17/1.63 thf(fact_83_llist_Ocoinduct, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist3) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ A) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist4) = ((coindu1046438764le_lhd @ A) @ Llist5)) & ((R @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ A) @ Llist5))))))))) => (Llist = Llist3)))))).
% 3.17/1.63 thf(fact_84_llist_Ocoinduct__strong, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist3) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ A) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist4) = ((coindu1046438764le_lhd @ A) @ Llist5)) & (((R @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ A) @ Llist5)) | (((coindu1047225960le_ltl @ A) @ Llist4) = ((coindu1047225960le_ltl @ A) @ Llist5)))))))))) => (Llist = Llist3)))))).
% 3.17/1.63 thf(fact_85_lzip_Octr_I1_J, axiom, (! [B:$tType,A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)) => (((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys) = (coindu1598213697e_LNil @ ((product_prod @ A) @ B))))))).
% 3.17/1.63 thf(fact_86_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A4:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A4) @ B3)) = ((A2 = A4) & (B2 = B3)))))).
% 3.17/1.63 thf(fact_87_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X23:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X23) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X23 = Y2)))))).
% 3.17/1.63 thf(fact_88_natural_Osimps_I4_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > T)]: ((((((code_case_natural @ T) @ F1) @ F2) @ (zero_zero @ code_natural)) = F1)))).
% 3.17/1.63 thf(fact_89_llist_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (((Llist = (coindu1598213697e_LNil @ A)) => (P @ F1)) & ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) => (P @ ((F2 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))).
% 3.17/1.63 thf(fact_90_llist_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (~ ((((Llist = (coindu1598213697e_LNil @ A)) & (~ ((P @ F1)))) | ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) & (~ ((P @ ((F2 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))))))).
% 3.17/1.63 thf(fact_91_unfold__llist__id, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((((((coindu1599971794_llist @ (coindu1593790203_llist @ A)) @ A) @ (coindu335574135_lnull @ A)) @ (coindu1046438764le_lhd @ A)) @ (coindu1047225960le_ltl @ A)) @ Xs) = Xs)))).
% 3.17/1.63 thf(fact_92_natural_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > (T > T))]: ((((((code_rec_natural @ T) @ F1) @ F2) @ (zero_zero @ code_natural)) = F1)))).
% 3.17/1.63 thf(fact_93_llist_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((coindu882539134_llist @ B) @ A) = (^ [F12:B,F22:(A > ((coindu1593790203_llist @ A) > B)),Llist2:(coindu1593790203_llist @ A)]: (((((if @ B) @ ((coindu335574135_lnull @ A) @ Llist2)) @ F12) @ ((F22 @ ((coindu1046438764le_lhd @ A) @ Llist2)) @ ((coindu1047225960le_ltl @ A) @ Llist2))))))))).
% 3.17/1.63 thf(fact_94_divides__aux__eq, axiom, (! [A:$tType]: ((((semiring_numeral_div @ A) @ (type2 @ A)) => (! [Q2:A,R2:A]: ((((semiri577515795es_aux @ A) @ ((((product_Pair @ A) @ A) @ Q2) @ R2)) = (R2 = (zero_zero @ A))))))))).
% 3.17/1.63 thf(fact_95_unfold__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),G21:(A > B),G22:(A > A),A2:A]: ((((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)) = (P3 @ A2))))).
% 3.17/1.63 thf(fact_96_unfold__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),G21:(A > B),G22:(A > A),A2:A]: (((~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)))) = (~ ((P3 @ A2))))))).
% 3.17/1.63 thf(fact_97_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B2:B,X:A,Xs:(coindu1593790203_llist @ A)]: (((((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B2) = (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((~ ((IS_LNIL @ B2))) & ((X = (LHD @ B2)) & (Xs = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B2))))))))).
% 3.17/1.63 thf(fact_98_unfold__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P3 @ A2) => ((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)))))).
% 3.17/1.63 thf(fact_99_unfold__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)))))))).
% 3.17/1.63 thf(fact_100_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2) = (((coindu1121789889_LCons @ B) @ (G21 @ A2)) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ (G22 @ A2)))))))).
% 3.17/1.63 thf(fact_101_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P3 @ A2) => (((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2) = (coindu1598213697e_LNil @ B)))))).
% 3.17/1.63 thf(fact_102_unfold__llist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (((coindu1047225960le_ltl @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)) = ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ (G22 @ A2))))))).
% 3.17/1.63 thf(fact_103_unfold__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (((coindu1046438764le_lhd @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)) = (G21 @ A2)))))).
% 3.17/1.63 thf(fact_104_llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),X21:A,X22:(coindu1593790203_llist @ A)]: (((((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 3.17/1.63 thf(fact_105_llist_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:(A > ((coindu1593790203_llist @ A) > B))]: (((((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ (coindu1598213697e_LNil @ A)) = F1)))).
% 3.17/1.63 thf(fact_106_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1599971794_llist @ A) @ B) = (^ [P4:(A > $o),G212:(A > B),G222:(A > A),A5:A]: (((((if @ (coindu1593790203_llist @ B)) @ (P4 @ A5)) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ (G212 @ A5)) @ ((((((coindu1599971794_llist @ A) @ B) @ P4) @ G212) @ G222) @ (G222 @ A5)))))))))).
% 3.17/1.63 thf(fact_107_ltl__unfold__llist, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),A2:B,LHD:(B > A),LTL:(B > B)]: ((((IS_LNIL @ A2) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = (coindu1598213697e_LNil @ A))) & ((~ ((IS_LNIL @ A2))) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ A2)))))))).
% 3.17/1.63 thf(fact_108_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X3:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y3))))))).
% 3.17/1.63 thf(fact_109_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A6:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B4)))) => (P @ P3))))).
% 3.17/1.63 thf(fact_110_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A4:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A4) @ B3)) => (~ (((A2 = A4) => (B2 != B3)))))))).
% 3.17/1.63 thf(fact_111_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A6:A,B4:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 3.17/1.63 thf(fact_112_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A6:A,B4:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 3.17/1.63 thf(fact_113_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A6:A,B4:B,C2:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 3.17/1.63 thf(fact_114_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F4:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: ((~ ((! [A6:A,B4:B,C2:C,D2:D,E2:E,F5:F4]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F5))))))))))))).
% 3.17/1.63 thf(fact_115_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F4:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))))]: ((~ ((! [A6:A,B4:B,C2:C,D2:D,E2:E,F5:F4,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G2)) @ E2) @ ((((product_Pair @ F4) @ G2) @ F5) @ G3)))))))))))))).
% 3.17/1.63 thf(fact_116_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A6:A,B4:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A6) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P @ X))))).
% 3.17/1.63 thf(fact_117_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A6:A,B4:B,C2:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P @ X))))).
% 3.17/1.63 thf(fact_118_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A6:A,B4:B,C2:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X))))).
% 3.17/1.63 thf(fact_119_prod__induct6, axiom, (! [F4:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))))]: (((! [A6:A,B4:B,C2:C,D2:D,E2:E,F5:F4]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F4))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F4)) @ D2) @ ((((product_Pair @ E) @ F4) @ E2) @ F5)))))))) => (P @ X))))).
% 3.17/1.63 thf(fact_120_prod__induct7, axiom, (! [G2:$tType,F4:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))))]: (((! [A6:A,B4:B,C2:C,D2:D,E2:E,F5:F4,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F4) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F4) @ G2)) @ E2) @ ((((product_Pair @ F4) @ G2) @ F5) @ G3))))))))) => (P @ X))))).
% 3.17/1.63 thf(fact_121_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A6:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A6) @ B4))))))))).
% 3.17/1.63 thf(fact_122_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A6:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B4)))) => (P @ Prod))))).
% 3.17/1.63 thf(fact_123_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 3.17/1.63 thf(fact_124_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 3.17/1.63 thf(fact_125_llexord_Ocases, axiom, (! [A:$tType,R2:(A > (A > $o)),A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R2) @ A1) @ A22) => ((! [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X3:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X3) @ Xs4)) => ((A22 = (((coindu1121789889_LCons @ A) @ X3) @ Ys3)) => (~ (((((coindu300403952lexord @ A) @ R2) @ Xs4) @ Ys3))))))) => ((! [X3:A]: (((? [Xs4:(coindu1593790203_llist @ A)]: ((A1 = (((coindu1121789889_LCons @ A) @ X3) @ Xs4)))) => (! [Y3:A]: (((? [Ys3:(coindu1593790203_llist @ A)]: ((A22 = (((coindu1121789889_LCons @ A) @ Y3) @ Ys3)))) => (~ (((R2 @ X3) @ Y3))))))))) => (~ (((A1 = (coindu1598213697e_LNil @ A)) => (! [Ys3:(coindu1593790203_llist @ A)]: ((A22 != Ys3)))))))))))).
% 3.17/1.63 thf(fact_126_llexord_Osimps, axiom, (! [A:$tType]: (((coindu300403952lexord @ A) = (^ [R3:(A > (A > $o)),A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),X2:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X2) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ X2) @ Ys2)) & ((((coindu300403952lexord @ A) @ R3) @ Xs3) @ Ys2))))) | ((? [X2:A,Y4:A,Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: (((A12 = (((coindu1121789889_LCons @ A) @ X2) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ Y4) @ Ys2)) & ((R3 @ X2) @ Y4))))) | (? [Ys2:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Ys2)))))))))))).
% 3.17/1.63 thf(fact_127_llexord_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A),R2:(A > (A > $o))]: ((((X4 @ X) @ Xa) => ((! [X3:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X4 @ X3) @ Xa2) => ((? [Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),Xb:A]: (((X3 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys4)) & (((X4 @ Xs5) @ Ys4) | ((((coindu300403952lexord @ A) @ R2) @ Xs5) @ Ys4)))))) | ((? [Xb:A,Y5:A,Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((X3 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Y5) @ Ys4)) & ((R2 @ Xb) @ Y5))))) | (? [Ys4:(coindu1593790203_llist @ A)]: (((X3 = (coindu1598213697e_LNil @ A)) & (Xa2 = Ys4))))))))) => ((((coindu300403952lexord @ A) @ R2) @ X) @ Xa)))))).
% 3.17/1.63 thf(fact_128_llexord__LCons__less, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A,Y:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((R2 @ X) @ Y) => ((((coindu300403952lexord @ A) @ R2) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 3.17/1.63 thf(fact_129_llexord__LCons__eq, axiom, (! [A:$tType,R2:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: ((((((coindu300403952lexord @ A) @ R2) @ Xs) @ Ys) => ((((coindu300403952lexord @ A) @ R2) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 3.17/1.63 thf(fact_130_llexord__LNil, axiom, (! [A:$tType,R2:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R2) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 3.17/1.63 thf(fact_131_natural_Osimps_I5_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > T),Natural:code_natural]: ((((((code_case_natural @ T) @ F1) @ F2) @ (code_Suc @ Natural)) = (F2 @ Natural))))).
% 3.17/1.63 thf(fact_132_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 3.17/1.63 thf(fact_133_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 3.17/1.63 thf(fact_134_natural_Oinject, axiom, (! [Natural:code_natural,Natural2:code_natural]: ((((code_Suc @ Natural) = (code_Suc @ Natural2)) = (Natural = Natural2))))).
% 3.17/1.63 thf(fact_135_natural_Osimps_I7_J, axiom, (! [T:$tType,F1:T,F2:(code_natural > (T > T)),Natural:code_natural]: ((((((code_rec_natural @ T) @ F1) @ F2) @ (code_Suc @ Natural)) = ((F2 @ Natural) @ ((((code_rec_natural @ T) @ F1) @ F2) @ Natural)))))).
% 3.17/1.63 thf(fact_136_natural_Oinducts, axiom, (! [P:(code_natural > $o),Natural:code_natural]: (((P @ (zero_zero @ code_natural)) => ((! [Natural3:code_natural]: (((P @ Natural3) => (P @ (code_Suc @ Natural3))))) => (P @ Natural)))))).
% 3.17/1.63 thf(fact_137_natural_Oexhaust, axiom, (! [Y:code_natural]: (((Y != (zero_zero @ code_natural)) => (~ ((! [Natural3:code_natural]: ((Y != (code_Suc @ Natural3)))))))))).
% 3.17/1.63 thf(fact_138_natural_Odistinct_I1_J, axiom, (! [Natural2:code_natural]: (((zero_zero @ code_natural) != (code_Suc @ Natural2))))).
% 3.17/1.63 thf(fact_139_natural_Odistinct_I2_J, axiom, (! [Natural4:code_natural]: (((code_Suc @ Natural4) != (zero_zero @ code_natural))))).
% 3.17/1.63 thf(fact_140_random__aux__set_Ocases, axiom, (! [X:((product_prod @ code_natural) @ code_natural)]: (((! [J:code_natural]: ((X != ((((product_Pair @ code_natural) @ code_natural) @ (zero_zero @ code_natural)) @ J)))) => (~ ((! [I2:code_natural,J:code_natural]: ((X != ((((product_Pair @ code_natural) @ code_natural) @ (code_Suc @ I2)) @ J)))))))))).
% 3.17/1.63 thf(fact_141_random__aux__rec, axiom, (! [A:$tType,Random_aux:(code_natural > A),Rhs:(code_natural > A),K:code_natural]: ((((Random_aux @ (zero_zero @ code_natural)) = (Rhs @ (zero_zero @ code_natural))) => ((! [K2:code_natural]: (((Random_aux @ (code_Suc @ K2)) = (Rhs @ (code_Suc @ K2))))) => ((Random_aux @ K) = (Rhs @ K))))))).
% 3.17/1.63 thf(fact_142_random__aux__set_Oinduct, axiom, (! [B:$tType]: ((((quickcheck_random @ B) @ (type2 @ B)) => (! [P:(code_natural > (code_natural > $o)),A0:code_natural,A1:code_natural]: (((! [X12:code_natural]: (((P @ (zero_zero @ code_natural)) @ X12))) => ((! [I2:code_natural,J:code_natural]: (((! [X5:((product_prod @ B) @ (product_unit > code_term))]: (((P @ I2) @ J))) => ((P @ (code_Suc @ I2)) @ J)))) => ((P @ A0) @ A1))))))))).
% 3.17/1.63 thf(fact_143_case__enat__0, axiom, (! [A:$tType,F:(nat > A),I:A]: ((((((extended_case_enat @ A) @ F) @ I) @ (zero_zero @ extended_enat)) = (F @ (zero_zero @ nat)))))).
% 3.17/1.63 thf(fact_144_the__enat__0, axiom, ((extended_the_enat @ (zero_zero @ extended_enat)) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_145_size__ne__size__imp__ne, axiom, (! [A:$tType]: ((((size @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((size_size @ A) @ X) != ((size_size @ A) @ Y)) => (X != Y)))))))).
% 3.17/1.63 thf(fact_146_lprefix__expand, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ A) @ Ys))) & ((((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys)) & (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 3.17/1.63 thf(fact_147_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 3.17/1.63 thf(fact_148_llist_Oleq__refl, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ X) @ X)))).
% 3.17/1.63 thf(fact_149_LCons__lprefix__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) & (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 3.17/1.63 thf(fact_150_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 3.17/1.63 thf(fact_151_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 3.17/1.63 thf(fact_152_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 3.17/1.63 thf(fact_153_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.17/1.63 thf(fact_154_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.17/1.63 thf(fact_155_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.17/1.63 thf(fact_156_LCons__lprefix__conv, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Ys5:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ X) @ Ys5)) & (((coindu1696667936prefix @ A) @ Xs) @ Ys5)))))))).
% 3.17/1.63 thf(fact_157_Le__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 3.17/1.63 thf(fact_158_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 3.17/1.63 thf(fact_159_lprefix__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys)))))).
% 3.17/1.63 thf(fact_160_lprefix__lappend__sameI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Zs) @ Xs)) @ (((coindu268472904append @ A) @ Zs) @ Ys)))))).
% 3.17/1.63 thf(fact_161_lprefix__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 3.17/1.63 thf(fact_162_lprefix__trans, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => (((coindu1696667936prefix @ A) @ Xs) @ Zs)))))).
% 3.17/1.63 thf(fact_163_llist_Oleq__trans, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A),Z:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ Z) => (((coindu1696667936prefix @ A) @ X) @ Z)))))).
% 3.17/1.63 thf(fact_164_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 3.17/1.63 thf(fact_165_llist_Oleq__antisym, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ X) => (X = Y)))))).
% 3.17/1.63 thf(fact_166_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Zs) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) | (((coindu1696667936prefix @ A) @ Ys) @ Xs))))))).
% 3.17/1.63 thf(fact_167_lprefixI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X4:(set @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)))]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs) @ Ys)) @ X4) => ((! [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs4) @ Ys3)) @ X4) => (((coindu335574135_lnull @ A) @ Xs4) | (? [X5:A,Xs6:(coindu1593790203_llist @ A),Ys6:(coindu1593790203_llist @ A)]: (((Xs4 = (((coindu1121789889_LCons @ A) @ X5) @ Xs6)) & ((Ys3 = (((coindu1121789889_LCons @ A) @ X5) @ Ys6)) & ((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs6) @ Ys6)) @ X4) | (((coindu1696667936prefix @ A) @ Xs6) @ Ys6)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 3.17/1.63 thf(fact_168_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((~ ((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 3.17/1.63 thf(fact_169_lprefix_Ocases, axiom, (! [A:$tType,A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ A1) @ A22) => (((A1 = (coindu1598213697e_LNil @ A)) => (! [Xs4:(coindu1593790203_llist @ A)]: ((A22 != Xs4)))) => (~ ((! [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X3:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X3) @ Xs4)) => ((A22 = (((coindu1121789889_LCons @ A) @ X3) @ Ys3)) => (~ ((((coindu1696667936prefix @ A) @ Xs4) @ Ys3)))))))))))))).
% 3.17/1.63 thf(fact_170_lprefix_Osimps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs3:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Xs3)))) | (? [Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),X2:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X2) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ X2) @ Ys2)) & (((coindu1696667936prefix @ A) @ Xs3) @ Ys2)))))))))))).
% 3.17/1.63 thf(fact_171_lprefix_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A)]: ((((X4 @ X) @ Xa) => ((! [X3:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X4 @ X3) @ Xa2) => ((? [Xs5:(coindu1593790203_llist @ A)]: (((X3 = (coindu1598213697e_LNil @ A)) & (Xa2 = Xs5)))) | (? [Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),Xb:A]: (((X3 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys4)) & (((X4 @ Xs5) @ Ys4) | (((coindu1696667936prefix @ A) @ Xs5) @ Ys4)))))))))) => (((coindu1696667936prefix @ A) @ X) @ Xa)))))).
% 3.17/1.63 thf(fact_172_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs2:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs2)) & (((coindu1696667936prefix @ A) @ Xs2) @ Ys))))))))).
% 3.17/1.63 thf(fact_173_lprefix__lhdD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys))))))).
% 3.17/1.63 thf(fact_174_lprefix__coinduct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((P @ Xs) @ Ys) => ((! [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: ((((P @ Xs4) @ Ys3) => ((((coindu335574135_lnull @ A) @ Ys3) => ((coindu335574135_lnull @ A) @ Xs4)) & ((~ (((coindu335574135_lnull @ A) @ Xs4))) => ((~ (((coindu335574135_lnull @ A) @ Ys3))) => ((((coindu1046438764le_lhd @ A) @ Xs4) = ((coindu1046438764le_lhd @ A) @ Ys3)) & (((P @ ((coindu1047225960le_ltl @ A) @ Xs4)) @ ((coindu1047225960le_ltl @ A) @ Ys3)) | (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs4)) @ ((coindu1047225960le_ltl @ A) @ Ys3)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 3.17/1.63 thf(fact_175_bool_Osize_I4_J, axiom, (((size_size @ $o) @ $false) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_176_bool_Osize_I3_J, axiom, (((size_size @ $o) @ $true) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_177_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu574146665prefix @ A) = (^ [Xs3:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs3) @ Ys2) & (Xs3 != Ys2)))))))).
% 3.17/1.63 thf(fact_178_size__bool, axiom, ((size_size @ $o) = (^ [B5:$o]: ((zero_zero @ nat))))).
