%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT117^1 : 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 : n013.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 08:44:49 AM UTC 2026
% Result : Theorem 2.89s 1.69s
% Output : Refutation 2.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT117^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n013.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 06:07:23 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : DAT117^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.46 % Domain : Data Structures
% 0.30/0.46 % Problem : Coinductive list 761
% 0.30/0.46 % Version : [Bla16] axioms : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.30/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.30/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bla16]
% 0.30/0.46 % Names : coinductive_list__761.p [Bla16]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.30/0.46 % Syntax : Number of formulae : 311 ( 123 unt; 38 typ; 0 def)
% 0.30/0.46 % Number of atoms : 721 ( 267 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 9 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3839 ( 106 ~; 20 |; 62 &;3324 @)
% 0.30/0.46 % ( 0 <=>; 327 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 24 ( 8 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 270 ( 270 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 40 ( 37 usr; 3 con; 0-8 aty)
% 0.30/0.46 % Number of variables : 1101 ( 56 ^; 973 !; 34 ?;1101 :)
% 0.30/0.46 % ( 38 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.46 % 2016-07-13 14:46:28.138
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 %----Could-be-implicit typings (5)
% 0.30/0.46 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.30/0.46 coindu1593790203_llist: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_itself,type,
% 0.30/0.46 itself: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 %----Explicit typings (33)
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.46 bounded_lattice:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.30/0.46 lattice:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.30/0.46 semilattice_sup:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.30/0.46 bounded_lattice_bot:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.30/0.46 bounde1808546759up_bot:
% 0.30/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset,type,
% 0.30/0.46 coindu1928975208n_lset:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.30/0.46 coindu268472904append:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.30/0.46 coindu1213758845finite:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.30/0.46 coindu1121789889_LCons:
% 0.30/0.46 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.30/0.46 coindu1598213697e_LNil:
% 0.30/0.46 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 0.30/0.46 coindu882539134_llist:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist,type,
% 0.30/0.46 coindu1244876290_llist:
% 0.30/0.46 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coindu1593790203_llist @ A ) ) > ( C > C ) > C > ( coindu1593790203_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.30/0.46 coindu1046438764le_lhd:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 0.30/0.46 coindu987187967t_all2:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.30/0.46 coindu335574135_lnull:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 0.30/0.46 coindu1112613586e_lset:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.30/0.46 coindu1047225960le_ltl:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Opred__llist,type,
% 0.30/0.46 coindu44415597_llist:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.30/0.46 coindu567634248member:
% 0.30/0.46 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.30/0.46 coindu1696667936prefix:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olsetp,type,
% 0.30/0.46 coindu1055736764_lsetp:
% 0.30/0.46 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.30/0.46 coindu1599971794_llist:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Complete__Partial__Order_Omonotone,type,
% 0.30/0.46 comple1396247847notone:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( B > B > $o ) > ( A > B ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If,type,
% 0.30/0.46 if:
% 0.30/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/0.46 sup_sup:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.46 bot_bot:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.30/0.46 product_Pair:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Pure_Otype,type,
% 0.30/0.46 type2:
% 0.30/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_x,type,
% 0.30/0.46 x: a ).
% 0.30/0.46
% 0.30/0.46 %----Relevant facts (254)
% 0.30/0.46 thf(fact_0_lprefix__refl,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_refl
% 0.30/0.46 thf(fact_1_llist_Oleq__refl,axiom,
% 0.30/0.46 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 0.30/0.46
% 0.30/0.46 % llist.leq_refl
% 0.30/0.46 thf(fact_2_llist_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.inject
% 0.30/0.46 thf(fact_3_LCons__lprefix__LCons,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( ( X = Y )
% 0.30/0.46 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LCons_lprefix_LCons
% 0.30/0.46 thf(fact_4_lprefix__trans,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_trans
% 0.30/0.46 thf(fact_5_llist_Oleq__trans,axiom,
% 0.30/0.46 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.leq_trans
% 0.30/0.46 thf(fact_6_lprefix__antisym,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_antisym
% 0.30/0.46 thf(fact_7_Le__LCons,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Le_LCons
% 0.30/0.46 thf(fact_8_llist_Oleq__antisym,axiom,
% 0.30/0.46 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.leq_antisym
% 0.30/0.46 thf(fact_9_LCons__lprefix__conv,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.30/0.46 = ( ? [Ys2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X @ Ys2 ) )
% 0.30/0.46 & ( coindu1696667936prefix @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LCons_lprefix_conv
% 0.30/0.46 thf(fact_10_lprefix__down__linear,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_down_linear
% 0.30/0.46 thf(fact_11_llist_Omonotone__if__bot,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Bound: coindu1593790203_llist @ A,G: ( coindu1593790203_llist @ A ) > B,Bot: B,F: ( coindu1593790203_llist @ A ) > B,Ord: B > B > $o] :
% 0.30/0.46 ( ! [X2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/0.46 => ( ( G @ X2 )
% 0.30/0.46 = Bot ) )
% 0.30/0.46 & ( ~ ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/0.46 => ( ( G @ X2 )
% 0.30/0.46 = ( F @ X2 ) ) ) )
% 0.30/0.46 => ( ! [X2: coindu1593790203_llist @ A,Y2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ X2 @ Y2 )
% 0.30/0.46 => ( ~ ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/0.46 => ( Ord @ ( F @ X2 ) @ ( F @ Y2 ) ) ) )
% 0.30/0.46 => ( ! [X2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/0.46 => ( Ord @ Bot @ ( F @ X2 ) ) )
% 0.30/0.46 => ( ( Ord @ Bot @ Bot )
% 0.30/0.46 => ( comple1396247847notone @ ( coindu1593790203_llist @ A ) @ B @ ( coindu1696667936prefix @ A ) @ Ord @ G ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.monotone_if_bot
% 0.30/0.46 thf(fact_12_lmember__code_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( ( X = Y )
% 0.30/0.46 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lmember_code(2)
% 0.30/0.46 thf(fact_13_monotoneD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Orda: A > A > $o,Ordb: B > B > $o,F: A > B,X: A,Y: A] :
% 0.30/0.46 ( ( comple1396247847notone @ A @ B @ Orda @ Ordb @ F )
% 0.30/0.46 => ( ( Orda @ X @ Y )
% 0.30/0.46 => ( Ordb @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % monotoneD
% 0.30/0.46 thf(fact_14_monotoneI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Orda: A > A > $o,Ordb: B > B > $o,F: A > B] :
% 0.30/0.46 ( ! [X2: A,Y2: A] :
% 0.30/0.46 ( ( Orda @ X2 @ Y2 )
% 0.30/0.46 => ( Ordb @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.30/0.46 => ( comple1396247847notone @ A @ B @ Orda @ Ordb @ F ) ) ).
% 0.30/0.46
% 0.30/0.46 % monotoneI
% 0.30/0.46 thf(fact_15_monotone__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( comple1396247847notone @ A @ B )
% 0.30/0.46 = ( ^ [Orda2: A > A > $o,Ordb2: B > B > $o,F2: A > B] :
% 0.30/0.46 ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( Orda2 @ X3 @ Y3 )
% 0.30/0.46 => ( Ordb2 @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % monotone_def
% 0.30/0.46 thf(fact_16_llist_Opred__inject_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,A2: A,Aa: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu44415597_llist @ A @ P @ ( coindu1121789889_LCons @ A @ A2 @ Aa ) )
% 0.30/0.46 = ( ( P @ A2 )
% 0.30/0.46 & ( coindu44415597_llist @ A @ P @ Aa ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.pred_inject(2)
% 0.30/0.46 thf(fact_17_lprefix__code_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_code(2)
% 0.30/0.46 thf(fact_18_lprefix_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 0.30/0.46 => ( ( ( A1
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ! [Xs2: coindu1593790203_llist @ A] : ( A22 != Xs2 ) )
% 0.30/0.46 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 0.30/0.46 ( ( A1
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.30/0.46 => ( ( A22
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 0.30/0.46 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix.cases
% 0.30/0.46 thf(fact_19_lprefix_Osimps,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A )
% 0.30/0.46 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( A12
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 & ( A23 = Xs3 ) )
% 0.30/0.46 | ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 0.30/0.46 ( ( A12
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.30/0.46 & ( A23