% 3.17/1.63 thf(fact_179_sum_Osize__neq, axiom, (! [A:$tType,B:$tType,X:((sum_sum @ A) @ B)]: ((((size_size @ ((sum_sum @ A) @ B)) @ X) != (zero_zero @ nat))))).
% 3.17/1.63 thf(fact_180_prod_Osize__neq, axiom, (! [A:$tType,B:$tType,X:((product_prod @ A) @ B)]: ((((size_size @ ((product_prod @ A) @ B)) @ X) != (zero_zero @ nat))))).
% 3.17/1.63 thf(fact_181_bool_Osize_I2_J, axiom, ((size_bool @ $false) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_182_bool_Osize_I1_J, axiom, ((size_bool @ $true) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_183_size__bool__overloaded__def, axiom, ((size_size @ $o) = (((product_rec_bool @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))).
% 3.17/1.63 thf(fact_184_old_Obool_Osimps_I5_J, axiom, (! [T:$tType,F1:T,F2:T]: ((((((product_rec_bool @ T) @ F1) @ F2) @ $true) = F1)))).
% 3.17/1.63 thf(fact_185_old_Obool_Osimps_I6_J, axiom, (! [T:$tType,F1:T,F2:T]: ((((((product_rec_bool @ T) @ F1) @ F2) @ $false) = F2)))).
% 3.17/1.63 thf(fact_186_size__bool__def, axiom, (size_bool = (((product_rec_bool @ nat) @ (zero_zero @ nat)) @ (zero_zero @ nat)))).
% 3.17/1.63 thf(fact_187_tuple__isomorphism_Osize__neq, axiom, (! [A:$tType,B:$tType,C:$tType,X:(((tuple_isomorphism @ A) @ B) @ C)]: ((((size_size @ (((tuple_isomorphism @ A) @ B) @ C)) @ X) != (zero_zero @ nat))))).
% 3.17/1.63 thf(fact_188_size__literal__def, axiom, ((size_size @ literal) = (^ [S:literal]: ((zero_zero @ nat))))).
% 3.17/1.63 thf(fact_189_typerep_Osize__neq, axiom, (! [X:typerep]: ((((size_size @ typerep) @ X) != (zero_zero @ nat))))).
% 3.17/1.63 thf(fact_190_option_Osize__neq, axiom, (! [A:$tType,X:(option @ A)]: ((((size_size @ (option @ A)) @ X) != (zero_zero @ nat))))).
% 3.17/1.63 thf(fact_191_size__unit__overloaded__def, axiom, ((size_size @ product_unit) = ((product_rec_unit @ nat) @ (zero_zero @ nat)))).
% 3.17/1.63 thf(fact_192_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R2:A,S2:B,R:(set @ ((product_prod @ A) @ B)),S3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R2) @ S2)) @ R) => ((S3 = S2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R2) @ S3)) @ R)))))).
% 3.17/1.63 thf(fact_193_size__unit__def, axiom, (product_size_unit = ((product_rec_unit @ nat) @ (zero_zero @ nat)))).
% 3.17/1.63 thf(fact_194_unit_Osize_I2_J, axiom, (((size_size @ product_unit) @ product_Unity) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_195_old_Ounit_Orec, axiom, (! [T:$tType,F1:T]: (((((product_rec_unit @ T) @ F1) @ product_Unity) = F1)))).
% 3.17/1.63 thf(fact_196_unit_Osize_I1_J, axiom, ((product_size_unit @ product_Unity) = (zero_zero @ nat))).
% 3.17/1.63 thf(fact_197_old_Ounit_Oinducts, axiom, (! [P:(product_unit > $o),Unit:product_unit]: (((P @ product_Unity) => (P @ Unit))))).
% 3.17/1.63 thf(fact_198_old_Ounit_Oexhaust, axiom, (! [Y:product_unit]: ((Y = product_Unity)))).
% 3.17/1.63 thf(fact_199_default__unit__def, axiom, ((default_default @ product_unit) = product_Unity)).
% 3.17/1.63 thf(fact_200_old_Ounit_Ocase, axiom, (! [A:$tType,F:A]: (((((product_case_unit @ A) @ F) @ product_Unity) = F)))).
% 3.17/1.63 thf(fact_201_unit_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F:A,Unit:product_unit]: (((H @ (((product_case_unit @ A) @ F) @ Unit)) = (((product_case_unit @ B) @ (H @ F)) @ Unit))))).
% 3.17/1.63 thf(fact_202_ltake_Osimps_I3_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.17/1.63 thf(fact_203_llist_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((coindu987187967t_all2 @ A) @ B) = (^ [R4:(A > (B > $o)),A5:(coindu1593790203_llist @ A),B5:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ A5) = ((coindu335574135_lnull @ B) @ B5)) & ((~ (((coindu335574135_lnull @ A) @ A5))) => ((~ (((coindu335574135_lnull @ B) @ B5))) => (((R4 @ ((coindu1046438764le_lhd @ A) @ A5)) @ ((coindu1046438764le_lhd @ B) @ B5)) & (((((coindu987187967t_all2 @ A) @ B) @ R4) @ ((coindu1047225960le_ltl @ A) @ A5)) @ ((coindu1047225960le_ltl @ B) @ B5)))))))))))).
% 3.17/1.63 thf(fact_204_ltake__is__lprefix, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ Xs)))).
% 3.17/1.63 thf(fact_205_ltake__LNil, axiom, (! [A:$tType,N:extended_enat]: (((((coindu1802687541_ltake @ A) @ N) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.17/1.63 thf(fact_206_llist_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,X22:(coindu1593790203_llist @ A),Y21:B,Y22:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22)) = (((R @ X21) @ Y21) & (((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22)))))).
% 3.17/1.63 thf(fact_207_ltake__lmap, axiom, (! [A:$tType,B:$tType,N:extended_enat,F:(B > A),Xs:(coindu1593790203_llist @ B)]: (((((coindu1802687541_ltake @ A) @ N) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ (((coindu1802687541_ltake @ B) @ N) @ Xs)))))).
% 3.17/1.63 thf(fact_208_lnull__ltake, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = (((coindu335574135_lnull @ A) @ Xs) | (N = (zero_zero @ extended_enat))))))).
% 3.17/1.63 thf(fact_209_ltake_Odisc__iff_I1_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.17/1.63 thf(fact_210_ltake_Odisc__iff_I2_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)))) = ((N != (zero_zero @ extended_enat)) & (~ (((coindu335574135_lnull @ A) @ Xs)))))))).
% 3.17/1.63 thf(fact_211_LNil__eq__ltake__iff, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((Xs = (coindu1598213697e_LNil @ A)) | (N = (zero_zero @ extended_enat))))))).
% 3.17/1.63 thf(fact_212_ltake__0, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ (zero_zero @ extended_enat)) @ Xs) = (coindu1598213697e_LNil @ A))))).
% 3.17/1.63 thf(fact_213_lhd__ltake, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => (((coindu1046438764le_lhd @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs)))))).
% 3.17/1.63 thf(fact_214_llist_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(coindu1593790203_llist @ A),B2:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ A2) @ B2) => (((A2 = (coindu1598213697e_LNil @ A)) => (B2 != (coindu1598213697e_LNil @ B))) => (~ ((! [X12:A,X24:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X12) @ X24)) => (! [Y12:B,Y23:(coindu1593790203_llist @ B)]: (((B2 = (((coindu1121789889_LCons @ B) @ Y12) @ Y23)) => (((R @ X12) @ Y12) => (~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X24) @ Y23))))))))))))))))).
% 3.17/1.63 thf(fact_215_llist_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:B,Y22:(coindu1593790203_llist @ B)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 3.17/1.63 thf(fact_216_llist_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) @ (coindu1598213697e_LNil @ B))))))).
% 3.17/1.63 thf(fact_217_ltake_Odisc_I2_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs))))))))).
% 3.17/1.63 thf(fact_218_ltake_Odisc_I1_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)) => ((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)))))).
% 3.17/1.63 thf(fact_219_ltake__eq__LNil__iff, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((((coindu1802687541_ltake @ A) @ N) @ Xs) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) | (N = (zero_zero @ extended_enat))))))).
% 3.17/1.63 thf(fact_220_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,Y21:B,X22:(coindu1593790203_llist @ A),Y22:(coindu1593790203_llist @ B)]: ((((R @ X21) @ Y21) => ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22) => (((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 3.17/1.63 thf(fact_221_llist_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ B))))).
% 3.17/1.63 thf(fact_222_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu987187967t_all2 @ A) @ A) @ (^ [Y6:A,Z2:A]: ((Y6 = Z2)))) = (^ [Y6:(coindu1593790203_llist @ A),Z2:(coindu1593790203_llist @ A)]: ((Y6 = Z2))))))).
% 3.17/1.63 thf(fact_223_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(coindu1593790203_llist @ B)]: (((! [X3:B]: (((Ra @ X3) @ X3))) => (((((coindu987187967t_all2 @ B) @ B) @ Ra) @ X) @ X))))).
% 3.17/1.63 thf(fact_224_ltake_Octr_I1_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)) => ((((coindu1802687541_ltake @ A) @ N) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 3.17/1.63 thf(fact_225_llist_Orel__coinduct, axiom, (! [A:$tType,B:$tType,P:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > $o)),X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ B),R:(A > (B > $o))]: ((((P @ X) @ Y) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ B)]: ((((P @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ B) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ B) @ Llist5))) => (((R @ ((coindu1046438764le_lhd @ A) @ Llist4)) @ ((coindu1046438764le_lhd @ B) @ Llist5)) & ((P @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ B) @ Llist5))))))))) => (((((coindu987187967t_all2 @ A) @ B) @ R) @ X) @ Y)))))).
% 3.17/1.63 thf(fact_226_ltake_Ocode, axiom, (! [A:$tType]: (((coindu1802687541_ltake @ A) = (^ [N2:extended_enat,Xs3:(coindu1593790203_llist @ A)]: (((((if @ (coindu1593790203_llist @ A)) @ ((N2 = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs3))) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs3)) @ (((coindu1802687541_ltake @ A) @ (coinductive_epred @ N2)) @ ((coindu1047225960le_ltl @ A) @ Xs3)))))))))).
% 3.17/1.63 thf(fact_227_ltake_Octr_I2_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => ((((coindu1802687541_ltake @ A) @ N) @ Xs) = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ (((coindu1802687541_ltake @ A) @ (coinductive_epred @ N)) @ ((coindu1047225960le_ltl @ A) @ Xs))))))))).
% 3.17/1.63 thf(fact_228_ltake__epred__ltl, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ (coinductive_epred @ N)) @ ((coindu1047225960le_ltl @ A) @ Xs)) = ((coindu1047225960le_ltl @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)))))).
% 3.17/1.63 thf(fact_229_epred__0, axiom, ((coinductive_epred @ (zero_zero @ extended_enat)) = (zero_zero @ extended_enat))).
% 3.17/1.63 thf(fact_230_epred__inject, axiom, (! [X:extended_enat,Y:extended_enat]: (((X != (zero_zero @ extended_enat)) => ((Y != (zero_zero @ extended_enat)) => (((coinductive_epred @ X) = (coinductive_epred @ Y)) = (X = Y))))))).
% 3.17/1.63 thf(fact_231_enat__coinduct, axiom, (! [P:(extended_enat > (extended_enat > $o)),M:extended_enat,N:extended_enat]: ((((P @ M) @ N) => ((! [M2:extended_enat,N3:extended_enat]: ((((P @ M2) @ N3) => (((M2 = (zero_zero @ extended_enat)) = (N3 = (zero_zero @ extended_enat))) & ((M2 != (zero_zero @ extended_enat)) => ((N3 != (zero_zero @ extended_enat)) => (((P @ (coinductive_epred @ M2)) @ (coinductive_epred @ N3)) | ((coinductive_epred @ M2) = (coinductive_epred @ N3))))))))) => (M = N)))))).
% 3.17/1.63 thf(fact_232_co_Oenat_Oexpand, axiom, (! [Enat:extended_enat,Enat2:extended_enat]: ((((Enat = (zero_zero @ extended_enat)) = (Enat2 = (zero_zero @ extended_enat))) => (((Enat != (zero_zero @ extended_enat)) => ((Enat2 != (zero_zero @ extended_enat)) => ((coinductive_epred @ Enat) = (coinductive_epred @ Enat2)))) => (Enat = Enat2)))))).
% 3.17/1.63 thf(fact_233_enat__coinduct2, axiom, (! [P:(extended_enat > (extended_enat > $o)),M:extended_enat,N:extended_enat]: ((((P @ M) @ N) => ((! [M2:extended_enat,N3:extended_enat]: ((((P @ M2) @ N3) => ((M2 = (zero_zero @ extended_enat)) = (N3 = (zero_zero @ extended_enat)))))) => ((! [M2:extended_enat,N3:extended_enat]: ((((P @ M2) @ N3) => ((M2 != (zero_zero @ extended_enat)) => ((N3 != (zero_zero @ extended_enat)) => (((P @ (coinductive_epred @ M2)) @ (coinductive_epred @ N3)) | ((coinductive_epred @ M2) = (coinductive_epred @ N3)))))))) => (M = N))))))).
% 3.17/1.63 thf(fact_234_ltake_Osimps_I4_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1047225960le_ltl @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = (((coindu1802687541_ltake @ A) @ (coinductive_epred @ N)) @ ((coindu1047225960le_ltl @ A) @ Xs)))))))).
% 3.17/1.63 thf(fact_235_epred__enat__unfold, axiom, (! [A:$tType,Stop:(A > $o),A2:A,Next:(A > A)]: ((((Stop @ A2) => ((coinductive_epred @ ((((coindu1491768222unfold @ A) @ Stop) @ Next) @ A2)) = (zero_zero @ extended_enat))) & ((~ ((Stop @ A2))) => ((coinductive_epred @ ((((coindu1491768222unfold @ A) @ Stop) @ Next) @ A2)) = ((((coindu1491768222unfold @ A) @ Stop) @ Next) @ (Next @ A2)))))))).
% 3.17/1.63 thf(fact_236_co_Oenat_Ocase__eq__if, axiom, (! [A:$tType]: (((coindu440805660e_enat @ A) = (^ [F12:A,F22:(extended_enat > A),Enat3:extended_enat]: (((((if @ A) @ (Enat3 = (zero_zero @ extended_enat))) @ F12) @ (F22 @ (coinductive_epred @ Enat3))))))))).
% 3.17/1.63 thf(fact_237_enat__unfold__stop, axiom, (! [A:$tType,Stop:(A > $o),A2:A,Next:(A > A)]: (((Stop @ A2) => (((((coindu1491768222unfold @ A) @ Stop) @ Next) @ A2) = (zero_zero @ extended_enat)))))).
% 3.17/1.63 thf(fact_238_enat__unfold__eq__0, axiom, (! [A:$tType,Stop:(A > $o),Next:(A > A),A2:A]: (((((((coindu1491768222unfold @ A) @ Stop) @ Next) @ A2) = (zero_zero @ extended_enat)) = (Stop @ A2))))).
% 3.17/1.63 thf(fact_239_enat__cocase__0, axiom, (! [A:$tType,Z:A,S2:(extended_enat > A)]: ((((((coindu440805660e_enat @ A) @ Z) @ S2) @ (zero_zero @ extended_enat)) = Z)))).
% 3.17/1.63 thf(fact_240_co_Oenat_Ocase_I1_J, axiom, (! [A:$tType,F1:A,F2:(extended_enat > A)]: ((((((coindu440805660e_enat @ A) @ F1) @ F2) @ (zero_zero @ extended_enat)) = F1)))).
% 3.17/1.63 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Code__Evaluation_Oterm__of, axiom, (! [A7:$tType]: ((((typerep2 @ A7) @ (type2 @ A7)) => ((code_term_of @ (coindu1593790203_llist @ A7)) @ (type2 @ (coindu1593790203_llist @ A7))))))).
% 3.17/1.63 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___HOL_Oequal, axiom, (! [A7:$tType]: (((cl_HOL_Oequal @ (coindu1593790203_llist @ A7)) @ (type2 @ (coindu1593790203_llist @ A7)))))).
% 3.17/1.63 thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1, axiom, (! [A7:$tType,A8:$tType,A9:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & (((typerep2 @ A8) @ (type2 @ A8)) & ((typerep2 @ A9) @ (type2 @ A9)))) => ((code_term_of @ (((tuple_isomorphism @ A7) @ A8) @ A9)) @ (type2 @ (((tuple_isomorphism @ A7) @ A8) @ A9))))))).
% 3.17/1.63 thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2, axiom, (! [A7:$tType,A8:$tType,A9:$tType]: (((cl_HOL_Oequal @ (((tuple_isomorphism @ A7) @ A8) @ A9)) @ (type2 @ (((tuple_isomorphism @ A7) @ A8) @ A9)))))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3, axiom, ((code_term_of @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4, axiom, ((cl_HOL_Oequal @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5, axiom, ((code_term_of @ code_term) @ (type2 @ code_term))).
% 3.17/1.63 thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6, axiom, ((cl_HOL_Oequal @ code_term) @ (type2 @ code_term))).
% 3.17/1.63 thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7, axiom, ((code_term_of @ product_unit) @ (type2 @ product_unit))).
% 3.17/1.63 thf(tcon_Product__Type_Ounit___HOL_Oequal_8, axiom, ((cl_HOL_Oequal @ product_unit) @ (type2 @ product_unit))).
% 3.17/1.63 thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9, axiom, (! [A7:$tType,A8:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8))) => ((code_term_of @ ((product_prod @ A7) @ A8)) @ (type2 @ ((product_prod @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Product__Type_Oprod___HOL_Oequal_10, axiom, (! [A7:$tType,A8:$tType]: (((cl_HOL_Oequal @ ((product_prod @ A7) @ A8)) @ (type2 @ ((product_prod @ A7) @ A8)))))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___Code__Evaluation_Oterm__of_11, axiom, ((code_term_of @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___HOL_Oequal_12, axiom, ((cl_HOL_Oequal @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_13, axiom, ((code_term_of @ typerep) @ (type2 @ typerep))).
% 3.17/1.63 thf(tcon_Typerep_Otyperep___HOL_Oequal_14, axiom, ((cl_HOL_Oequal @ typerep) @ (type2 @ typerep))).
% 3.17/1.63 thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_15, axiom, ((code_term_of @ literal) @ (type2 @ literal))).
% 3.17/1.63 thf(tcon_String_Oliteral___HOL_Oequal_16, axiom, ((cl_HOL_Oequal @ literal) @ (type2 @ literal))).
% 3.17/1.63 thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_17, axiom, (! [A7:$tType]: ((((typerep2 @ A7) @ (type2 @ A7)) => ((code_term_of @ (option @ A7)) @ (type2 @ (option @ A7))))))).
% 3.17/1.63 thf(tcon_Option_Ooption___HOL_Oequal_18, axiom, (! [A7:$tType]: (((cl_HOL_Oequal @ (option @ A7)) @ (type2 @ (option @ A7)))))).
% 3.17/1.63 thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_19, axiom, (! [A7:$tType,A8:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8))) => ((code_term_of @ ((sum_sum @ A7) @ A8)) @ (type2 @ ((sum_sum @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Sum__Type_Osum___HOL_Oequal_20, axiom, (! [A7:$tType,A8:$tType]: (((cl_HOL_Oequal @ ((sum_sum @ A7) @ A8)) @ (type2 @ ((sum_sum @ A7) @ A8)))))).
% 3.17/1.63 thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_21, axiom, ((code_term_of @ $o) @ (type2 @ $o))).
% 3.17/1.63 thf(tcon_HOL_Obool___HOL_Oequal_22, axiom, ((cl_HOL_Oequal @ $o) @ (type2 @ $o))).
% 3.17/1.63 thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_23, axiom, (! [A7:$tType]: ((((typerep2 @ A7) @ (type2 @ A7)) => ((code_term_of @ (set @ A7)) @ (type2 @ (set @ A7))))))).
% 3.17/1.63 thf(tcon_Set_Oset___HOL_Oequal_24, axiom, (! [A7:$tType]: ((((cl_HOL_Oequal @ A7) @ (type2 @ A7)) => ((cl_HOL_Oequal @ (set @ A7)) @ (type2 @ (set @ A7))))))).
% 3.17/1.63 thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_25, axiom, ((code_term_of @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Nat_Onat___HOL_Oequal_26, axiom, ((cl_HOL_Oequal @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_fun___Code__Evaluation_Oterm__of_27, axiom, (! [A7:$tType,A8:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8))) => ((code_term_of @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.17/1.63 thf(tcon_fun___HOL_Oequal_28, axiom, (! [A7:$tType,A8:$tType]: (((((enum @ A7) @ (type2 @ A7)) & ((cl_HOL_Oequal @ A8) @ (type2 @ A8))) => ((cl_HOL_Oequal @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.17/1.63 thf(tcon_fun___Typerep_Otyperep, axiom, (! [A7:$tType,A8:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8))) => ((typerep2 @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.17/1.63 thf(tcon_fun___Enum_Oenum, axiom, (! [A7:$tType,A8:$tType]: (((((enum @ A7) @ (type2 @ A7)) & ((enum @ A8) @ (type2 @ A8))) => ((enum @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.17/1.63 thf(tcon_Nat_Onat___Typerep_Otyperep_29, axiom, ((typerep2 @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Set_Oset___Typerep_Otyperep_30, axiom, (! [A7:$tType]: ((((typerep2 @ A7) @ (type2 @ A7)) => ((typerep2 @ (set @ A7)) @ (type2 @ (set @ A7))))))).
% 3.17/1.63 thf(tcon_Set_Oset___Enum_Oenum_31, axiom, (! [A7:$tType]: ((((enum @ A7) @ (type2 @ A7)) => ((enum @ (set @ A7)) @ (type2 @ (set @ A7))))))).
% 3.17/1.63 thf(tcon_HOL_Obool___Typerep_Otyperep_32, axiom, ((typerep2 @ $o) @ (type2 @ $o))).
% 3.17/1.63 thf(tcon_HOL_Obool___Enum_Oenum_33, axiom, ((enum @ $o) @ (type2 @ $o))).
% 3.17/1.63 thf(tcon_Sum__Type_Osum___Typerep_Otyperep_34, axiom, (! [A7:$tType,A8:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8))) => ((typerep2 @ ((sum_sum @ A7) @ A8)) @ (type2 @ ((sum_sum @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Sum__Type_Osum___Enum_Oenum_35, axiom, (! [A7:$tType,A8:$tType]: (((((enum @ A7) @ (type2 @ A7)) & ((enum @ A8) @ (type2 @ A8))) => ((enum @ ((sum_sum @ A7) @ A8)) @ (type2 @ ((sum_sum @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Option_Ooption___Typerep_Otyperep_36, axiom, (! [A7:$tType]: ((((typerep2 @ A7) @ (type2 @ A7)) => ((typerep2 @ (option @ A7)) @ (type2 @ (option @ A7))))))).
% 3.17/1.63 thf(tcon_Option_Ooption___Enum_Oenum_37, axiom, (! [A7:$tType]: ((((enum @ A7) @ (type2 @ A7)) => ((enum @ (option @ A7)) @ (type2 @ (option @ A7))))))).
% 3.17/1.63 thf(tcon_String_Oliteral___Typerep_Otyperep_38, axiom, ((typerep2 @ literal) @ (type2 @ literal))).
% 3.17/1.63 thf(tcon_Typerep_Otyperep___Typerep_Otyperep_39, axiom, ((typerep2 @ typerep) @ (type2 @ typerep))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___Typerep_Otyperep_40, axiom, ((typerep2 @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Product__Type_Oprod___Typerep_Otyperep_41, axiom, (! [A7:$tType,A8:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & ((typerep2 @ A8) @ (type2 @ A8))) => ((typerep2 @ ((product_prod @ A7) @ A8)) @ (type2 @ ((product_prod @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Product__Type_Oprod___Enum_Oenum_42, axiom, (! [A7:$tType,A8:$tType]: (((((enum @ A7) @ (type2 @ A7)) & ((enum @ A8) @ (type2 @ A8))) => ((enum @ ((product_prod @ A7) @ A8)) @ (type2 @ ((product_prod @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Product__Type_Ounit___Typerep_Otyperep_43, axiom, ((typerep2 @ product_unit) @ (type2 @ product_unit))).
% 3.17/1.63 thf(tcon_Product__Type_Ounit___Enum_Oenum_44, axiom, ((enum @ product_unit) @ (type2 @ product_unit))).
% 3.17/1.63 thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_45, axiom, ((typerep2 @ code_term) @ (type2 @ code_term))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_46, axiom, ((typerep2 @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_47, axiom, (! [A7:$tType,A8:$tType,A9:$tType]: (((((typerep2 @ A7) @ (type2 @ A7)) & (((typerep2 @ A8) @ (type2 @ A8)) & ((typerep2 @ A9) @ (type2 @ A9)))) => ((typerep2 @ (((tuple_isomorphism @ A7) @ A8) @ A9)) @ (type2 @ (((tuple_isomorphism @ A7) @ A8) @ A9))))))).
% 3.17/1.63 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Typerep_Otyperep_48, axiom, (! [A7:$tType]: ((((typerep2 @ A7) @ (type2 @ A7)) => ((typerep2 @ (coindu1593790203_llist @ A7)) @ (type2 @ (coindu1593790203_llist @ A7))))))).
% 3.17/1.63 thf(tcon_fun___Quickcheck__Random_Orandom, axiom, (! [A7:$tType,A8:$tType]: (((((code_term_of @ A7) @ (type2 @ A7)) & (((cl_HOL_Oequal @ A7) @ (type2 @ A7)) & ((quickcheck_random @ A8) @ (type2 @ A8)))) => ((quickcheck_random @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.17/1.63 thf(tcon_Nat_Onat___Divides_Osemiring__numeral__div, axiom, ((semiring_numeral_div @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_49, axiom, ((quickcheck_random @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Nat_Onat___Rings_Osemiring__1, axiom, ((semiring_1 @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Nat_Onat___Groups_Ozero, axiom, ((zero @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Nat_Onat___Nat_Osize, axiom, ((size @ nat) @ (type2 @ nat))).
% 3.17/1.63 thf(tcon_Set_Oset___Quickcheck__Random_Orandom_50, axiom, (! [A7:$tType]: ((((quickcheck_random @ A7) @ (type2 @ A7)) => ((quickcheck_random @ (set @ A7)) @ (type2 @ (set @ A7))))))).
% 3.17/1.63 thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_51, axiom, ((quickcheck_random @ $o) @ (type2 @ $o))).
% 3.17/1.63 thf(tcon_HOL_Obool___Nat_Osize_52, axiom, ((size @ $o) @ (type2 @ $o))).
% 3.17/1.63 thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_53, axiom, (! [A7:$tType,A8:$tType]: (((((quickcheck_random @ A7) @ (type2 @ A7)) & ((quickcheck_random @ A8) @ (type2 @ A8))) => ((quickcheck_random @ ((sum_sum @ A7) @ A8)) @ (type2 @ ((sum_sum @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Sum__Type_Osum___Nat_Osize_54, axiom, (! [A7:$tType,A8:$tType]: (((size @ ((sum_sum @ A7) @ A8)) @ (type2 @ ((sum_sum @ A7) @ A8)))))).
% 3.17/1.63 thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_55, axiom, (! [A7:$tType]: ((((quickcheck_random @ A7) @ (type2 @ A7)) => ((quickcheck_random @ (option @ A7)) @ (type2 @ (option @ A7))))))).
% 3.17/1.63 thf(tcon_Option_Ooption___Nat_Osize_56, axiom, (! [A7:$tType]: (((size @ (option @ A7)) @ (type2 @ (option @ A7)))))).
% 3.17/1.63 thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_57, axiom, ((quickcheck_random @ literal) @ (type2 @ literal))).
% 3.17/1.63 thf(tcon_String_Oliteral___Nat_Osize_58, axiom, ((size @ literal) @ (type2 @ literal))).
% 3.17/1.63 thf(tcon_Typerep_Otyperep___Nat_Osize_59, axiom, ((size @ typerep) @ (type2 @ typerep))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___Quickcheck__Random_Orandom_60, axiom, ((quickcheck_random @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___Rings_Osemiring__1_61, axiom, ((semiring_1 @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___Groups_Ozero_62, axiom, ((zero @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Extended__Nat_Oenat___Nat_Osize_63, axiom, ((size @ extended_enat) @ (type2 @ extended_enat))).
% 3.17/1.63 thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_64, axiom, (! [A7:$tType,A8:$tType]: (((((quickcheck_random @ A7) @ (type2 @ A7)) & ((quickcheck_random @ A8) @ (type2 @ A8))) => ((quickcheck_random @ ((product_prod @ A7) @ A8)) @ (type2 @ ((product_prod @ A7) @ A8))))))).
% 3.17/1.63 thf(tcon_Product__Type_Oprod___Nat_Osize_65, axiom, (! [A7:$tType,A8:$tType]: (((size @ ((product_prod @ A7) @ A8)) @ (type2 @ ((product_prod @ A7) @ A8)))))).
% 3.17/1.63 thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_66, axiom, ((quickcheck_random @ product_unit) @ (type2 @ product_unit))).
% 3.17/1.63 thf(tcon_Product__Type_Ounit___Nat_Osize_67, axiom, ((size @ product_unit) @ (type2 @ product_unit))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_68, axiom, ((quickcheck_random @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___Rings_Osemiring__1_69, axiom, ((semiring_1 @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_70, axiom, ((zero @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Code__Numeral_Onatural___Nat_Osize_71, axiom, ((size @ code_natural) @ (type2 @ code_natural))).
% 3.17/1.63 thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_72, axiom, (! [A7:$tType,A8:$tType,A9:$tType]: (((((code_term_of @ A7) @ (type2 @ A7)) & (((cl_HOL_Oequal @ A7) @ (type2 @ A7)) & (((quickcheck_random @ A7) @ (type2 @ A7)) & (((quickcheck_random @ A8) @ (type2 @ A8)) & ((quickcheck_random @ A9) @ (type2 @ A9)))))) => ((quickcheck_random @ (((tuple_isomorphism @ A7) @ A8) @ A9)) @ (type2 @ (((tuple_isomorphism @ A7) @ A8) @ A9))))))).
% 3.17/1.63 thf(tcon_Record_Otuple__isomorphism___Nat_Osize_73, axiom, (! [A7:$tType,A8:$tType,A9:$tType]: (((size @ (((tuple_isomorphism @ A7) @ A8) @ A9)) @ (type2 @ (((tuple_isomorphism @ A7) @ A8) @ A9)))))).
% 3.17/1.63 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Quickcheck__Random_Orandom_74, axiom, (! [A7:$tType]: ((((quickcheck_random @ A7) @ (type2 @ A7)) => ((quickcheck_random @ (coindu1593790203_llist @ A7)) @ (type2 @ (coindu1593790203_llist @ A7))))))).
% 3.17/1.63 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.17/1.63 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 3.17/1.63 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 3.17/1.63 thf(conj_0, hypothesis, (~ (((coindu335574135_lnull @ a) @ xs)))).
% 3.17/1.63 thf(conj_1, conjecture, (((coindu1046438764le_lhd @ a) @ xs) = (((coindu749330388e_lnth @ a) @ xs) @ (zero_zero @ nat)))).
% 3.17/1.63 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2DTF7992.p
% 3.17/1.63 ------------------------
% 3.17/1.68 ---- Cleaned THF ---
% 3.17/1.68 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 3.17/1.68 coindu1593790203_llist: $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Record_Otuple__isomorphism,type,
% 3.17/1.68 tuple_isomorphism: $tType > $tType > $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Code__Numeral_Onatural,type,
% 3.17/1.68 code_natural: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Code__Evaluation_Oterm,type,
% 3.17/1.68 code_term: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Product__Type_Ounit,type,
% 3.17/1.68 product_unit: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Product__Type_Oprod,type,
% 3.17/1.68 product_prod: $tType > $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Extended__Nat_Oenat,type,
% 3.17/1.68 extended_enat: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Typerep_Otyperep,type,
% 3.17/1.68 typerep: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_String_Oliteral,type,
% 3.17/1.68 literal: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Sum__Type_Osum,type,
% 3.17/1.68 sum_sum: $tType > $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Option_Ooption,type,
% 3.17/1.68 option: $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Set_Oset,type,
% 3.17/1.68 set: $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_Nat_Onat,type,
% 3.17/1.68 nat: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_t_itself,type,
% 3.17/1.68 itself: $tType > $tType ).
% 3.17/1.68
% 3.17/1.68 thf(ty_tf_a,type,
% 3.17/1.68 a: $tType ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Enum_Oenum,type,
% 3.17/1.68 enum:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Typerep_Otyperep,type,
% 3.17/1.68 typerep2:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_HOL_Otype,type,
% 3.17/1.68 type:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_HOL_Oequal,type,
% 3.17/1.68 cl_HOL_Oequal:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Code__Evaluation_Oterm__of,type,
% 3.17/1.68 code_term_of:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Nat_Osize,type,
% 3.17/1.68 size:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Groups_Ozero,type,
% 3.17/1.68 zero:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Rings_Osemiring__1,type,
% 3.17/1.68 semiring_1:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Quickcheck__Random_Orandom,type,
% 3.17/1.68 quickcheck_random:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_cl_Divides_Osemiring__numeral__div,type,
% 3.17/1.68 semiring_numeral_div:
% 3.17/1.68 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Code__Numeral_OSuc,type,
% 3.17/1.68 code_Suc: code_natural > code_natural ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Code__Numeral_Onatural_Ocase__natural,type,
% 3.17/1.68 code_case_natural:
% 3.17/1.68 !>[T: $tType] : ( T > ( code_natural > T ) > code_natural > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Code__Numeral_Onatural_Orec__natural,type,
% 3.17/1.68 code_rec_natural:
% 3.17/1.68 !>[T: $tType] : ( T > ( code_natural > T > T ) > code_natural > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Code__Numeral_Onatural_Osize__natural,type,
% 3.17/1.68 code_size_natural: code_natural > nat ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oiterates,type,
% 3.17/1.68 coindu1529956631erates:
% 3.17/1.68 !>[A: $tType] : ( ( A > A ) > A > ( coindu1593790203_llist @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 3.17/1.68 coindu268472904append:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 3.17/1.68 coindu300403952lexord:
% 3.17/1.68 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 3.17/1.68 coindu1121789889_LCons:
% 3.17/1.68 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 3.17/1.68 coindu1598213697e_LNil:
% 3.17/1.68 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 3.17/1.68 coindu882539134_llist:
% 3.17/1.68 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 3.17/1.68 coindu1046438764le_lhd:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 3.17/1.68 coindu987187967t_all2:
% 3.17/1.68 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olmap,type,
% 3.17/1.68 coindu1062782156e_lmap:
% 3.17/1.68 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ Aa ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 3.17/1.68 coindu335574135_lnull:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 3.17/1.68 coindu1047225960le_ltl:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 3.17/1.68 coindu567634248member:
% 3.17/1.68 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olnth,type,
% 3.17/1.68 coindu749330388e_lnth:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > nat > A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 3.17/1.68 coindu1696667936prefix:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 3.17/1.68 coindu574146665prefix:
% 3.17/1.68 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake,type,
% 3.17/1.68 coindu1802687541_ltake:
% 3.17/1.68 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 3.17/1.68 coindu721411036eWhile:
% 3.17/1.68 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olzip,type,
% 3.17/1.68 coindu847746867e_lzip:
% 3.17/1.68 !>[A: $tType,B: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > ( coindu1593790203_llist @ ( product_prod @ A @ B ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 3.17/1.68 coindu1599971794_llist:
% 3.17/1.68 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__Nat_Oco_Oenat_Ocase__enat,type,
% 3.17/1.68 coindu440805660e_enat:
% 3.17/1.68 !>[A: $tType] : ( A > ( extended_enat > A ) > extended_enat > A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__Nat_Oco_Oenat_Oepred,type,
% 3.17/1.68 coinductive_epred: extended_enat > extended_enat ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Coinductive__Nat_Oenat__unfold,type,
% 3.17/1.68 coindu1491768222unfold:
% 3.17/1.68 !>[A: $tType] : ( ( A > $o ) > ( A > A ) > A > extended_enat ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Divides_Osemiring__numeral__div__class_Odivides__aux,type,
% 3.17/1.68 semiri577515795es_aux:
% 3.17/1.68 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Extended__Nat_Oenat_Ocase__enat,type,
% 3.17/1.68 extended_case_enat:
% 3.17/1.68 !>[T: $tType] : ( ( nat > T ) > T > extended_enat > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Extended__Nat_Othe__enat,type,
% 3.17/1.68 extended_the_enat: extended_enat > nat ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.17/1.68 zero_zero:
% 3.17/1.68 !>[A: $tType] : A ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_HOL_Obool_Osize__bool,type,
% 3.17/1.68 size_bool: $o > nat ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 3.17/1.68 default_default:
% 3.17/1.68 !>[A: $tType] : A ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_If,type,
% 3.17/1.68 if:
% 3.17/1.68 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Nat_Oold_Onat_Orec__nat,type,
% 3.17/1.68 rec_nat:
% 3.17/1.68 !>[T: $tType] : ( T > ( nat > T > T ) > nat > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux,type,
% 3.17/1.68 semiri532925092at_aux:
% 3.17/1.68 !>[A: $tType] : ( ( A > A ) > nat > A > A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Nat_Osize__class_Osize,type,
% 3.17/1.68 size_size:
% 3.17/1.68 !>[A: $tType] : ( A > nat ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_OPair,type,
% 3.17/1.68 product_Pair:
% 3.17/1.68 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_OUnity,type,
% 3.17/1.68 product_Unity: product_unit ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 3.17/1.68 produc2004651681e_prod:
% 3.17/1.68 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_Oold_Obool_Orec__bool,type,
% 3.17/1.68 product_rec_bool:
% 3.17/1.68 !>[T: $tType] : ( T > T > $o > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 3.17/1.68 product_rec_prod:
% 3.17/1.68 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 3.17/1.68 product_rec_unit:
% 3.17/1.68 !>[T: $tType] : ( T > product_unit > T ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_Ounit_Ocase__unit,type,
% 3.17/1.68 product_case_unit:
% 3.17/1.68 !>[A: $tType] : ( A > product_unit > A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Product__Type_Ounit_Osize__unit,type,
% 3.17/1.68 product_size_unit: product_unit > nat ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Pure_Otype,type,
% 3.17/1.68 type2:
% 3.17/1.68 !>[A: $tType] : ( itself @ A ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_Set_OCollect,type,
% 3.17/1.68 collect:
% 3.17/1.68 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_c_member,type,
% 3.17/1.68 member:
% 3.17/1.68 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.17/1.68
% 3.17/1.68 thf(sy_v_xs,type,
% 3.17/1.68 xs: coindu1593790203_llist @ a ).