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 0.30/0.46 & ( coindu1696667936prefix @ A @ Xs3 @ Ys4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix.simps
% 0.30/0.46 thf(fact_20_lprefix_Ocoinduct,axiom,
% 0.30/0.46 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( X4 @ X @ Xa )
% 0.30/0.46 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( X4 @ X2 @ Xa2 )
% 0.30/0.46 => ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( X2
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 & ( Xa2 = Xs4 ) )
% 0.30/0.46 | ? [Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 0.30/0.46 ( ( X2
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.30/0.46 & ( Xa2
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 0.30/0.46 & ( ( X4 @ Xs4 @ Ys5 )
% 0.30/0.46 | ( coindu1696667936prefix @ A @ Xs4 @ Ys5 ) ) ) ) )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix.coinduct
% 0.30/0.46 thf(fact_21_lprefix__LCons__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.30/0.46 & ( coindu1696667936prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_LCons_conv
% 0.30/0.46 thf(fact_22_unfold__llist__eq__LCons,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( ~ ( IS_LNIL @ B2 )
% 0.30/0.46 & ( X
% 0.30/0.46 = ( LHD @ B2 ) )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist_eq_LCons
% 0.30/0.46 thf(fact_23_lsetp_Ointros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A,X5: A] :
% 0.30/0.46 ( ( coindu1055736764_lsetp @ A @ Xs @ X )
% 0.30/0.46 => ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % lsetp.intros(2)
% 0.30/0.46 thf(fact_24_lprefix__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_code(1)
% 0.30/0.46 thf(fact_25_lmember__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A] :
% 0.30/0.46 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lmember_code(1)
% 0.30/0.46 thf(fact_26_unfold__llist_Octr_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/0.46 ( ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.30/0.46 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.ctr(1)
% 0.30/0.46 thf(fact_27_llist_Opred__inject_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] : ( coindu44415597_llist @ A @ P @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.pred_inject(1)
% 0.30/0.46 thf(fact_28_unfold__llist_Ocode,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( coindu1599971794_llist @ A @ B )
% 0.30/0.46 = ( ^ [P3: A > $o,G212: A > B,G222: A > A,A3: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P3 @ A3 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A3 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.code
% 0.30/0.46 thf(fact_29_LNil__lprefix,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.30/0.46
% 0.30/0.46 % LNil_lprefix
% 0.30/0.46 thf(fact_30_neq__LNil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_LNil_conv
% 0.30/0.46 thf(fact_31_llist_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.exhaust
% 0.30/0.46 thf(fact_32_llist_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1598213697e_LNil @ A )
% 0.30/0.46 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.distinct(1)
% 0.30/0.46 thf(fact_33_unfold__llist_Octr_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.30/0.46 = ( coindu1121789889_LCons @ B @ ( G21 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.ctr(2)
% 0.30/0.46 thf(fact_34_lsetp_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,X1: coindu1593790203_llist @ A,X23: A,P: ( coindu1593790203_llist @ A ) > A > $o] :
% 0.30/0.46 ( ( coindu1055736764_lsetp @ A @ X1 @ X23 )
% 0.30/0.46 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) @ X2 )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A,X6: A] :
% 0.30/0.46 ( ( coindu1055736764_lsetp @ A @ Xs2 @ X2 )
% 0.30/0.46 => ( ( P @ Xs2 @ X2 )
% 0.30/0.46 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) @ X2 ) ) )
% 0.30/0.46 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lsetp.inducts
% 0.30/0.46 thf(fact_35_lsetp_Osimps,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu1055736764_lsetp @ A )
% 0.30/0.46 = ( ^ [A12: coindu1593790203_llist @ A,A23: A] :
% 0.30/0.46 ( ? [X3: A,Xs3: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( A12
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.30/0.46 & ( A23 = X3 ) )
% 0.30/0.46 | ? [Xs3: coindu1593790203_llist @ A,X3: A,X7: A] :
% 0.30/0.46 ( ( A12
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X7 @ Xs3 ) )
% 0.30/0.46 & ( A23 = X3 )
% 0.30/0.46 & ( coindu1055736764_lsetp @ A @ Xs3 @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lsetp.simps
% 0.30/0.46 thf(fact_36_lsetp_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: A] :
% 0.30/0.46 ( ( coindu1055736764_lsetp @ A @ A1 @ A22 )
% 0.30/0.46 => ( ! [X2: A] :
% 0.30/0.46 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( A1
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.30/0.46 => ( A22 != X2 ) )
% 0.30/0.46 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ? [X6: A] :
% 0.30/0.46 ( A1
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) )
% 0.30/0.46 => ~ ( coindu1055736764_lsetp @ A @ Xs2 @ A22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lsetp.cases
% 0.30/0.46 thf(fact_37_lsetp_Ointros_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ X ) ).