% 3.17/1.68
% 3.17/1.68 thf(fact_0_lzip_Oexhaust,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ( coindu335574135_lnull @ B @ Ys ) )
% 3.17/1.68 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_1_lappend_Oexhaust,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 3.17/1.68 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_2_ltakeWhile_Oexhaust,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.68 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 3.17/1.68 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_3_ltakeWhile_Odisc__iff_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 3.17/1.68 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 & ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_4_ltakeWhile_Odisc__iff_I1_J,axiom,
% 3.17/1.68 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 3.17/1.68 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_5_ltakeWhile_Odisc_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.17/1.68 => ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_6_ltakeWhile_Odisc_I1_J,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.68 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 3.17/1.68 => ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_7_ltakeWhile_Osimps_I3_J,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.17/1.68 => ( ( coindu1046438764le_lhd @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 3.17/1.68 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_8_zero__natural_Orsp,axiom,
% 3.17/1.68 ( ( zero_zero @ nat )
% 3.17/1.68 = ( zero_zero @ nat ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_9_zero__reorient,axiom,
% 3.17/1.68 ! [A: $tType] :
% 3.17/1.68 ( ( zero @ A @ ( type2 @ A ) )
% 3.17/1.68 => ! [X: A] :
% 3.17/1.68 ( ( ( zero_zero @ A )
% 3.17/1.68 = X )
% 3.17/1.68 = ( X
% 3.17/1.68 = ( zero_zero @ A ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_10_lzip_Odisc__iff_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ( ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) )
% 3.17/1.68 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 & ~ ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_11_lzip_Odisc__iff_I1_J,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 3.17/1.68 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_12_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,F: A > A,X: A] :
% 3.17/1.68 ( ( coindu1046438764le_lhd @ A @ ( coindu1529956631erates @ A @ F @ X ) )
% 3.17/1.68 = X ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_13_ltake_Oexhaust,axiom,
% 3.17/1.68 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ~ ( ( N
% 3.17/1.68 = ( zero_zero @ extended_enat ) )
% 3.17/1.68 | ( coindu335574135_lnull @ A @ Xs ) )
% 3.17/1.68 => ~ ( ( N
% 3.17/1.68 != ( zero_zero @ extended_enat ) )
% 3.17/1.68 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_14_lzip_Odisc_I1_J,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ( coindu335574135_lnull @ B @ Ys ) )
% 3.17/1.68 => ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_15_lzip_Odisc_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.17/1.68 => ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_16_iterates_Odisc__iff,axiom,
% 3.17/1.68 ! [A: $tType,F: A > A,X: A] :
% 3.17/1.68 ~ ( coindu335574135_lnull @ A @ ( coindu1529956631erates @ A @ F @ X ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_17_natural_Osize_I1_J,axiom,
% 3.17/1.68 ( ( code_size_natural @ ( zero_zero @ code_natural ) )
% 3.17/1.68 = ( zero_zero @ nat ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_18_natural_Osize_I3_J,axiom,
% 3.17/1.68 ( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
% 3.17/1.68 = ( zero_zero @ nat ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_19_lzip_Osimps_I3_J,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.17/1.68 => ( ( coindu1046438764le_lhd @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 3.17/1.68 = ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ B @ Ys ) ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_20_ltakeWhile_Octr_I1_J,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.68 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 3.17/1.68 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 3.17/1.68 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_21_ltakeWhile_Osimps_I4_J,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.17/1.68 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 3.17/1.68 = ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_22_of__nat__aux_Osimps_I1_J,axiom,
% 3.17/1.68 ! [A: $tType] :
% 3.17/1.68 ( ( semiring_1 @ A @ ( type2 @ A ) )
% 3.17/1.68 => ! [Inc: A > A,I: A] :
% 3.17/1.68 ( ( semiri532925092at_aux @ A @ Inc @ ( zero_zero @ nat ) @ I )
% 3.17/1.68 = I ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_23_lnth__0,axiom,
% 3.17/1.68 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu749330388e_lnth @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( zero_zero @ nat ) )
% 3.17/1.68 = X ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_24_llist_Omap__sel_I1_J,axiom,
% 3.17/1.68 ! [B: $tType,A: $tType,A2: coindu1593790203_llist @ A,F: A > B] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 3.17/1.68 => ( ( coindu1046438764le_lhd @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 3.17/1.68 = ( F @ ( coindu1046438764le_lhd @ A @ A2 ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_25_lhd__lappend,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.17/1.68 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 3.17/1.68 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.17/1.68 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_26_old_Onat_Osimps_I6_J,axiom,
% 3.17/1.68 ! [T: $tType,F1: T,F2: nat > T > T] :
% 3.17/1.68 ( ( rec_nat @ T @ F1 @ F2 @ ( zero_zero @ nat ) )
% 3.17/1.68 = F1 ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_27_llist_Oinject,axiom,
% 3.17/1.68 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 3.17/1.68 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 3.17/1.68 = ( ( X21 = Y21 )
% 3.17/1.68 & ( X22 = Y22 ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_28_lappend_Odisc__iff_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 3.17/1.68 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_29_lnull__lappend,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.17/1.68 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_30_lappend__code_I2_J,axiom,
% 3.17/1.68 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 3.17/1.68 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_31_llist_Omap__disc__iff,axiom,
% 3.17/1.68 ! [B: $tType,A: $tType,F: A > B,A2: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu335574135_lnull @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 3.17/1.68 = ( coindu335574135_lnull @ A @ A2 ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_32_lappend__LNil2,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.68 = Xs ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_33_lappend__code_I1_J,axiom,
% 3.17/1.68 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 3.17/1.68 = Ys ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_34_ltl__lmap,axiom,
% 3.17/1.68 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.17/1.68 ( ( coindu1047225960le_ltl @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.17/1.68 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1047225960le_ltl @ B @ Xs ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_35_ltl__lappend,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.17/1.68 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 3.17/1.68 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.17/1.68 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_36_lhd__LCons__ltl,axiom,
% 3.17/1.68 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 3.17/1.68 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 3.17/1.68 = Llist ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_37_eq__LConsD,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( Xs
% 3.17/1.68 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.17/1.68 => ( ( Xs
% 3.17/1.68 != ( coindu1598213697e_LNil @ A ) )
% 3.17/1.68 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 3.17/1.68 = Y )
% 3.17/1.68 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 3.17/1.68 = Ys ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_38_llist_Oexhaust__sel,axiom,
% 3.17/1.68 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ( Llist
% 3.17/1.68 != ( coindu1598213697e_LNil @ A ) )
% 3.17/1.68 => ( Llist
% 3.17/1.68 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_39_lappend__ltl,axiom,
% 3.17/1.68 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.68 => ( ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys )
% 3.17/1.68 = ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_40_llist_Omap__sel_I2_J,axiom,
% 3.17/1.68 ! [B: $tType,A: $tType,A2: coindu1593790203_llist @ A,F: A > B] :
% 3.17/1.68 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 3.17/1.68 => ( ( coindu1047225960le_ltl @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 3.17/1.68 = ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1047225960le_ltl @ A @ A2 ) ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_41_mem__Collect__eq,axiom,
% 3.17/1.68 ! [A: $tType,A2: A,P: A > $o] :
% 3.17/1.68 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.17/1.68 = ( P @ A2 ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_42_Collect__mem__eq,axiom,
% 3.17/1.68 ! [A: $tType,A3: set @ A] :
% 3.17/1.68 ( ( collect @ A
% 3.17/1.68 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 3.17/1.68 = A3 ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_43_Collect__cong,axiom,
% 3.17/1.68 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.17/1.68 ( ! [X3: A] :
% 3.17/1.68 ( ( P @ X3 )
% 3.17/1.68 = ( Q @ X3 ) )
% 3.17/1.68 => ( ( collect @ A @ P )
% 3.17/1.68 = ( collect @ A @ Q ) ) ) ).
% 3.17/1.68
% 3.17/1.68 thf(fact_44_ext,axiom,
% 3.17/1.68 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.17/1.68 ( ! [X3: A] :
% 3.17/1.68 ( ( F @ X3 )
% 3.17/1.68 = ( G @ X3 ) )
% 3.17/1.68 => ( F = G ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_45_lappend__snocL1__conv__LCons2,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 3.17/1.69 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_46_lmap__lappend__distrib,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Ys: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu268472904append @ B @ Xs @ Ys ) )
% 3.17/1.69 = ( coindu268472904append @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) @ ( coindu1062782156e_lmap @ B @ A @ F @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_47_lappend__eq__LNil__iff,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ( Ys
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_48_LNil__eq__lappend__iff,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu1598213697e_LNil @ A )
% 3.17/1.69 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.17/1.69 = ( ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ( Ys
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_49_lmap__eq__LCons__conv,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.17/1.69 = ( ? [X2: B,Xs2: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( Xs
% 3.17/1.69 = ( coindu1121789889_LCons @ B @ X2 @ Xs2 ) )
% 3.17/1.69 & ( Y
% 3.17/1.69 = ( F @ X2 ) )
% 3.17/1.69 & ( Ys
% 3.17/1.69 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_50_lappend__LNil__LNil,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_51_neq__LNil__conv,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Xs
% 3.17/1.69 != ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( ? [X2: A,Xs2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( Xs
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_52_llist_Oexhaust,axiom,
% 3.17/1.69 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Y
% 3.17/1.69 != ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_53_lappend__assoc,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 3.17/1.69 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_54_lmap__eq__LNil,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_55_LNil__eq__lmap,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( ( coindu1598213697e_LNil @ A )
% 3.17/1.69 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.17/1.69 = ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_56_llist_Odistinct_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1598213697e_LNil @ A )
% 3.17/1.69 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_57_llist_Osimps_I12_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,F: A > B] :
% 3.17/1.69 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( coindu1598213697e_LNil @ B ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_58_llist_Osimps_I13_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.17/1.69 = ( coindu1121789889_LCons @ B @ ( F @ X21 ) @ ( coindu1062782156e_lmap @ A @ B @ F @ X22 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_59_ltl__simps_I1_J,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_60_ltl__simps_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.17/1.69 = X22 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_61_lappend_Octr_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.17/1.69 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_62_lzip_Ocode,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType] :
% 3.17/1.69 ( ( coindu847746867e_lzip @ A @ B )
% 3.17/1.69 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ B] :
% 3.17/1.69 ( if @ ( coindu1593790203_llist @ ( product_prod @ A @ B ) )
% 3.17/1.69 @ ( ( coindu335574135_lnull @ A @ Xs3 )
% 3.17/1.69 | ( coindu335574135_lnull @ B @ Ys2 ) )
% 3.17/1.69 @ ( coindu1598213697e_LNil @ ( product_prod @ A @ B ) )
% 3.17/1.69 @ ( coindu1121789889_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs3 ) @ ( coindu1046438764le_lhd @ B @ Ys2 ) ) @ ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs3 ) @ ( coindu1047225960le_ltl @ B @ Ys2 ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_63_ltakeWhile_Ocode,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu721411036eWhile @ A )
% 3.17/1.69 = ( ^ [P2: A > $o,Xs3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( if @ ( coindu1593790203_llist @ A )
% 3.17/1.69 @ ( ( coindu335574135_lnull @ A @ Xs3 )
% 3.17/1.69 | ~ ( P2 @ ( coindu1046438764le_lhd @ A @ Xs3 ) ) )
% 3.17/1.69 @ ( coindu1598213697e_LNil @ A )
% 3.17/1.69 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs3 ) @ ( coindu721411036eWhile @ A @ P2 @ ( coindu1047225960le_ltl @ A @ Xs3 ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_64_lzip_Octr_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.17/1.69 => ( ( coindu847746867e_lzip @ A @ B @ Xs @ Ys )
% 3.17/1.69 = ( coindu1121789889_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ B @ Ys ) ) @ ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ B @ Ys ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_65_lzip_Osimps_I4_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.17/1.69 => ( ( coindu1047225960le_ltl @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 3.17/1.69 = ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ B @ Ys ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_66_lnull__ltlI,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_67_llist_Odisc_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_68_llist_OdiscI_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Llist
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.17/1.69 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_69_not__lnull__conv,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 3.17/1.69 = ( ? [X2: A,Xs2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( Xs
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_70_lappend_Odisc_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 3.17/1.69 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_71_lappend_Odisc_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.17/1.69 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_72_lappend__lnull1,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.17/1.69 = Ys ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_73_lappend__lnull2,axiom,
% 3.17/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Ys )
% 3.17/1.69 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.17/1.69 = Xs ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_74_lhd__LCons,axiom,
% 3.17/1.69 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.17/1.69 = X21 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_75_llist_Odisc_I1_J,axiom,
% 3.17/1.69 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_76_llist_OdiscI_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Llist
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_77_llist_Ocollapse_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Llist )
% 3.17/1.69 => ( Llist
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_78_lnull__def,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A )
% 3.17/1.69 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( Llist2
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_79_Coinductive__List__Mirabelle__kmikjhschf_Oiterates_Osimps_I3_J,axiom,
% 3.17/1.69 ! [A: $tType,F: A > A,X: A] :
% 3.17/1.69 ( ( coindu1047225960le_ltl @ A @ ( coindu1529956631erates @ A @ F @ X ) )
% 3.17/1.69 = ( coindu1529956631erates @ A @ F @ ( F @ X ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_80_iterates_Ocode,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu1529956631erates @ A )
% 3.17/1.69 = ( ^ [F3: A > A,X2: A] : ( coindu1121789889_LCons @ A @ X2 @ ( coindu1529956631erates @ A @ F3 @ ( F3 @ X2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_81_ltakeWhile_Octr_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.17/1.69 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.17/1.69 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_82_llist_Oexpand,axiom,
% 3.17/1.69 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu335574135_lnull @ A @ Llist )
% 3.17/1.69 = ( coindu335574135_lnull @ A @ Llist3 ) )
% 3.17/1.69 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 3.17/1.69 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Llist3 ) )
% 3.17/1.69 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 3.17/1.69 = ( coindu1047225960le_ltl @ A @ Llist3 ) ) ) ) )
% 3.17/1.69 => ( Llist = Llist3 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_83_llist_Ocoinduct,axiom,
% 3.17/1.69 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( R @ Llist @ Llist3 )
% 3.17/1.69 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( R @ Llist4 @ Llist5 )
% 3.17/1.69 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 3.17/1.69 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 3.17/1.69 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 3.17/1.69 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 3.17/1.69 & ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 3.17/1.69 => ( Llist = Llist3 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_84_llist_Ocoinduct__strong,axiom,
% 3.17/1.69 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( R @ Llist @ Llist3 )
% 3.17/1.69 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( R @ Llist4 @ Llist5 )
% 3.17/1.69 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 3.17/1.69 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 3.17/1.69 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 3.17/1.69 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 3.17/1.69 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) )
% 3.17/1.69 | ( ( coindu1047225960le_ltl @ A @ Llist4 )
% 3.17/1.69 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 3.17/1.69 => ( Llist = Llist3 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_85_lzip_Octr_I1_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 | ( coindu335574135_lnull @ B @ Ys ) )
% 3.17/1.69 => ( ( coindu847746867e_lzip @ A @ B @ Xs @ Ys )
% 3.17/1.69 = ( coindu1598213697e_LNil @ ( product_prod @ A @ B ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_86_old_Oprod_Oinject,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,A2: A,B2: B,A4: A,B3: B] :
% 3.17/1.69 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.17/1.69 = ( product_Pair @ A @ B @ A4 @ B3 ) )
% 3.17/1.69 = ( ( A2 = A4 )
% 3.17/1.69 & ( B2 = B3 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_87_prod_Oinject,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y2: B] :
% 3.17/1.69 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 3.17/1.69 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 3.17/1.69 = ( ( X1 = Y1 )
% 3.17/1.69 & ( X23 = Y2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_88_natural_Osimps_I4_J,axiom,
% 3.17/1.69 ! [T: $tType,F1: T,F2: code_natural > T] :
% 3.17/1.69 ( ( code_case_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 3.17/1.69 = F1 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_89_llist_Osplit__sel,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 3.17/1.69 = ( ( ( Llist
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 => ( P @ F1 ) )
% 3.17/1.69 & ( ( Llist
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 3.17/1.69 => ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_90_llist_Osplit__sel__asm,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 3.17/1.69 = ( ~ ( ( ( Llist
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ~ ( P @ F1 ) )
% 3.17/1.69 | ( ( Llist
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 3.17/1.69 & ~ ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_91_unfold__llist__id,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 3.17/1.69 = Xs ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_92_natural_Osimps_I6_J,axiom,
% 3.17/1.69 ! [T: $tType,F1: T,F2: code_natural > T > T] :
% 3.17/1.69 ( ( code_rec_natural @ T @ F1 @ F2 @ ( zero_zero @ code_natural ) )
% 3.17/1.69 = F1 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_93_llist_Ocase__eq__if,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType] :
% 3.17/1.69 ( ( coindu882539134_llist @ B @ A )
% 3.17/1.69 = ( ^ [F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist2: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist2 ) @ F12 @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_94_divides__aux__eq,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( semiring_numeral_div @ A @ ( type2 @ A ) )
% 3.17/1.69 => ! [Q2: A,R2: A] :
% 3.17/1.69 ( ( semiri577515795es_aux @ A @ ( product_Pair @ A @ A @ Q2 @ R2 ) )
% 3.17/1.69 = ( R2
% 3.17/1.69 = ( zero_zero @ A ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_95_unfold__llist_Odisc__iff_I1_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 3.17/1.69 = ( P3 @ A2 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_96_unfold__llist_Odisc__iff_I2_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 3.17/1.69 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) )
% 3.17/1.69 = ( ~ ( P3 @ A2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_97_unfold__llist__eq__LCons,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 3.17/1.69 = ( ~ ( IS_LNIL @ B2 )
% 3.17/1.69 & ( X
% 3.17/1.69 = ( LHD @ B2 ) )
% 3.17/1.69 & ( Xs
% 3.17/1.69 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_98_unfold__llist_Odisc_I1_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 3.17/1.69 ( ( P3 @ A2 )
% 3.17/1.69 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_99_unfold__llist_Odisc_I2_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 3.17/1.69 ( ~ ( P3 @ A2 )
% 3.17/1.69 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_100_unfold__llist_Octr_I2_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 3.17/1.69 ( ~ ( P3 @ A2 )
% 3.17/1.69 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 3.17/1.69 = ( coindu1121789889_LCons @ B @ ( G21 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_101_unfold__llist_Octr_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 3.17/1.69 ( ( P3 @ A2 )
% 3.17/1.69 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 3.17/1.69 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_102_unfold__llist_Osimps_I4_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 3.17/1.69 ( ~ ( P3 @ A2 )
% 3.17/1.69 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 3.17/1.69 = ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_103_unfold__llist_Osimps_I3_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 3.17/1.69 ( ~ ( P3 @ A2 )
% 3.17/1.69 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 3.17/1.69 = ( G21 @ A2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_104_llist_Osimps_I5_J,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.17/1.69 = ( F2 @ X21 @ X22 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_105_llist_Osimps_I4_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B] :
% 3.17/1.69 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = F1 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_106_unfold__llist_Ocode,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType] :
% 3.17/1.69 ( ( coindu1599971794_llist @ A @ B )
% 3.17/1.69 = ( ^ [P4: A > $o,G212: A > B,G222: A > A,A5: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P4 @ A5 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A5 ) @ ( coindu1599971794_llist @ A @ B @ P4 @ G212 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_107_ltl__unfold__llist,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 3.17/1.69 ( ( ( IS_LNIL @ A2 )
% 3.17/1.69 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) )
% 3.17/1.69 & ( ~ ( IS_LNIL @ A2 )
% 3.17/1.69 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 3.17/1.69 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_108_surj__pair,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 3.17/1.69 ? [X3: A,Y3: B] :
% 3.17/1.69 ( P3
% 3.17/1.69 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_109_prod__cases,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 3.17/1.69 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 3.17/1.69 => ( P @ P3 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_110_Pair__inject,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,A2: A,B2: B,A4: A,B3: B] :
% 3.17/1.69 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 3.17/1.69 = ( product_Pair @ A @ B @ A4 @ B3 ) )
% 3.17/1.69 => ~ ( ( A2 = A4 )
% 3.17/1.69 => ( B2 != B3 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_111_prod__cases3,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.17/1.69 ~ ! [A6: A,B4: B,C2: C] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_112_prod__cases4,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.17/1.69 ~ ! [A6: A,B4: B,C2: C,D2: D] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_113_prod__cases5,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.17/1.69 ~ ! [A6: A,B4: B,C2: C,D2: D,E2: E] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_114_prod__cases6,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F4: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 3.17/1.69 ~ ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_115_prod__cases7,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F4: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 3.17/1.69 ~ ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4,G3: G2] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_116_prod__induct3,axiom,
% 3.17/1.69 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 3.17/1.69 ( ! [A6: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A6 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 3.17/1.69 => ( P @ X ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_117_prod__induct4,axiom,
% 3.17/1.69 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 3.17/1.69 ( ! [A6: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 3.17/1.69 => ( P @ X ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_118_prod__induct5,axiom,
% 3.17/1.69 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 3.17/1.69 ( ! [A6: A,B4: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 3.17/1.69 => ( P @ X ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_119_prod__induct6,axiom,
% 3.17/1.69 ! [F4: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) )] :
% 3.17/1.69 ( ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F4 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F4 ) @ D2 @ ( product_Pair @ E @ F4 @ E2 @ F5 ) ) ) ) ) )
% 3.17/1.69 => ( P @ X ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_120_prod__induct7,axiom,
% 3.17/1.69 ! [G2: $tType,F4: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) )] :
% 3.17/1.69 ( ! [A6: A,B4: B,C2: C,D2: D,E2: E,F5: F4,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F4 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F4 @ G2 ) @ E2 @ ( product_Pair @ F4 @ G2 @ F5 @ G3 ) ) ) ) ) ) )
% 3.17/1.69 => ( P @ X ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_121_old_Oprod_Oexhaust,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 3.17/1.69 ~ ! [A6: A,B4: B] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( product_Pair @ A @ B @ A6 @ B4 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_122_old_Oprod_Oinducts,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 3.17/1.69 ( ! [A6: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B4 ) )
% 3.17/1.69 => ( P @ Prod ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_123_old_Oprod_Orec,axiom,
% 3.17/1.69 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 3.17/1.69 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 3.17/1.69 = ( F1 @ A2 @ B2 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_124_internal__case__prod__conv,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 3.17/1.69 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 3.17/1.69 = ( C3 @ A2 @ B2 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_125_llexord_Ocases,axiom,
% 3.17/1.69 ! [A: $tType,R2: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu300403952lexord @ A @ R2 @ A1 @ A22 )
% 3.17/1.69 => ( ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X3: A] :
% 3.17/1.69 ( ( A1
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) )
% 3.17/1.69 => ( ( A22
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X3 @ Ys3 ) )
% 3.17/1.69 => ~ ( coindu300403952lexord @ A @ R2 @ Xs4 @ Ys3 ) ) )
% 3.17/1.69 => ( ! [X3: A] :
% 3.17/1.69 ( ? [Xs4: coindu1593790203_llist @ A] :
% 3.17/1.69 ( A1
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) )
% 3.17/1.69 => ! [Y3: A] :
% 3.17/1.69 ( ? [Ys3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( A22
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Y3 @ Ys3 ) )
% 3.17/1.69 => ~ ( R2 @ X3 @ Y3 ) ) )
% 3.17/1.69 => ~ ( ( A1
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 => ! [Ys3: coindu1593790203_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_126_llexord_Osimps,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu300403952lexord @ A )
% 3.17/1.69 = ( ^ [R3: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ? [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 3.17/1.69 ( ( A12
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 3.17/1.69 & ( A23
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 3.17/1.69 & ( coindu300403952lexord @ A @ R3 @ Xs3 @ Ys2 ) )
% 3.17/1.69 | ? [X2: A,Y4: A,Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( A12
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 3.17/1.69 & ( A23
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Y4 @ Ys2 ) )
% 3.17/1.69 & ( R3 @ X2 @ Y4 ) )
% 3.17/1.69 | ? [Ys2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( A12
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ( A23 = Ys2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_127_llexord_Ocoinduct,axiom,
% 3.17/1.69 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R2: A > A > $o] :
% 3.17/1.69 ( ( X4 @ X @ Xa )
% 3.17/1.69 => ( ! [X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( X4 @ X3 @ Xa2 )
% 3.17/1.69 => ( ? [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 3.17/1.69 ( ( X3
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 3.17/1.69 & ( Xa2
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 3.17/1.69 & ( ( X4 @ Xs5 @ Ys4 )
% 3.17/1.69 | ( coindu300403952lexord @ A @ R2 @ Xs5 @ Ys4 ) ) )
% 3.17/1.69 | ? [Xb: A,Y5: A,Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( X3
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 3.17/1.69 & ( Xa2
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Y5 @ Ys4 ) )
% 3.17/1.69 & ( R2 @ Xb @ Y5 ) )
% 3.17/1.69 | ? [Ys4: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( X3
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ( Xa2 = Ys4 ) ) ) )
% 3.17/1.69 => ( coindu300403952lexord @ A @ R2 @ X @ Xa ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_128_llexord__LCons__less,axiom,
% 3.17/1.69 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( R2 @ X @ Y )
% 3.17/1.69 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_129_llexord__LCons__eq,axiom,
% 3.17/1.69 ! [A: $tType,R2: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 3.17/1.69 ( ( coindu300403952lexord @ A @ R2 @ Xs @ Ys )
% 3.17/1.69 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_130_llexord__LNil,axiom,
% 3.17/1.69 ! [A: $tType,R2: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R2 @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_131_natural_Osimps_I5_J,axiom,
% 3.17/1.69 ! [T: $tType,F1: T,F2: code_natural > T,Natural: code_natural] :
% 3.17/1.69 ( ( code_case_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 3.17/1.69 = ( F2 @ Natural ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_132_lmember__code_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,X: A] :
% 3.17/1.69 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_133_lmember__code_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.17/1.69 = ( ( X = Y )
% 3.17/1.69 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_134_natural_Oinject,axiom,
% 3.17/1.69 ! [Natural: code_natural,Natural2: code_natural] :
% 3.17/1.69 ( ( ( code_Suc @ Natural )
% 3.17/1.69 = ( code_Suc @ Natural2 ) )
% 3.17/1.69 = ( Natural = Natural2 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_135_natural_Osimps_I7_J,axiom,
% 3.17/1.69 ! [T: $tType,F1: T,F2: code_natural > T > T,Natural: code_natural] :
% 3.17/1.69 ( ( code_rec_natural @ T @ F1 @ F2 @ ( code_Suc @ Natural ) )
% 3.17/1.69 = ( F2 @ Natural @ ( code_rec_natural @ T @ F1 @ F2 @ Natural ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_136_natural_Oinducts,axiom,
% 3.17/1.69 ! [P: code_natural > $o,Natural: code_natural] :
% 3.17/1.69 ( ( P @ ( zero_zero @ code_natural ) )
% 3.17/1.69 => ( ! [Natural3: code_natural] :
% 3.17/1.69 ( ( P @ Natural3 )
% 3.17/1.69 => ( P @ ( code_Suc @ Natural3 ) ) )
% 3.17/1.69 => ( P @ Natural ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_137_natural_Oexhaust,axiom,
% 3.17/1.69 ! [Y: code_natural] :
% 3.17/1.69 ( ( Y
% 3.17/1.69 != ( zero_zero @ code_natural ) )
% 3.17/1.69 => ~ ! [Natural3: code_natural] :
% 3.17/1.69 ( Y
% 3.17/1.69 != ( code_Suc @ Natural3 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_138_natural_Odistinct_I1_J,axiom,
% 3.17/1.69 ! [Natural2: code_natural] :
% 3.17/1.69 ( ( zero_zero @ code_natural )
% 3.17/1.69 != ( code_Suc @ Natural2 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_139_natural_Odistinct_I2_J,axiom,
% 3.17/1.69 ! [Natural4: code_natural] :
% 3.17/1.69 ( ( code_Suc @ Natural4 )
% 3.17/1.69 != ( zero_zero @ code_natural ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_140_random__aux__set_Ocases,axiom,
% 3.17/1.69 ! [X: product_prod @ code_natural @ code_natural] :
% 3.17/1.69 ( ! [J: code_natural] :
% 3.17/1.69 ( X
% 3.17/1.69 != ( product_Pair @ code_natural @ code_natural @ ( zero_zero @ code_natural ) @ J ) )
% 3.17/1.69 => ~ ! [I2: code_natural,J: code_natural] :
% 3.17/1.69 ( X
% 3.17/1.69 != ( product_Pair @ code_natural @ code_natural @ ( code_Suc @ I2 ) @ J ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_141_random__aux__rec,axiom,
% 3.17/1.69 ! [A: $tType,Random_aux: code_natural > A,Rhs: code_natural > A,K: code_natural] :
% 3.17/1.69 ( ( ( Random_aux @ ( zero_zero @ code_natural ) )
% 3.17/1.69 = ( Rhs @ ( zero_zero @ code_natural ) ) )
% 3.17/1.69 => ( ! [K2: code_natural] :
% 3.17/1.69 ( ( Random_aux @ ( code_Suc @ K2 ) )
% 3.17/1.69 = ( Rhs @ ( code_Suc @ K2 ) ) )
% 3.17/1.69 => ( ( Random_aux @ K )
% 3.17/1.69 = ( Rhs @ K ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_142_random__aux__set_Oinduct,axiom,
% 3.17/1.69 ! [B: $tType] :
% 3.17/1.69 ( ( quickcheck_random @ B @ ( type2 @ B ) )
% 3.17/1.69 => ! [P: code_natural > code_natural > $o,A0: code_natural,A1: code_natural] :
% 3.17/1.69 ( ! [X12: code_natural] : ( P @ ( zero_zero @ code_natural ) @ X12 )
% 3.17/1.69 => ( ! [I2: code_natural,J: code_natural] :
% 3.17/1.69 ( ! [X5: product_prod @ B @ ( product_unit > code_term )] : ( P @ I2 @ J )
% 3.17/1.69 => ( P @ ( code_Suc @ I2 ) @ J ) )
% 3.17/1.69 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_143_case__enat__0,axiom,
% 3.17/1.69 ! [A: $tType,F: nat > A,I: A] :
% 3.17/1.69 ( ( extended_case_enat @ A @ F @ I @ ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( F @ ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_144_the__enat__0,axiom,
% 3.17/1.69 ( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_145_size__ne__size__imp__ne,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( size @ A @ ( type2 @ A ) )
% 3.17/1.69 => ! [X: A,Y: A] :
% 3.17/1.69 ( ( ( size_size @ A @ X )
% 3.17/1.69 != ( size_size @ A @ Y ) )
% 3.17/1.69 => ( X != Y ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_146_lprefix__expand,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 3.17/1.69 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 3.17/1.69 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_147_lprefix__refl,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_148_llist_Oleq__refl,axiom,
% 3.17/1.69 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_149_LCons__lprefix__LCons,axiom,
% 3.17/1.69 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.17/1.69 = ( ( X = Y )
% 3.17/1.69 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_150_lprefix__code_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_151_lprefix__LNil,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_152_lnull__lprefix,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_153_lprefix__lnull,axiom,
% 3.17/1.69 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ Ys )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_154_lprefix__lnullD,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.17/1.69 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_155_lprefix__not__lnullD,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_156_LCons__lprefix__conv,axiom,
% 3.17/1.69 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 3.17/1.69 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Ys
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X @ Ys5 ) )
% 3.17/1.69 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_157_Le__LCons,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_158_LNil__lprefix,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_159_lprefix__ltlI,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_160_lprefix__lappend__sameI,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_161_lprefix__lappend,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_162_lprefix__trans,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_163_llist_Oleq__trans,axiom,
% 3.17/1.69 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ X @ Y )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_164_lprefix__antisym,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 3.17/1.69 => ( Xs = Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_165_llist_Oleq__antisym,axiom,
% 3.17/1.69 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ X @ Y )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 3.17/1.69 => ( X = Y ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_166_lprefix__down__linear,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 3.17/1.69 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_167_lprefixI,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 3.17/1.69 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 3.17/1.69 => ( ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs4 @ Ys3 ) @ X4 )
% 3.17/1.69 => ( ( coindu335574135_lnull @ A @ Xs4 )
% 3.17/1.69 | ? [X5: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Xs4
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X5 @ Xs6 ) )
% 3.17/1.69 & ( Ys3
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X5 @ Ys6 ) )
% 3.17/1.69 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 3.17/1.69 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_168_lprefix__code_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_169_lprefix_Ocases,axiom,
% 3.17/1.69 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 3.17/1.69 => ( ( ( A1
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 => ! [Xs4: coindu1593790203_llist @ A] : ( A22 != Xs4 ) )
% 3.17/1.69 => ~ ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X3: A] :
% 3.17/1.69 ( ( A1
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) )
% 3.17/1.69 => ( ( A22
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X3 @ Ys3 ) )
% 3.17/1.69 => ~ ( coindu1696667936prefix @ A @ Xs4 @ Ys3 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_170_lprefix_Osimps,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A )
% 3.17/1.69 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ? [Xs3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( A12
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ( A23 = Xs3 ) )
% 3.17/1.69 | ? [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 3.17/1.69 ( ( A12
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 3.17/1.69 & ( A23
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 3.17/1.69 & ( coindu1696667936prefix @ A @ Xs3 @ Ys2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_171_lprefix_Ocoinduct,axiom,
% 3.17/1.69 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( X4 @ X @ Xa )
% 3.17/1.69 => ( ! [X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( X4 @ X3 @ Xa2 )
% 3.17/1.69 => ( ? [Xs5: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( X3
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 & ( Xa2 = Xs5 ) )
% 3.17/1.69 | ? [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 3.17/1.69 ( ( X3
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 3.17/1.69 & ( Xa2
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 3.17/1.69 & ( ( X4 @ Xs5 @ Ys4 )
% 3.17/1.69 | ( coindu1696667936prefix @ A @ Xs5 @ Ys4 ) ) ) ) )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_172_lprefix__LCons__conv,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.17/1.69 = ( ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 | ? [Xs2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( Xs
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ Y @ Xs2 ) )
% 3.17/1.69 & ( coindu1696667936prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_173_lprefix__lhdD,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_174_lprefix__coinduct,axiom,
% 3.17/1.69 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( P @ Xs @ Ys )
% 3.17/1.69 => ( ! [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( P @ Xs4 @ Ys3 )
% 3.17/1.69 => ( ( ( coindu335574135_lnull @ A @ Ys3 )
% 3.17/1.69 => ( coindu335574135_lnull @ A @ Xs4 ) )
% 3.17/1.69 & ( ~ ( coindu335574135_lnull @ A @ Xs4 )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Ys3 )
% 3.17/1.69 => ( ( ( coindu1046438764le_lhd @ A @ Xs4 )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Ys3 ) )
% 3.17/1.69 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs4 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) )
% 3.17/1.69 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs4 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) ) ) ) ) ) ) )
% 3.17/1.69 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_175_bool_Osize_I4_J,axiom,
% 3.17/1.69 ( ( size_size @ $o @ $false )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_176_bool_Osize_I3_J,axiom,
% 3.17/1.69 ( ( size_size @ $o @ $true )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_177_lstrict__prefix__def,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu574146665prefix @ A )
% 3.17/1.69 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1696667936prefix @ A @ Xs3 @ Ys2 )
% 3.17/1.69 & ( Xs3 != Ys2 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_178_size__bool,axiom,
% 3.17/1.69 ( ( size_size @ $o )
% 3.17/1.69 = ( ^ [B5: $o] : ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_179_sum_Osize__neq,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,X: sum_sum @ A @ B] :
% 3.17/1.69 ( ( size_size @ ( sum_sum @ A @ B ) @ X )
% 3.17/1.69 != ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_180_prod_Osize__neq,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,X: product_prod @ A @ B] :
% 3.17/1.69 ( ( size_size @ ( product_prod @ A @ B ) @ X )
% 3.17/1.69 != ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_181_bool_Osize_I2_J,axiom,
% 3.17/1.69 ( ( size_bool @ $false )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_182_bool_Osize_I1_J,axiom,
% 3.17/1.69 ( ( size_bool @ $true )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_183_size__bool__overloaded__def,axiom,
% 3.17/1.69 ( ( size_size @ $o )
% 3.17/1.69 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_184_old_Obool_Osimps_I5_J,axiom,
% 3.17/1.69 ! [T: $tType,F1: T,F2: T] :
% 3.17/1.69 ( ( product_rec_bool @ T @ F1 @ F2 @ $true )
% 3.17/1.69 = F1 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_185_old_Obool_Osimps_I6_J,axiom,
% 3.17/1.69 ! [T: $tType,F1: T,F2: T] :
% 3.17/1.69 ( ( product_rec_bool @ T @ F1 @ F2 @ $false )
% 3.17/1.69 = F2 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_186_size__bool__def,axiom,
% 3.17/1.69 ( size_bool
% 3.17/1.69 = ( product_rec_bool @ nat @ ( zero_zero @ nat ) @ ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_187_tuple__isomorphism_Osize__neq,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,C: $tType,X: tuple_isomorphism @ A @ B @ C] :
% 3.17/1.69 ( ( size_size @ ( tuple_isomorphism @ A @ B @ C ) @ X )
% 3.17/1.69 != ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_188_size__literal__def,axiom,
% 3.17/1.69 ( ( size_size @ literal )
% 3.17/1.69 = ( ^ [S: literal] : ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_189_typerep_Osize__neq,axiom,
% 3.17/1.69 ! [X: typerep] :
% 3.17/1.69 ( ( size_size @ typerep @ X )
% 3.17/1.69 != ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_190_option_Osize__neq,axiom,
% 3.17/1.69 ! [A: $tType,X: option @ A] :
% 3.17/1.69 ( ( size_size @ ( option @ A ) @ X )
% 3.17/1.69 != ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_191_size__unit__overloaded__def,axiom,
% 3.17/1.69 ( ( size_size @ product_unit )
% 3.17/1.69 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_192_ssubst__Pair__rhs,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType,R2: A,S2: B,R: set @ ( product_prod @ A @ B ),S3: B] :
% 3.17/1.69 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S2 ) @ R )
% 3.17/1.69 => ( ( S3 = S2 )
% 3.17/1.69 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R2 @ S3 ) @ R ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_193_size__unit__def,axiom,
% 3.17/1.69 ( product_size_unit
% 3.17/1.69 = ( product_rec_unit @ nat @ ( zero_zero @ nat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_194_unit_Osize_I2_J,axiom,
% 3.17/1.69 ( ( size_size @ product_unit @ product_Unity )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_195_old_Ounit_Orec,axiom,
% 3.17/1.69 ! [T: $tType,F1: T] :
% 3.17/1.69 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 3.17/1.69 = F1 ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_196_unit_Osize_I1_J,axiom,
% 3.17/1.69 ( ( product_size_unit @ product_Unity )
% 3.17/1.69 = ( zero_zero @ nat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_197_old_Ounit_Oinducts,axiom,
% 3.17/1.69 ! [P: product_unit > $o,Unit: product_unit] :
% 3.17/1.69 ( ( P @ product_Unity )
% 3.17/1.69 => ( P @ Unit ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_198_old_Ounit_Oexhaust,axiom,
% 3.17/1.69 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_199_default__unit__def,axiom,
% 3.17/1.69 ( ( default_default @ product_unit )
% 3.17/1.69 = product_Unity ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_200_old_Ounit_Ocase,axiom,
% 3.17/1.69 ! [A: $tType,F: A] :
% 3.17/1.69 ( ( product_case_unit @ A @ F @ product_Unity )
% 3.17/1.69 = F ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_201_unit_Ocase__distrib,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,H: A > B,F: A,Unit: product_unit] :
% 3.17/1.69 ( ( H @ ( product_case_unit @ A @ F @ Unit ) )
% 3.17/1.69 = ( product_case_unit @ B @ ( H @ F ) @ Unit ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_202_ltake_Osimps_I3_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( N
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_203_llist_Orel__sel,axiom,
% 3.17/1.69 ! [B: $tType,A: $tType] :
% 3.17/1.69 ( ( coindu987187967t_all2 @ A @ B )
% 3.17/1.69 = ( ^ [R4: A > B > $o,A5: coindu1593790203_llist @ A,B5: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( ( coindu335574135_lnull @ A @ A5 )
% 3.17/1.69 = ( coindu335574135_lnull @ B @ B5 ) )
% 3.17/1.69 & ( ~ ( coindu335574135_lnull @ A @ A5 )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ B @ B5 )
% 3.17/1.69 => ( ( R4 @ ( coindu1046438764le_lhd @ A @ A5 ) @ ( coindu1046438764le_lhd @ B @ B5 ) )