% 0.30/0.46
% 0.30/0.46 % lsetp.intros(1)
% 0.30/0.46 thf(fact_38_gen__lset__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( coindu1928975208n_lset @ A @ A4 @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % gen_lset_code(1)
% 0.30/0.46 thf(fact_39_llist_Ocorec__code,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( coindu1244876290_llist @ C @ A )
% 0.30/0.46 = ( ^ [P3: C > $o,G212: C > A,Q22: C > $o,G221: C > ( coindu1593790203_llist @ A ),G2222: C > C,A3: C] : ( if @ ( coindu1593790203_llist @ A ) @ ( P3 @ A3 ) @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ A @ ( G212 @ A3 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q22 @ G221 @ G2222 @ ( G2222 @ A3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_code
% 0.30/0.46 thf(fact_40_lfinite_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ X )
% 0.30/0.46 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite.inducts
% 0.30/0.46 thf(fact_41_lfinite_Osimps,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu1213758845finite @ A )
% 0.30/0.46 = ( ^ [A3: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 | ? [Xs3: coindu1593790203_llist @ A,X3: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.30/0.46 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite.simps
% 0.30/0.46 thf(fact_42_lfinite_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ A2 )
% 0.30/0.46 => ( ( A2
% 0.30/0.46 != ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ? [X2: A] :
% 0.30/0.46 ( A2
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.30/0.46 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite.cases
% 0.30/0.46 thf(fact_43_lappend__snocL1__conv__LCons2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.30/0.46 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_snocL1_conv_LCons2
% 0.30/0.46 thf(fact_44_lprefix__LNil,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_LNil
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 = ( Q @ X2 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( F @ X2 )
% 0.30/0.46 = ( G @ X2 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_ltl__unfold__llist,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.30/0.46 ( ( ( IS_LNIL @ A2 )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) )
% 0.30/0.46 & ( ~ ( IS_LNIL @ A2 )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.30/0.46 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ltl_unfold_llist
% 0.30/0.46 thf(fact_50_llist_Orel__cases,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 0.30/0.46 => ( ( ( A2
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ( B2
% 0.30/0.46 != ( coindu1598213697e_LNil @ B ) ) )
% 0.30/0.46 => ~ ! [X12: A,X24: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X12 @ X24 ) )
% 0.30/0.46 => ! [Y1: B,Y23: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 = ( coindu1121789889_LCons @ B @ Y1 @ Y23 ) )
% 0.30/0.46 => ( ( R @ X12 @ Y1 )
% 0.30/0.46 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X24 @ Y23 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_cases
% 0.30/0.46 thf(fact_51_llist_Orel__distinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.30/0.46 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_distinct(1)
% 0.30/0.46 thf(fact_52_llist_Orel__inject_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 0.30/0.46 = ( ( R @ X21 @ Y21 )
% 0.30/0.46 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_inject(2)
% 0.30/0.46 thf(fact_53_lnull__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_lappend
% 0.30/0.46 thf(fact_54_lappend_Odisc__iff_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.30/0.46 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.disc_iff(2)
% 0.30/0.46 thf(fact_55_lappend__code_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_code(2)
% 0.30/0.46 thf(fact_56_lfinite__code_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.30/0.46 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_code(2)
% 0.30/0.46 thf(fact_57_lfinite__LCons,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_LCons
% 0.30/0.46 thf(fact_58_lappend__LNil2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_LNil2
% 0.30/0.46 thf(fact_59_lappend__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.30/0.46 = Ys ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_code(1)
% 0.30/0.46 thf(fact_60_lfinite__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_code(1)
% 0.30/0.46 thf(fact_61_lfinite__ltl,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.30/0.46 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_ltl
% 0.30/0.46 thf(fact_62_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.30/0.46 = ( P2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.disc_iff(1)
% 0.30/0.46 thf(fact_63_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.30/0.46 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) )
% 0.30/0.46 = ( ~ ( P2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.disc_iff(2)
% 0.30/0.46 thf(fact_64_lfinite__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_lappend
% 0.30/0.46 thf(fact_65_llist_Ocorec__disc__iff_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A2: C] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/0.46 = ( P2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_disc_iff(1)
% 0.30/0.46 thf(fact_66_llist_Ocorec__disc__iff_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A2: C] :
% 0.30/0.46 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) ) )
% 0.30/0.46 = ( ~ ( P2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_disc_iff(2)
% 0.30/0.46 thf(fact_67_ltl__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ltl_lappend
% 0.30/0.46 thf(fact_68_lprefix__lappend__same,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) )
% 0.30/0.46 = ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ Ys @ Zs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_lappend_same