% 3.17/1.69 & ( coindu987187967t_all2 @ A @ B @ R4 @ ( coindu1047225960le_ltl @ A @ A5 ) @ ( coindu1047225960le_ltl @ B @ B5 ) ) ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_204_ltake__is__lprefix,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ Xs ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_205_ltake__LNil,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat] :
% 3.17/1.69 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_206_llist_Orel__inject_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 3.17/1.69 = ( ( R @ X21 @ Y21 )
% 3.17/1.69 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_207_ltake__lmap,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,N: extended_enat,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.17/1.69 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1802687541_ltake @ B @ N @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_208_lnull__ltake,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.17/1.69 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 | ( N
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_209_ltake_Odisc__iff_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.17/1.69 = ( ( N
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 | ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_210_ltake_Odisc__iff_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) )
% 3.17/1.69 = ( ( N
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 & ~ ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_211_LNil__eq__ltake__iff,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu1598213697e_LNil @ A )
% 3.17/1.69 = ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.17/1.69 = ( ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 | ( N
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_212_ltake__0,axiom,
% 3.17/1.69 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1802687541_ltake @ A @ ( zero_zero @ extended_enat ) @ Xs )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_213_lhd__ltake,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( N
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.17/1.69 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_214_llist_Orel__cases,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 3.17/1.69 => ( ( ( A2
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 => ( B2
% 3.17/1.69 != ( coindu1598213697e_LNil @ B ) ) )
% 3.17/1.69 => ~ ! [X12: A,X24: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( A2
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ X12 @ X24 ) )
% 3.17/1.69 => ! [Y12: B,Y23: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( B2
% 3.17/1.69 = ( coindu1121789889_LCons @ B @ Y12 @ Y23 ) )
% 3.17/1.69 => ( ( R @ X12 @ Y12 )
% 3.17/1.69 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X24 @ Y23 ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_215_llist_Orel__distinct_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 3.17/1.69 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_216_llist_Orel__distinct_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 3.17/1.69 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_217_ltake_Odisc_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( N
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_218_ltake_Odisc_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( N
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 | ( coindu335574135_lnull @ A @ Xs ) )
% 3.17/1.69 => ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_219_ltake__eq__LNil__iff,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 = ( ( Xs
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) )
% 3.17/1.69 | ( N
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_220_llist_Orel__intros_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( R @ X21 @ Y21 )
% 3.17/1.69 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 3.17/1.69 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_221_llist_Octr__transfer_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_222_llist_Orel__eq,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu987187967t_all2 @ A @ A
% 3.17/1.69 @ ^ [Y6: A,Z2: A] : ( Y6 = Z2 ) )
% 3.17/1.69 = ( ^ [Y6: coindu1593790203_llist @ A,Z2: coindu1593790203_llist @ A] : ( Y6 = Z2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_223_llist_Orel__refl,axiom,
% 3.17/1.69 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 3.17/1.69 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_224_ltake_Octr_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( ( N
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 | ( coindu335574135_lnull @ A @ Xs ) )
% 3.17/1.69 => ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.17/1.69 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_225_llist_Orel__coinduct,axiom,
% 3.17/1.69 ! [A: $tType,B: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,R: A > B > $o] :
% 3.17/1.69 ( ( P @ X @ Y )
% 3.17/1.69 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ B] :
% 3.17/1.69 ( ( P @ Llist4 @ Llist5 )
% 3.17/1.69 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 3.17/1.69 = ( coindu335574135_lnull @ B @ Llist5 ) )
% 3.17/1.69 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ B @ Llist5 )
% 3.17/1.69 => ( ( R @ ( coindu1046438764le_lhd @ A @ Llist4 ) @ ( coindu1046438764le_lhd @ B @ Llist5 ) )
% 3.17/1.69 & ( P @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ B @ Llist5 ) ) ) ) ) ) )
% 3.17/1.69 => ( coindu987187967t_all2 @ A @ B @ R @ X @ Y ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_226_ltake_Ocode,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu1802687541_ltake @ A )
% 3.17/1.69 = ( ^ [N2: extended_enat,Xs3: coindu1593790203_llist @ A] :
% 3.17/1.69 ( if @ ( coindu1593790203_llist @ A )
% 3.17/1.69 @ ( ( N2
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 | ( coindu335574135_lnull @ A @ Xs3 ) )
% 3.17/1.69 @ ( coindu1598213697e_LNil @ A )
% 3.17/1.69 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs3 ) @ ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N2 ) @ ( coindu1047225960le_ltl @ A @ Xs3 ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_227_ltake_Octr_I2_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( N
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.17/1.69 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N ) @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_228_ltake__epred__ltl,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N ) @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 3.17/1.69 = ( coindu1047225960le_ltl @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_229_epred__0,axiom,
% 3.17/1.69 ( ( coinductive_epred @ ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_230_epred__inject,axiom,
% 3.17/1.69 ! [X: extended_enat,Y: extended_enat] :
% 3.17/1.69 ( ( X
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( Y
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( ( coinductive_epred @ X )
% 3.17/1.69 = ( coinductive_epred @ Y ) )
% 3.17/1.69 = ( X = Y ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_231_enat__coinduct,axiom,
% 3.17/1.69 ! [P: extended_enat > extended_enat > $o,M: extended_enat,N: extended_enat] :
% 3.17/1.69 ( ( P @ M @ N )
% 3.17/1.69 => ( ! [M2: extended_enat,N3: extended_enat] :
% 3.17/1.69 ( ( P @ M2 @ N3 )
% 3.17/1.69 => ( ( ( M2
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( N3
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) )
% 3.17/1.69 & ( ( M2
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( N3
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( P @ ( coinductive_epred @ M2 ) @ ( coinductive_epred @ N3 ) )
% 3.17/1.69 | ( ( coinductive_epred @ M2 )
% 3.17/1.69 = ( coinductive_epred @ N3 ) ) ) ) ) ) )
% 3.17/1.69 => ( M = N ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_232_co_Oenat_Oexpand,axiom,
% 3.17/1.69 ! [Enat: extended_enat,Enat2: extended_enat] :
% 3.17/1.69 ( ( ( Enat
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( Enat2
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) )
% 3.17/1.69 => ( ( ( Enat
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( Enat2
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( coinductive_epred @ Enat )
% 3.17/1.69 = ( coinductive_epred @ Enat2 ) ) ) )
% 3.17/1.69 => ( Enat = Enat2 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_233_enat__coinduct2,axiom,
% 3.17/1.69 ! [P: extended_enat > extended_enat > $o,M: extended_enat,N: extended_enat] :
% 3.17/1.69 ( ( P @ M @ N )
% 3.17/1.69 => ( ! [M2: extended_enat,N3: extended_enat] :
% 3.17/1.69 ( ( P @ M2 @ N3 )
% 3.17/1.69 => ( ( M2
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( N3
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) ) )
% 3.17/1.69 => ( ! [M2: extended_enat,N3: extended_enat] :
% 3.17/1.69 ( ( P @ M2 @ N3 )
% 3.17/1.69 => ( ( M2
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( N3
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ( P @ ( coinductive_epred @ M2 ) @ ( coinductive_epred @ N3 ) )
% 3.17/1.69 | ( ( coinductive_epred @ M2 )
% 3.17/1.69 = ( coinductive_epred @ N3 ) ) ) ) ) )
% 3.17/1.69 => ( M = N ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_234_ltake_Osimps_I4_J,axiom,
% 3.17/1.69 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.17/1.69 ( ( N
% 3.17/1.69 != ( zero_zero @ extended_enat ) )
% 3.17/1.69 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.17/1.69 => ( ( coindu1047225960le_ltl @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.17/1.69 = ( coindu1802687541_ltake @ A @ ( coinductive_epred @ N ) @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_235_epred__enat__unfold,axiom,
% 3.17/1.69 ! [A: $tType,Stop: A > $o,A2: A,Next: A > A] :
% 3.17/1.69 ( ( ( Stop @ A2 )
% 3.17/1.69 => ( ( coinductive_epred @ ( coindu1491768222unfold @ A @ Stop @ Next @ A2 ) )
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) )
% 3.17/1.69 & ( ~ ( Stop @ A2 )
% 3.17/1.69 => ( ( coinductive_epred @ ( coindu1491768222unfold @ A @ Stop @ Next @ A2 ) )
% 3.17/1.69 = ( coindu1491768222unfold @ A @ Stop @ Next @ ( Next @ A2 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_236_co_Oenat_Ocase__eq__if,axiom,
% 3.17/1.69 ! [A: $tType] :
% 3.17/1.69 ( ( coindu440805660e_enat @ A )
% 3.17/1.69 = ( ^ [F12: A,F22: extended_enat > A,Enat3: extended_enat] :
% 3.17/1.69 ( if @ A
% 3.17/1.69 @ ( Enat3
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 @ F12
% 3.17/1.69 @ ( F22 @ ( coinductive_epred @ Enat3 ) ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_237_enat__unfold__stop,axiom,
% 3.17/1.69 ! [A: $tType,Stop: A > $o,A2: A,Next: A > A] :
% 3.17/1.69 ( ( Stop @ A2 )
% 3.17/1.69 => ( ( coindu1491768222unfold @ A @ Stop @ Next @ A2 )
% 3.17/1.69 = ( zero_zero @ extended_enat ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_238_enat__unfold__eq__0,axiom,
% 3.17/1.69 ! [A: $tType,Stop: A > $o,Next: A > A,A2: A] :
% 3.17/1.69 ( ( ( coindu1491768222unfold @ A @ Stop @ Next @ A2 )
% 3.17/1.69 = ( zero_zero @ extended_enat ) )
% 3.17/1.69 = ( Stop @ A2 ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_239_enat__cocase__0,axiom,
% 3.17/1.69 ! [A: $tType,Z: A,S2: extended_enat > A] :
% 3.17/1.69 ( ( coindu440805660e_enat @ A @ Z @ S2 @ ( zero_zero @ extended_enat ) )
% 3.17/1.69 = Z ) ).
% 3.17/1.69
% 3.17/1.69 thf(fact_240_co_Oenat_Ocase_I1_J,axiom,
% 3.17/1.69 ! [A: $tType,F1: A,F2: extended_enat > A] :
% 3.17/1.69 ( ( coindu440805660e_enat @ A @ F1 @ F2 @ ( zero_zero @ extended_enat ) )
% 3.17/1.69 = F1 ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Code__Evaluation_Oterm__of,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( code_term_of @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___HOL_Oequal,axiom,
% 3.17/1.69 ! [A7: $tType] : ( cl_HOL_Oequal @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Record_Otuple__isomorphism___Code__Evaluation_Oterm__of_1,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType,A9: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) )
% 3.17/1.69 & ( typerep2 @ A9 @ ( type2 @ A9 ) ) )
% 3.17/1.69 => ( code_term_of @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Record_Otuple__isomorphism___HOL_Oequal_2,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType,A9: $tType] : ( cl_HOL_Oequal @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___Code__Evaluation_Oterm__of_3,axiom,
% 3.17/1.69 code_term_of @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___HOL_Oequal_4,axiom,
% 3.17/1.69 cl_HOL_Oequal @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Evaluation_Oterm___Code__Evaluation_Oterm__of_5,axiom,
% 3.17/1.69 code_term_of @ code_term @ ( type2 @ code_term ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Evaluation_Oterm___HOL_Oequal_6,axiom,
% 3.17/1.69 cl_HOL_Oequal @ code_term @ ( type2 @ code_term ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Ounit___Code__Evaluation_Oterm__of_7,axiom,
% 3.17/1.69 code_term_of @ product_unit @ ( type2 @ product_unit ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Ounit___HOL_Oequal_8,axiom,
% 3.17/1.69 cl_HOL_Oequal @ product_unit @ ( type2 @ product_unit ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Oprod___Code__Evaluation_Oterm__of_9,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( code_term_of @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Oprod___HOL_Oequal_10,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___Code__Evaluation_Oterm__of_11,axiom,
% 3.17/1.69 code_term_of @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___HOL_Oequal_12,axiom,
% 3.17/1.69 cl_HOL_Oequal @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Typerep_Otyperep___Code__Evaluation_Oterm__of_13,axiom,
% 3.17/1.69 code_term_of @ typerep @ ( type2 @ typerep ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Typerep_Otyperep___HOL_Oequal_14,axiom,
% 3.17/1.69 cl_HOL_Oequal @ typerep @ ( type2 @ typerep ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_String_Oliteral___Code__Evaluation_Oterm__of_15,axiom,
% 3.17/1.69 code_term_of @ literal @ ( type2 @ literal ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_String_Oliteral___HOL_Oequal_16,axiom,
% 3.17/1.69 cl_HOL_Oequal @ literal @ ( type2 @ literal ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Option_Ooption___Code__Evaluation_Oterm__of_17,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( code_term_of @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Option_Ooption___HOL_Oequal_18,axiom,
% 3.17/1.69 ! [A7: $tType] : ( cl_HOL_Oequal @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Sum__Type_Osum___Code__Evaluation_Oterm__of_19,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( code_term_of @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Sum__Type_Osum___HOL_Oequal_20,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_HOL_Obool___Code__Evaluation_Oterm__of_21,axiom,
% 3.17/1.69 code_term_of @ $o @ ( type2 @ $o ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_HOL_Obool___HOL_Oequal_22,axiom,
% 3.17/1.69 cl_HOL_Oequal @ $o @ ( type2 @ $o ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Set_Oset___Code__Evaluation_Oterm__of_23,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( code_term_of @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Set_Oset___HOL_Oequal_24,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( cl_HOL_Oequal @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Code__Evaluation_Oterm__of_25,axiom,
% 3.17/1.69 code_term_of @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___HOL_Oequal_26,axiom,
% 3.17/1.69 cl_HOL_Oequal @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_fun___Code__Evaluation_Oterm__of_27,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( code_term_of @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_fun___HOL_Oequal_28,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( cl_HOL_Oequal @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( cl_HOL_Oequal @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_fun___Typerep_Otyperep,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( typerep2 @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_fun___Enum_Oenum,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( enum @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( enum @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Typerep_Otyperep_29,axiom,
% 3.17/1.69 typerep2 @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Set_Oset___Typerep_Otyperep_30,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( typerep2 @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Set_Oset___Enum_Oenum_31,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( enum @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( enum @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_HOL_Obool___Typerep_Otyperep_32,axiom,
% 3.17/1.69 typerep2 @ $o @ ( type2 @ $o ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_HOL_Obool___Enum_Oenum_33,axiom,
% 3.17/1.69 enum @ $o @ ( type2 @ $o ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Sum__Type_Osum___Typerep_Otyperep_34,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( typerep2 @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Sum__Type_Osum___Enum_Oenum_35,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( enum @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( enum @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Option_Ooption___Typerep_Otyperep_36,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( typerep2 @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Option_Ooption___Enum_Oenum_37,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( enum @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( enum @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_String_Oliteral___Typerep_Otyperep_38,axiom,
% 3.17/1.69 typerep2 @ literal @ ( type2 @ literal ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Typerep_Otyperep___Typerep_Otyperep_39,axiom,
% 3.17/1.69 typerep2 @ typerep @ ( type2 @ typerep ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___Typerep_Otyperep_40,axiom,
% 3.17/1.69 typerep2 @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Oprod___Typerep_Otyperep_41,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( typerep2 @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Oprod___Enum_Oenum_42,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( enum @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( enum @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( enum @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Ounit___Typerep_Otyperep_43,axiom,
% 3.17/1.69 typerep2 @ product_unit @ ( type2 @ product_unit ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Ounit___Enum_Oenum_44,axiom,
% 3.17/1.69 enum @ product_unit @ ( type2 @ product_unit ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Evaluation_Oterm___Typerep_Otyperep_45,axiom,
% 3.17/1.69 typerep2 @ code_term @ ( type2 @ code_term ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___Typerep_Otyperep_46,axiom,
% 3.17/1.69 typerep2 @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Record_Otuple__isomorphism___Typerep_Otyperep_47,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType,A9: $tType] :
% 3.17/1.69 ( ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( typerep2 @ A8 @ ( type2 @ A8 ) )
% 3.17/1.69 & ( typerep2 @ A9 @ ( type2 @ A9 ) ) )
% 3.17/1.69 => ( typerep2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Typerep_Otyperep_48,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( typerep2 @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( typerep2 @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_fun___Quickcheck__Random_Orandom,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( code_term_of @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( quickcheck_random @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Divides_Osemiring__numeral__div,axiom,
% 3.17/1.69 semiring_numeral_div @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Quickcheck__Random_Orandom_49,axiom,
% 3.17/1.69 quickcheck_random @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Rings_Osemiring__1,axiom,
% 3.17/1.69 semiring_1 @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 3.17/1.69 zero @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 3.17/1.69 size @ nat @ ( type2 @ nat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Set_Oset___Quickcheck__Random_Orandom_50,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( quickcheck_random @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_HOL_Obool___Quickcheck__Random_Orandom_51,axiom,
% 3.17/1.69 quickcheck_random @ $o @ ( type2 @ $o ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_HOL_Obool___Nat_Osize_52,axiom,
% 3.17/1.69 size @ $o @ ( type2 @ $o ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Sum__Type_Osum___Quickcheck__Random_Orandom_53,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( quickcheck_random @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Sum__Type_Osum___Nat_Osize_54,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] : ( size @ ( sum_sum @ A7 @ A8 ) @ ( type2 @ ( sum_sum @ A7 @ A8 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Option_Ooption___Quickcheck__Random_Orandom_55,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( quickcheck_random @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Option_Ooption___Nat_Osize_56,axiom,
% 3.17/1.69 ! [A7: $tType] : ( size @ ( option @ A7 ) @ ( type2 @ ( option @ A7 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_String_Oliteral___Quickcheck__Random_Orandom_57,axiom,
% 3.17/1.69 quickcheck_random @ literal @ ( type2 @ literal ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_String_Oliteral___Nat_Osize_58,axiom,
% 3.17/1.69 size @ literal @ ( type2 @ literal ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Typerep_Otyperep___Nat_Osize_59,axiom,
% 3.17/1.69 size @ typerep @ ( type2 @ typerep ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___Quickcheck__Random_Orandom_60,axiom,
% 3.17/1.69 quickcheck_random @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___Rings_Osemiring__1_61,axiom,
% 3.17/1.69 semiring_1 @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___Groups_Ozero_62,axiom,
% 3.17/1.69 zero @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Extended__Nat_Oenat___Nat_Osize_63,axiom,
% 3.17/1.69 size @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Oprod___Quickcheck__Random_Orandom_64,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] :
% 3.17/1.69 ( ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) ) )
% 3.17/1.69 => ( quickcheck_random @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Oprod___Nat_Osize_65,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType] : ( size @ ( product_prod @ A7 @ A8 ) @ ( type2 @ ( product_prod @ A7 @ A8 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Ounit___Quickcheck__Random_Orandom_66,axiom,
% 3.17/1.69 quickcheck_random @ product_unit @ ( type2 @ product_unit ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Product__Type_Ounit___Nat_Osize_67,axiom,
% 3.17/1.69 size @ product_unit @ ( type2 @ product_unit ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___Quickcheck__Random_Orandom_68,axiom,
% 3.17/1.69 quickcheck_random @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___Rings_Osemiring__1_69,axiom,
% 3.17/1.69 semiring_1 @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___Groups_Ozero_70,axiom,
% 3.17/1.69 zero @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Code__Numeral_Onatural___Nat_Osize_71,axiom,
% 3.17/1.69 size @ code_natural @ ( type2 @ code_natural ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Record_Otuple__isomorphism___Quickcheck__Random_Orandom_72,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType,A9: $tType] :
% 3.17/1.69 ( ( ( code_term_of @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( cl_HOL_Oequal @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 & ( quickcheck_random @ A8 @ ( type2 @ A8 ) )
% 3.17/1.69 & ( quickcheck_random @ A9 @ ( type2 @ A9 ) ) )
% 3.17/1.69 => ( quickcheck_random @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Record_Otuple__isomorphism___Nat_Osize_73,axiom,
% 3.17/1.69 ! [A7: $tType,A8: $tType,A9: $tType] : ( size @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) @ ( type2 @ ( tuple_isomorphism @ A7 @ A8 @ A9 ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(tcon_Coinductive__List__Mirabelle__kmikjhschf_Ollist___Quickcheck__Random_Orandom_74,axiom,
% 3.17/1.69 ! [A7: $tType] :
% 3.17/1.69 ( ( quickcheck_random @ A7 @ ( type2 @ A7 ) )
% 3.17/1.69 => ( quickcheck_random @ ( coindu1593790203_llist @ A7 ) @ ( type2 @ ( coindu1593790203_llist @ A7 ) ) ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(help_If_3_1_T,axiom,
% 3.17/1.69 ! [P: $o] :
% 3.17/1.69 ( ( P = $true )
% 3.17/1.69 | ( P = $false ) ) ).
% 3.17/1.69
% 3.17/1.69 thf(help_If_2_1_T,axiom,
% 3.17/1.69 ! [A: $tType,X: A,Y: A] :
% 3.17/1.69 ( ( if @ A @ $false @ X @ Y )
% 3.17/1.69 = Y ) ).
% 3.17/1.69
% 3.17/1.69 thf(help_If_1_1_T,axiom,
% 3.17/1.69 ! [A: $tType,X: A,Y: A] :
% 3.17/1.69 ( ( if @ A @ $true @ X @ Y )
% 3.17/1.69 = X ) ).
% 3.17/1.69
% 3.17/1.69 thf(conj_0,hypothesis,
% 3.17/1.69 ~ ( coindu335574135_lnull @ a @ xs ) ).
% 3.17/1.69
% 3.17/1.69 thf(conj_1,conjecture,
% 3.17/1.69 ( ( coindu1046438764le_lhd @ a @ xs )
% 3.17/1.69 = ( coindu749330388e_lnth @ a @ xs @ ( zero_zero @ nat ) ) ) ).
% 3.17/1.69 ------------------------
% 3.27/1.72 % (8092)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/183Mi)
% 3.27/1.72 % (8095)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/2Mi)
% 3.27/1.72 % (8096)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/2Mi)
% 3.27/1.72 % (8097)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/275Mi)
% 3.27/1.72 % (8094)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/27Mi)
% 3.27/1.72 % (8093)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/4Mi)
% 3.27/1.72 % (8098)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/18Mi)
% 3.27/1.73 % (8096)Instruction limit reached!
% 3.27/1.73 % (8096)------------------------------
% 3.27/1.73 % (8096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (8096)Termination reason: Unknown
% 3.27/1.73 % (8096)Termination phase: shuffling
% 3.27/1.73
% 3.27/1.73 % (8096)Memory used [KB]: 1407
% 3.27/1.73 % (8096)Time elapsed: 0.003 s
% 3.27/1.73 % (8096)Instructions burned: 2 (million)
% 3.27/1.73 % (8096)------------------------------
% 3.27/1.73 % (8096)------------------------------
% 3.27/1.73 % (8095)Instruction limit reached!
% 3.27/1.73 % (8095)------------------------------
% 3.27/1.73 % (8095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (8095)Termination reason: Unknown
% 3.27/1.73 % (8095)Termination phase: shuffling
% 3.27/1.73
% 3.27/1.73 % (8095)Memory used [KB]: 1407
% 3.27/1.73 % (8095)Time elapsed: 0.004 s
% 3.27/1.73 % (8095)Instructions burned: 3 (million)
% 3.27/1.73 % (8095)------------------------------
% 3.27/1.73 % (8095)------------------------------
% 3.27/1.73 % (8093)Instruction limit reached!
% 3.27/1.73 % (8093)------------------------------
% 3.27/1.73 % (8093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (8093)Termination reason: Unknown
% 3.27/1.73 % (8093)Termination phase: shuffling
% 3.27/1.73
% 3.27/1.73 % (8093)Memory used [KB]: 1535
% 3.27/1.73 % (8093)Time elapsed: 0.005 s
% 3.27/1.73 % (8093)Instructions burned: 5 (million)
% 3.27/1.73 % (8093)------------------------------
% 3.27/1.73 % (8093)------------------------------
% 3.27/1.73 % (8098)Instruction limit reached!
% 3.27/1.73 % (8098)------------------------------
% 3.27/1.73 % (8098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.73 % (8098)Termination reason: Unknown
% 3.27/1.73 % (8098)Termination phase: shuffling
% 3.27/1.73
% 3.27/1.73 % (8098)Memory used [KB]: 1918
% 3.27/1.73 % (8098)Time elapsed: 0.012 s
% 3.27/1.73 % (8098)Instructions burned: 19 (million)
% 3.27/1.73 % (8098)------------------------------
% 3.27/1.73 % (8098)------------------------------
% 3.27/1.74 % (8094)Instruction limit reached!
% 3.27/1.74 % (8094)------------------------------
% 3.27/1.74 % (8094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.74 % (8094)Termination reason: Unknown
% 3.27/1.74 % (8094)Termination phase: Property scanning
% 3.27/1.74
% 3.27/1.74 % (8094)Memory used [KB]: 1918
% 3.27/1.74 % (8094)Time elapsed: 0.016 s
% 3.27/1.74 % (8094)Instructions burned: 28 (million)
% 3.27/1.74 % (8094)------------------------------
% 3.27/1.74 % (8094)------------------------------
% 3.27/1.74 % (8099)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 3.27/1.74 % (8100)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/37Mi)
% 3.27/1.74 % (8099)Instruction limit reached!
% 3.27/1.74 % (8099)------------------------------
% 3.27/1.74 % (8099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.74 % (8101)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/15Mi)
% 3.27/1.74 % (8099)Termination reason: Unknown
% 3.27/1.74 % (8099)Termination phase: shuffling
% 3.27/1.74
% 3.27/1.74 % (8099)Memory used [KB]: 1407
% 3.27/1.74 % (8099)Time elapsed: 0.003 s
% 3.27/1.74 % (8099)Instructions burned: 3 (million)
% 3.27/1.74 % (8099)------------------------------
% 3.27/1.74 % (8099)------------------------------
% 3.27/1.74 % (8097)Refutation not found, incomplete strategy
% 3.27/1.74 % (8097)------------------------------
% 3.27/1.74 % (8097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.74 % (8097)Termination reason: Refutation not found, incomplete strategy
% 3.27/1.74
% 3.27/1.74
% 3.27/1.74 % (8097)Memory used [KB]: 6524
% 3.27/1.74 % (8097)Time elapsed: 0.022 s
% 3.27/1.74 % (8097)Instructions burned: 37 (million)
% 3.27/1.74 % (8097)------------------------------
% 3.27/1.74 % (8097)------------------------------
% 3.27/1.75 % (8101)Instruction limit reached!
% 3.27/1.75 % (8101)------------------------------
% 3.27/1.75 % (8101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.75 % (8101)Termination reason: Unknown
% 3.27/1.75 % (8101)Termination phase: shuffling
% 3.27/1.75
% 3.27/1.75 % (8101)Memory used [KB]: 1791
% 3.27/1.75 % (8101)Time elapsed: 0.009 s
% 3.27/1.75 % (8101)Instructions burned: 15 (million)
% 3.27/1.75 % (8101)------------------------------
% 3.27/1.75 % (8101)------------------------------
% 3.27/1.75 % (8102)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 3.27/1.75 % (8102)Instruction limit reached!
% 3.27/1.75 % (8102)------------------------------
% 3.27/1.75 % (8102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.75 % (8102)Termination reason: Unknown
% 3.27/1.75 % (8102)Termination phase: shuffling
% 3.27/1.75
% 3.27/1.75 % (8102)Memory used [KB]: 1407
% 3.27/1.75 % (8102)Time elapsed: 0.003 s
% 3.27/1.75 % (8102)Instructions burned: 3 (million)
% 3.27/1.75 % (8102)------------------------------
% 3.27/1.75 % (8102)------------------------------
% 3.27/1.75 % (8103)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/1041Mi)
% 3.27/1.76 % (8104)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/7Mi)
% 3.27/1.76 % (8100)Instruction limit reached!
% 3.27/1.76 % (8100)------------------------------
% 3.27/1.76 % (8100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.76 % (8100)Termination reason: Unknown
% 3.27/1.76 % (8100)Termination phase: shuffling
% 3.27/1.76
% 3.27/1.76 % (8100)Memory used [KB]: 2174
% 3.27/1.76 % (8100)Time elapsed: 0.019 s
% 3.27/1.76 % (8100)Instructions burned: 37 (million)
% 3.27/1.76 % (8100)------------------------------
% 3.27/1.76 % (8100)------------------------------
% 3.27/1.76 % (8105)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/16Mi)
% 3.27/1.76 % (8104)Instruction limit reached!
% 3.27/1.76 % (8104)------------------------------
% 3.27/1.76 % (8104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.76 % (8104)Termination reason: Unknown
% 3.27/1.76 % (8104)Termination phase: shuffling
% 3.27/1.76
% 3.27/1.76 % (8104)Memory used [KB]: 1535
% 3.27/1.76 % (8104)Time elapsed: 0.005 s
% 3.27/1.76 % (8104)Instructions burned: 7 (million)
% 3.27/1.76 % (8104)------------------------------
% 3.27/1.76 % (8104)------------------------------
% 3.27/1.77 % (8106)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 3.27/1.77 % (8107)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 3.27/1.77 % (8106)Instruction limit reached!
% 3.27/1.77 % (8106)------------------------------
% 3.27/1.77 % (8106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.77 % (8106)Termination reason: Unknown
% 3.27/1.77 % (8106)Termination phase: shuffling
% 3.27/1.77
% 3.27/1.77 % (8106)Memory used [KB]: 1407
% 3.27/1.77 % (8106)Time elapsed: 0.003 s
% 3.27/1.77 % (8106)Instructions burned: 3 (million)
% 3.27/1.77 % (8106)------------------------------
% 3.27/1.77 % (8106)------------------------------
% 3.27/1.77 % (8107)Instruction limit reached!
% 3.27/1.77 % (8107)------------------------------
% 3.27/1.77 % (8107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.77 % (8107)Termination reason: Unknown
% 3.27/1.77 % (8107)Termination phase: shuffling
% 3.27/1.77
% 3.27/1.77 % (8107)Memory used [KB]: 1407
% 3.27/1.77 % (8107)Time elapsed: 0.003 s
% 3.27/1.77 % (8107)Instructions burned: 3 (million)
% 3.27/1.77 % (8107)------------------------------
% 3.27/1.77 % (8107)------------------------------
% 3.27/1.77 % (8105)Instruction limit reached!
% 3.27/1.77 % (8105)------------------------------
% 3.27/1.77 % (8105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.77 % (8105)Termination reason: Unknown
% 3.27/1.77 % (8105)Termination phase: shuffling
% 3.27/1.77
% 3.27/1.77 % (8105)Memory used [KB]: 1918
% 3.27/1.77 % (8105)Time elapsed: 0.010 s
% 3.27/1.77 % (8105)Instructions burned: 17 (million)
% 3.27/1.77 % (8105)------------------------------
% 3.27/1.77 % (8105)------------------------------
% 3.27/1.78 % (8108)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/7Mi)
% 3.27/1.78 % (8109)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/3Mi)
% 3.27/1.78 % (8108)Instruction limit reached!
% 3.27/1.78 % (8108)------------------------------
% 3.27/1.78 % (8108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.78 % (8108)Termination reason: Unknown
% 3.27/1.78 % (8108)Termination phase: shuffling
% 3.27/1.78
% 3.27/1.78 % (8108)Memory used [KB]: 1535
% 3.27/1.78 % (8108)Time elapsed: 0.005 s
% 3.27/1.78 % (8108)Instructions burned: 7 (million)
% 3.27/1.78 % (8108)------------------------------
% 3.27/1.78 % (8108)------------------------------
% 3.27/1.78 % (8109)Instruction limit reached!
% 3.27/1.78 % (8109)------------------------------
% 3.27/1.78 % (8109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.78 % (8109)Termination reason: Unknown
% 3.27/1.78 % (8109)Termination phase: shuffling
% 3.27/1.78
% 3.27/1.78 % (8109)Memory used [KB]: 1407
% 3.27/1.78 % (8109)Time elapsed: 0.003 s
% 3.27/1.78 % (8109)Instructions burned: 3 (million)
% 3.27/1.78 % (8109)------------------------------
% 3.27/1.78 % (8109)------------------------------
% 3.27/1.78 % (8110)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/4Mi)
% 3.27/1.79 % (8111)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/18Mi)
% 3.27/1.79 % (8112)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/710Mi)
% 3.27/1.79 % (8110)Instruction limit reached!
% 3.27/1.79 % (8110)------------------------------
% 3.27/1.79 % (8110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.79 % (8110)Termination reason: Unknown
% 3.27/1.79 % (8110)Termination phase: shuffling
% 3.27/1.79
% 3.27/1.79 % (8110)Memory used [KB]: 1535
% 3.27/1.79 % (8110)Time elapsed: 0.004 s
% 3.27/1.79 % (8110)Instructions burned: 5 (million)
% 3.27/1.79 % (8110)------------------------------
% 3.27/1.79 % (8110)------------------------------
% 3.27/1.80 % (8111)Instruction limit reached!
% 3.27/1.80 % (8111)------------------------------
% 3.27/1.80 % (8111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (8111)Termination reason: Unknown
% 3.27/1.80 % (8111)Termination phase: shuffling
% 3.27/1.80
% 3.27/1.80 % (8111)Memory used [KB]: 1918
% 3.27/1.80 % (8111)Time elapsed: 0.011 s
% 3.27/1.80 % (8111)Instructions burned: 18 (million)
% 3.27/1.80 % (8111)------------------------------
% 3.27/1.80 % (8111)------------------------------
% 3.27/1.80 % (8113)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/6Mi)
% 3.27/1.80 % (8114)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/902Mi)
% 3.27/1.80 % (8113)Instruction limit reached!
% 3.27/1.80 % (8113)------------------------------
% 3.27/1.80 % (8113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.80 % (8113)Termination reason: Unknown
% 3.27/1.80 % (8113)Termination phase: shuffling
% 3.27/1.80
% 3.27/1.80 % (8113)Memory used [KB]: 1535
% 3.27/1.80 % (8113)Time elapsed: 0.005 s
% 3.27/1.80 % (8113)Instructions burned: 7 (million)
% 3.27/1.80 % (8113)------------------------------
% 3.27/1.80 % (8113)------------------------------
% 3.27/1.80 % (8115)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/21Mi)
% 3.27/1.81 % (8116)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/5Mi)
% 3.27/1.81 % (8115)Instruction limit reached!
% 3.27/1.81 % (8115)------------------------------
% 3.27/1.81 % (8115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.81 % (8115)Termination reason: Unknown
% 3.27/1.81 % (8115)Termination phase: shuffling
% 3.27/1.81
% 3.27/1.81 % (8115)Memory used [KB]: 1918
% 3.27/1.81 % (8115)Time elapsed: 0.012 s
% 3.27/1.81 % (8115)Instructions burned: 21 (million)
% 3.27/1.81 % (8115)------------------------------
% 3.27/1.81 % (8115)------------------------------
% 3.27/1.81 % (8116)Instruction limit reached!
% 3.27/1.81 % (8116)------------------------------
% 3.27/1.81 % (8116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.81 % (8116)Termination reason: Unknown
% 3.27/1.81 % (8116)Termination phase: shuffling
% 3.27/1.81
% 3.27/1.81 % (8116)Memory used [KB]: 1535
% 3.27/1.81 % (8116)Time elapsed: 0.004 s
% 3.27/1.81 % (8116)Instructions burned: 5 (million)
% 3.27/1.81 % (8116)------------------------------
% 3.27/1.81 % (8116)------------------------------
% 3.27/1.81 % (8092)Instruction limit reached!
% 3.27/1.81 % (8092)------------------------------
% 3.27/1.81 % (8092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.81 % (8092)Termination reason: Unknown
% 3.27/1.81 % (8092)Termination phase: Saturation
% 3.27/1.81
% 3.27/1.81 % (8092)Memory used [KB]: 7419
% 3.27/1.81 % (8092)Time elapsed: 0.091 s
% 3.27/1.81 % (8092)Instructions burned: 183 (million)
% 3.27/1.81 % (8092)------------------------------
% 3.27/1.81 % (8092)------------------------------
% 3.27/1.82 % (8117)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7992 for (2999ds/6Mi)
% 3.27/1.82 % (8117)Instruction limit reached!
% 3.27/1.82 % (8117)------------------------------
% 3.27/1.82 % (8117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.82 % (8117)Termination reason: Unknown
% 3.27/1.82 % (8117)Termination phase: shuffling
% 3.27/1.82
% 3.27/1.82 % (8117)Memory used [KB]: 1535
% 3.27/1.82 % (8117)Time elapsed: 0.004 s
% 3.27/1.82 % (8117)Instructions burned: 6 (million)
% 3.27/1.82 % (8117)------------------------------
% 3.27/1.82 % (8117)------------------------------
% 3.27/1.83 % (8118)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/377Mi)
% 3.27/1.83 % (8119)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/779Mi)
% 3.27/1.83 % (8120)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/19Mi)
% 3.27/1.83 % (8121)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/879Mi)
% 3.27/1.84 % (8120)Instruction limit reached!
% 3.27/1.84 % (8120)------------------------------
% 3.27/1.84 % (8120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.84 % (8120)Termination reason: Unknown
% 3.27/1.84 % (8120)Termination phase: shuffling
% 3.27/1.84
% 3.27/1.84 % (8120)Memory used [KB]: 1791
% 3.27/1.84 % (8120)Time elapsed: 0.011 s
% 3.27/1.84 % (8120)Instructions burned: 20 (million)
% 3.27/1.84 % (8120)------------------------------
% 3.27/1.84 % (8120)------------------------------
% 3.27/1.86 % (8122)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/17Mi)
% 3.27/1.86 % (8114)Refutation not found, incomplete strategy
% 3.27/1.86 % (8114)------------------------------
% 3.27/1.86 % (8114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.86 % (8114)Termination reason: Refutation not found, incomplete strategy
% 3.27/1.86
% 3.27/1.86
% 3.27/1.86 % (8114)Memory used [KB]: 7547
% 3.27/1.86 % (8114)Time elapsed: 0.065 s
% 3.27/1.86 % (8114)Instructions burned: 126 (million)
% 3.27/1.86 % (8114)------------------------------
% 3.27/1.86 % (8114)------------------------------
% 3.27/1.87 % (8122)Instruction limit reached!
% 3.27/1.87 % (8122)------------------------------
% 3.27/1.87 % (8122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.87 % (8122)Termination reason: Unknown
% 3.27/1.87 % (8122)Termination phase: shuffling
% 3.27/1.87
% 3.27/1.87 % (8122)Memory used [KB]: 1918
% 3.27/1.87 % (8122)Time elapsed: 0.011 s
% 3.27/1.87 % (8122)Instructions burned: 18 (million)
% 3.27/1.87 % (8122)------------------------------
% 3.27/1.87 % (8122)------------------------------
% 3.27/1.88 % (8123)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/3Mi)
% 3.27/1.88 % (8123)Instruction limit reached!
% 3.27/1.88 % (8123)------------------------------
% 3.27/1.88 % (8123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.88 % (8123)Termination reason: Unknown
% 3.27/1.88 % (8123)Termination phase: shuffling
% 3.27/1.88
% 3.27/1.88 % (8123)Memory used [KB]: 1535
% 3.27/1.88 % (8123)Time elapsed: 0.004 s
% 3.27/1.88 % (8123)Instructions burned: 4 (million)
% 3.27/1.88 % (8123)------------------------------
% 3.27/1.88 % (8123)------------------------------
% 3.27/1.88 % (8124)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/30Mi)
% 3.27/1.90 % (8125)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7992 for (2998ds/127Mi)
% 3.27/1.90 % (8124)Instruction limit reached!
% 3.27/1.90 % (8124)------------------------------
% 3.27/1.90 % (8124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.90 % (8124)Termination reason: Unknown
% 3.27/1.90 % (8124)Termination phase: Property scanning
% 3.27/1.90
% 3.27/1.90 % (8124)Memory used [KB]: 2046
% 3.27/1.90 % (8124)Time elapsed: 0.017 s
% 3.27/1.90 % (8124)Instructions burned: 31 (million)
% 3.27/1.90 % (8124)------------------------------
% 3.27/1.90 % (8124)------------------------------
% 3.27/1.91 % (8126)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7992 for (2997ds/100Mi)
% 3.27/1.95 % (8119)First to succeed.
% 3.27/1.95 % (8119)Refutation found. Thanks to Tanya!
% 3.27/1.95 % SZS status Theorem for DTF2THF_7992
% 3.27/1.95 % SZS output start Proof for DTF2THF_7992
% 3.27/1.95 thf(type_def_5, type, itself: ($tType) > $tType).
% 3.27/1.95 thf(type_def_7, type, code_natural: $tType).
% 3.27/1.95 thf(type_def_8, type, nat: $tType).
% 3.27/1.95 thf(type_def_9, type, coindu1593790203_llist: ($tType) > $tType).
% 3.27/1.95 thf(type_def_10, type, extended_enat: $tType).
% 3.27/1.95 thf(type_def_11, type, product_prod: ($tType * $tType) > $tType).
% 3.27/1.95 thf(type_def_12, type, product_unit: $tType).
% 3.27/1.95 thf(type_def_13, type, set: ($tType) > $tType).
% 3.27/1.95 thf(type_def_14, type, a: $tType).
% 3.27/1.95 thf(type_def_15, type, code_term: $tType).
% 3.27/1.95 thf(type_def_16, type, sum_sum: ($tType * $tType) > $tType).
% 3.27/1.95 thf(type_def_17, type, tuple_isomorphism: ($tType * $tType * $tType) > $tType).
% 3.27/1.95 thf(type_def_18, type, literal: $tType).
% 3.27/1.95 thf(type_def_19, type, typerep: $tType).
% 3.27/1.95 thf(type_def_20, type, option: ($tType) > $tType).
% 3.27/1.95 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 3.27/1.95 thf(func_def_1, type, tuple_isomorphism: ($tType * $tType * $tType) > $tType).
% 3.27/1.95 thf(func_def_2, type, code_natural: $tType).
% 3.27/1.95 thf(func_def_3, type, code_term: $tType).
% 3.27/1.95 thf(func_def_4, type, product_unit: $tType).
% 3.27/1.95 thf(func_def_5, type, product_prod: ($tType * $tType) > $tType).
% 3.27/1.95 thf(func_def_6, type, extended_enat: $tType).
% 3.27/1.95 thf(func_def_7, type, typerep: $tType).
% 3.27/1.95 thf(func_def_8, type, literal: $tType).
% 3.27/1.95 thf(func_def_9, type, sum_sum: ($tType * $tType) > $tType).
% 3.27/1.95 thf(func_def_10, type, option: ($tType) > $tType).
% 3.27/1.95 thf(func_def_11, type, set: ($tType) > $tType).
% 3.27/1.95 thf(func_def_12, type, nat: $tType).
% 3.27/1.95 thf(func_def_13, type, itself: ($tType) > $tType).
% 3.27/1.95 thf(func_def_14, type, a: $tType).
% 3.27/1.95 thf(func_def_15, type, enum: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_16, type, typerep2: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_17, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_18, type, cl_HOL_Oequal: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_19, type, code_term_of: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_20, type, size: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_21, type, zero: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_22, type, semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_23, type, quickcheck_random: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_24, type, semiring_numeral_div: !>[X0: $tType]:(itself @ X0 > $o)).
% 3.27/1.95 thf(func_def_25, type, code_Suc: code_natural > code_natural).
% 3.27/1.95 thf(func_def_26, type, code_case_natural: !>[X0: $tType]:(X0 > (code_natural > X0) > code_natural > X0)).
% 3.27/1.95 thf(func_def_27, type, code_rec_natural: !>[X0: $tType]:(X0 > (code_natural > X0 > X0) > code_natural > X0)).
% 3.27/1.95 thf(func_def_28, type, code_size_natural: code_natural > nat).
% 3.27/1.95 thf(func_def_29, type, coindu1529956631erates: !>[X0: $tType]:((X0 > X0) > X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_30, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_31, type, coindu300403952lexord: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 3.27/1.95 thf(func_def_32, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_33, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_34, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0)).
% 3.27/1.95 thf(func_def_35, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 3.27/1.95 thf(func_def_36, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o)).
% 3.27/1.95 thf(func_def_37, type, coindu1062782156e_lmap: !>[X0: $tType, X1: $tType]:((X0 > X1) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1)).
% 3.27/1.95 thf(func_def_38, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 3.27/1.95 thf(func_def_39, type, coindu1047225960le_ltl: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_40, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 3.27/1.95 thf(func_def_41, type, coindu749330388e_lnth: !>[X0: $tType]:(coindu1593790203_llist @ X0 > nat > X0)).
% 3.27/1.95 thf(func_def_42, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 3.27/1.95 thf(func_def_43, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 3.27/1.95 thf(func_def_44, type, coindu1802687541_ltake: !>[X0: $tType]:(extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_45, type, coindu721411036eWhile: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_46, type, coindu847746867e_lzip: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > coindu1593790203_llist @ product_prod @ X0 @ X1)).
% 3.27/1.95 thf(func_def_47, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 3.27/1.95 thf(func_def_48, type, coindu440805660e_enat: !>[X0: $tType]:(X0 > (extended_enat > X0) > extended_enat > X0)).
% 3.27/1.95 thf(func_def_49, type, coinductive_epred: extended_enat > extended_enat).
% 3.27/1.95 thf(func_def_50, type, coindu1491768222unfold: !>[X0: $tType]:((X0 > $o) > (X0 > X0) > X0 > extended_enat)).
% 3.27/1.95 thf(func_def_51, type, semiri577515795es_aux: !>[X0: $tType]:(product_prod @ X0 @ X0 > $o)).
% 3.27/1.95 thf(func_def_52, type, extended_case_enat: !>[X0: $tType]:((nat > X0) > X0 > extended_enat > X0)).
% 3.27/1.95 thf(func_def_53, type, extended_the_enat: extended_enat > nat).
% 3.27/1.95 thf(func_def_54, type, zero_zero: !>[X0: $tType]:(X0)).
% 3.27/1.95 thf(func_def_55, type, size_bool: $o > nat).
% 3.27/1.95 thf(func_def_56, type, default_default: !>[X0: $tType]:(X0)).
% 3.27/1.95 thf(func_def_57, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 3.27/1.95 thf(func_def_58, type, rec_nat: !>[X0: $tType]:(X0 > (nat > X0 > X0) > nat > X0)).
% 3.27/1.95 thf(func_def_59, type, semiri532925092at_aux: !>[X0: $tType]:((X0 > X0) > nat > X0 > X0)).
% 3.27/1.95 thf(func_def_60, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 3.27/1.95 thf(func_def_61, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 3.27/1.95 thf(func_def_62, type, product_Unity: product_unit).
% 3.27/1.95 thf(func_def_63, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.27/1.95 thf(func_def_64, type, product_rec_bool: !>[X0: $tType]:(X0 > X0 > $o > X0)).
% 3.27/1.95 thf(func_def_65, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 3.27/1.95 thf(func_def_66, type, product_rec_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 3.27/1.95 thf(func_def_67, type, product_case_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 3.27/1.95 thf(func_def_68, type, product_size_unit: product_unit > nat).
% 3.27/1.95 thf(func_def_69, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.27/1.95 thf(func_def_70, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.27/1.95 thf(func_def_71, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.27/1.95 thf(func_def_72, type, xs: coindu1593790203_llist @ a).
% 3.27/1.95 thf(func_def_95, type, sK1: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 3.27/1.95 thf(func_def_96, type, sK2: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 3.27/1.95 thf(func_def_97, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X0)).
% 3.27/1.95 thf(func_def_98, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > $o) > X3)).
% 3.27/1.95 thf(func_def_99, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X2)).
% 3.27/1.95 thf(func_def_100, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X1)).
% 3.27/1.95 thf(func_def_101, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1)).
% 3.27/1.95 thf(func_def_102, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2)).
% 3.27/1.95 thf(func_def_103, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1)).
% 3.27/1.95 thf(func_def_104, type, sK10: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_105, type, sK11: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_106, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X2 @ X1 > X1)).
% 3.27/1.95 thf(func_def_107, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X2 @ X1 > X2)).
% 3.27/1.95 thf(func_def_108, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X1 @ product_prod @ X2 @ X0 > X1)).
% 3.27/1.95 thf(func_def_109, type, sK15: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_110, type, sK16: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0)).
% 3.27/1.95 thf(func_def_111, type, sK17: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_112, type, sK18: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_113, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.27/1.95 thf(func_def_114, type, sK20: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_115, type, sK21: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_116, type, sK22: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_117, type, sK23: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_118, type, sK24: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 3.27/1.95 thf(func_def_119, type, sK25: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 3.27/1.95 thf(func_def_120, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X1)).
% 3.27/1.95 thf(func_def_121, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X3)).
% 3.27/1.95 thf(func_def_122, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > X2)).
% 3.27/1.95 thf(func_def_123, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > X1)).
% 3.27/1.95 thf(func_def_124, type, sK30: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X0)).
% 3.27/1.95 thf(func_def_125, type, sK31: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > X1)).
% 3.27/1.95 thf(f2208,plain,(
% 3.27/1.95 $false),
% 3.27/1.95 inference(trivial_inequality_removal,[status(thm)],[f2207])).
% 3.27/1.95 thf(f2207,plain,(
% 3.27/1.95 ($true = $false)),
% 3.27/1.95 inference(forward_demodulation,[status(thm)],[f2194,f1600])).
% 3.27/1.95 thf(f1600,plain,(
% 3.27/1.95 ((coindu335574135_lnull @ a @ xs) = $false)),
% 3.27/1.95 inference(not_proxy_clausification,[status(thm)],[f1117])).
% 3.27/1.95 thf(f1117,plain,(
% 3.27/1.95 ($true = (~ (coindu335574135_lnull @ a @ xs)))),
% 3.27/1.95 inference(cnf_transformation,[status(thm)],[f898])).
% 3.27/1.95 thf(f898,plain,(
% 3.27/1.95 ($true = (~ (coindu335574135_lnull @ a @ xs)))),
% 3.27/1.95 inference(fool_elimination,[status(thm)],[f897])).
% 3.27/1.95 thf(f897,plain,(
% 3.27/1.95 ~(coindu335574135_lnull @ a @ xs)),
% 3.27/1.95 inference(rectify,[status(thm)],[f328])).
% 3.27/1.95 thf(f328,axiom,(
% 3.27/1.95 ~(coindu335574135_lnull @ a @ xs)),
% 3.27/1.95 file('/export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2THF_7992.p',conj_0)).
% 3.27/1.95 thf(f2194,plain,(
% 3.27/1.95 ((coindu335574135_lnull @ a @ xs) = $true)),
% 3.27/1.95 inference(superposition,[status(thm)],[f1082,f2193])).
% 3.27/1.95 thf(f2193,plain,(
% 3.27/1.95 (xs = coindu1598213697e_LNil @ a)),
% 3.27/1.95 inference(trivial_inequality_removal,[status(thm)],[f2192])).
% 3.27/1.95 thf(f2192,plain,(
% 3.27/1.95 (xs = coindu1598213697e_LNil @ a) | ((coindu1046438764le_lhd @ a @ xs) != (coindu1046438764le_lhd @ a @ xs))),
% 3.27/1.95 inference(superposition,[status(thm)],[f1170,f2069])).
% 3.27/1.95 thf(f2069,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((coindu749330388e_lnth @ X0 @ X1 @ zero_zero @ nat) = (coindu1046438764le_lhd @ X0 @ X1)) | (coindu1598213697e_LNil @ X0 = X1)) )),
% 3.27/1.95 inference(superposition,[status(thm)],[f1817,f1756])).
% 3.27/1.95 thf(f1756,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)) = X1) | (coindu1598213697e_LNil @ X0 = X1)) )),
% 3.27/1.95 inference(equality_proxy_clausification,[status(thm)],[f1755])).
% 3.27/1.95 thf(f1755,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = (coindu1598213697e_LNil @ X0 = X1)) | ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)) = X1)) )),
% 3.27/1.95 inference(not_proxy_clausification,[status(thm)],[f1754])).
% 3.27/1.95 thf(f1754,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)) = X1) | ((~ (coindu1598213697e_LNil @ X0 = X1)) = $false)) )),
% 3.27/1.95 inference(equality_proxy_clausification,[status(thm)],[f1753])).
% 3.27/1.95 thf(f1753,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)) = X1)) | ((~ (coindu1598213697e_LNil @ X0 = X1)) = $false)) )),
% 3.27/1.95 inference(binary_proxy_clausification,[status(thm)],[f1752])).
% 3.27/1.95 thf(f1752,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = ((~ (coindu1598213697e_LNil @ X0 = X1)) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)) = X1)))) )),
% 3.27/1.95 inference(beta_eta_normalization,[status(thm)],[f1751])).
% 3.27/1.95 thf(f1751,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : coindu1593790203_llist @ X0]: ((~ (coindu1598213697e_LNil @ X0 = Y0)) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ Y0) @ (coindu1047225960le_ltl @ X0 @ Y0)) = Y0))) @ X1))) )),
% 3.27/1.95 inference(pi_clausification,[status(thm)],[f1111])).
% 3.27/1.95 thf(f1111,plain,(
% 3.27/1.95 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: ((~ (coindu1598213697e_LNil @ X0 = Y0)) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ Y0) @ (coindu1047225960le_ltl @ X0 @ Y0)) = Y0)))))) )),
% 3.27/1.95 inference(cnf_transformation,[status(thm)],[f974])).
% 3.27/1.95 thf(f974,plain,(
% 3.27/1.95 ! [X0 : $tType] : ($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: ((~ (coindu1598213697e_LNil @ X0 = Y0)) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ Y0) @ (coindu1047225960le_ltl @ X0 @ Y0)) = Y0)))))),
% 3.27/1.95 inference(closure,[status(thm)],[f768])).
% 3.27/1.95 thf(f768,plain,(
% 3.27/1.95 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: ((~ (coindu1598213697e_LNil @ X0 = Y0)) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ Y0) @ (coindu1047225960le_ltl @ X0 @ Y0)) = Y0)))))) )),
% 3.27/1.95 inference(fool_elimination,[status(thm)],[f767])).
% 3.27/1.95 thf(f767,plain,(
% 3.27/1.95 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 != X1) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X1) @ (coindu1047225960le_ltl @ X0 @ X1)) = X1))),
% 3.27/1.95 inference(rectify,[status(thm)],[f39])).
% 3.27/1.95 thf(f39,axiom,(
% 3.27/1.95 ! [X0 : $tType,X21 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 != X21) => ((coindu1121789889_LCons @ X0 @ (coindu1046438764le_lhd @ X0 @ X21) @ (coindu1047225960le_ltl @ X0 @ X21)) = X21))),
% 3.27/1.95 file('/export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2THF_7992.p',fact_38_llist_Oexhaust__sel)).
% 3.27/1.95 thf(f1817,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist @ X0] : (((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X2 @ X1) @ zero_zero @ nat) = X2)) )),
% 3.27/1.95 inference(equality_proxy_clausification,[status(thm)],[f1816])).
% 3.27/1.95 thf(f1816,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist @ X0] : (($true = ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X2 @ X1) @ zero_zero @ nat) = X2))) )),
% 3.27/1.95 inference(beta_eta_normalization,[status(thm)],[f1815])).
% 3.27/1.95 thf(f1815,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X2 : X0,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : X0]: ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ Y0 @ X1) @ zero_zero @ nat) = Y0)) @ X2))) )),
% 3.27/1.95 inference(pi_clausification,[status(thm)],[f1814])).
% 3.27/1.95 thf(f1814,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = (!! @ X0 @ (^[Y0 : X0]: ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ Y0 @ X1) @ zero_zero @ nat) = Y0))))) )),
% 3.27/1.95 inference(beta_eta_normalization,[status(thm)],[f1813])).
% 3.27/1.95 thf(f1813,plain,(
% 3.27/1.95 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : coindu1593790203_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ Y1 @ Y0) @ zero_zero @ nat) = Y1)))) @ X1))) )),
% 3.27/1.95 inference(pi_clausification,[status(thm)],[f1084])).
% 3.27/1.95 thf(f1084,plain,(
% 3.27/1.95 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ Y1 @ Y0) @ zero_zero @ nat) = Y1))))))) )),
% 3.27/1.95 inference(cnf_transformation,[status(thm)],[f982])).
% 3.27/1.95 thf(f982,plain,(
% 3.27/1.95 ! [X0 : $tType] : ($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ Y1 @ Y0) @ zero_zero @ nat) = Y1))))))),
% 3.27/1.95 inference(closure,[status(thm)],[f589])).
% 3.27/1.95 thf(f589,plain,(
% 3.27/1.95 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ X0 @ (^[Y1 : X0]: ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ Y1 @ Y0) @ zero_zero @ nat) = Y1))))))) )),
% 3.27/1.95 inference(fool_elimination,[status(thm)],[f588])).
% 3.27/1.95 thf(f588,plain,(
% 3.27/1.95 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0] : ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ zero_zero @ nat) = X1)),
% 3.27/1.95 inference(rectify,[status(thm)],[f24])).
% 3.27/1.95 thf(f24,axiom,(
% 3.27/1.95 ! [X0 : $tType,X8 : X0,X5 : coindu1593790203_llist @ X0] : ((coindu749330388e_lnth @ X0 @ (coindu1121789889_LCons @ X0 @ X8 @ X5) @ zero_zero @ nat) = X8)),
% 3.27/1.95 file('/export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2THF_7992.p',fact_23_lnth__0)).
% 3.27/1.95 thf(f1170,plain,(
% 3.27/1.95 ((coindu1046438764le_lhd @ a @ xs) != (coindu749330388e_lnth @ a @ xs @ zero_zero @ nat))),
% 3.27/1.95 inference(equality_proxy_clausification,[status(thm)],[f1169])).
% 3.27/1.95 thf(f1169,plain,(
% 3.27/1.95 ($false = ((coindu1046438764le_lhd @ a @ xs) = (coindu749330388e_lnth @ a @ xs @ zero_zero @ nat)))),
% 3.27/1.95 inference(not_proxy_clausification,[status(thm)],[f1115])).
% 3.27/1.95 thf(f1115,plain,(
% 3.27/1.95 ($true = (~ ((coindu1046438764le_lhd @ a @ xs) = (coindu749330388e_lnth @ a @ xs @ zero_zero @ nat))))),
% 3.27/1.95 inference(cnf_transformation,[status(thm)],[f703])).
% 3.27/1.95 thf(f703,plain,(
% 3.27/1.95 ($true = (~ ((coindu1046438764le_lhd @ a @ xs) = (coindu749330388e_lnth @ a @ xs @ zero_zero @ nat))))),
% 3.27/1.95 inference(fool_elimination,[status(thm)],[f330])).
% 3.27/1.95 thf(f330,negated_conjecture,(
% 3.27/1.95 ~((coindu1046438764le_lhd @ a @ xs) = (coindu749330388e_lnth @ a @ xs @ zero_zero @ nat))),
% 3.27/1.95 inference(negated_conjecture,[status(cth)],[f329])).
% 3.27/1.95 thf(f329,conjecture,(
% 3.27/1.95 ((coindu1046438764le_lhd @ a @ xs) = (coindu749330388e_lnth @ a @ xs @ zero_zero @ nat))),
% 3.27/1.95 file('/export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2THF_7992.p',conj_1)).
% 3.27/1.95 thf(f1082,plain,(
% 3.27/1.95 ( ! [X0 : $tType] : (((coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0) = $true)) )),
% 3.27/1.95 inference(cnf_transformation,[status(thm)],[f984])).
% 3.27/1.95 thf(f984,plain,(
% 3.27/1.95 ! [X0 : $tType] : ((coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0) = $true)),
% 3.27/1.95 inference(closure,[status(thm)],[f517])).
% 3.27/1.95 thf(f517,plain,(
% 3.27/1.95 ( ! [X0 : $tType] : (((coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0) = $true)) )),
% 3.27/1.95 inference(fool_elimination,[status(thm)],[f516])).
% 3.27/1.95 thf(f516,plain,(
% 3.27/1.95 ! [X0 : $tType] : (coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0)),
% 3.27/1.95 inference(rectify,[status(thm)],[f76])).
% 3.27/1.95 thf(f76,axiom,(
% 3.27/1.95 ! [X0 : $tType] : (coindu335574135_lnull @ X0 @ coindu1598213697e_LNil @ X0)),
% 3.27/1.95 file('/export/starexec/sandbox2/tmp/tmp.6TdYbkpEd4/DTF2THF_7992.p',fact_75_llist_Odisc_I1_J)).
% 3.27/1.95 % SZS output end Proof for DTF2THF_7992
% 3.27/1.95 % (8119)------------------------------
% 3.27/1.95 % (8119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.27/1.95 % (8119)Termination reason: Refutation
% 3.27/1.95
% 3.27/1.95 % (8119)Memory used [KB]: 7419
% 3.27/1.95 % (8119)Time elapsed: 0.141 s
% 3.27/1.95 % (8119)Instructions burned: 238 (million)
% 3.27/1.95 % (8119)------------------------------
% 3.27/1.95 % (8119)------------------------------
% 3.27/1.95 % (8091)Success in time 0.265 s
%------------------------------------------------------------------------------