% 0.30/0.46 thf(fact_69_llist_Orel__refl,axiom,
% 0.30/0.46 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ! [X2: B] : ( Ra @ X2 @ X2 )
% 0.30/0.46 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_refl
% 0.30/0.46 thf(fact_70_llist_Orel__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu987187967t_all2 @ A @ A
% 0.30/0.46 @ ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.30/0.46 = ( ^ [Y4: coindu1593790203_llist @ A,Z2: coindu1593790203_llist @ A] : ( Y4 = Z2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_eq
% 0.30/0.46 thf(fact_71_lnull__imp__lfinite,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_imp_lfinite
% 0.30/0.46 thf(fact_72_lappend_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.exhaust
% 0.30/0.46 thf(fact_73_lfinite__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/0.46 => ( P @ Xs2 ) )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/0.46 => ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.30/0.46 => ( P @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_induct
% 0.30/0.46 thf(fact_74_lappend__lnull2,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/0.46 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_lnull2
% 0.30/0.46 thf(fact_75_lappend__lnull1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/0.46 = Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_lnull1
% 0.30/0.46 thf(fact_76_lappend__assoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.30/0.46 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_assoc
% 0.30/0.46 thf(fact_77_lappend__ltl,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys )
% 0.30/0.46 = ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_ltl
% 0.30/0.46 thf(fact_78_lappend__inf,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_inf
% 0.30/0.46 thf(fact_79_lnull__ltlI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_ltlI
% 0.30/0.46 thf(fact_80_llist_Ocorec__disc_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/0.46 ( ( P2 @ A2 )
% 0.30/0.46 => ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_disc(1)
% 0.30/0.46 thf(fact_81_llist_Ocorec__disc_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_disc(2)
% 0.30/0.46 thf(fact_82_llist_Ocorec__sel_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,A2: C,Q222: C > $o,G21: C > A,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ( ( ( Q222 @ A2 )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/0.46 = ( G2212 @ A2 ) ) )
% 0.30/0.46 & ( ~ ( Q222 @ A2 )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/0.46 = ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ ( G2223 @ A2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_sel(2)
% 0.30/0.46 thf(fact_83_lappend_Odisc_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/0.46 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.disc(1)
% 0.30/0.46 thf(fact_84_lappend_Odisc_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.30/0.46 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.disc(2)
% 0.30/0.46 thf(fact_85_lappend_Octr_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/0.46 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.ctr(1)
% 0.30/0.46 thf(fact_86_lnull__lprefix,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_lprefix
% 0.30/0.46 thf(fact_87_lprefix__lnull,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_lnull
% 0.30/0.46 thf(fact_88_lprefix__lnullD,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/0.46 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_lnullD
% 0.30/0.46 thf(fact_89_lprefix__not__lnullD,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_not_lnullD
% 0.30/0.46 thf(fact_90_llist_Odisc_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/0.46 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.disc(2)
% 0.30/0.46 thf(fact_91_llist_OdiscI_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Llist
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/0.46 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.discI(2)
% 0.30/0.46 thf(fact_92_not__lnull__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.30/0.46 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_lnull_conv
% 0.30/0.46 thf(fact_93_lnull__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A )
% 0.30/0.46 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( Llist2
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_def
% 0.30/0.46 thf(fact_94_llist_Ocollapse_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu335574135_lnull @ A @ Llist )
% 0.30/0.46 => ( Llist
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.collapse(1)
% 0.30/0.46 thf(fact_95_llist_OdiscI_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Llist
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.discI(1)
% 0.30/0.46 thf(fact_96_llist_Odisc_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.disc(1)
% 0.30/0.46 thf(fact_97_llist_Orel__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( R @ X21 @ Y21 )
% 0.30/0.46 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 0.30/0.46 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_intros(2)
% 0.30/0.46 thf(fact_98_llist_Octr__transfer_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.ctr_transfer(1)
% 0.30/0.46 thf(fact_99_lprefix__ltlI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_ltlI
% 0.30/0.46 thf(fact_100_ltl__simps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/0.46 = X22 ) ).
% 0.30/0.46
% 0.30/0.46 % ltl_simps(2)
% 0.30/0.46 thf(fact_101_unfold__llist_Odisc_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/0.46 ( ( P2 @ A2 )
% 0.30/0.46 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.disc(1)
% 0.30/0.46 thf(fact_102_unfold__llist_Odisc_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.disc(2)
% 0.30/0.46 thf(fact_103_ltl__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % ltl_simps(1)
% 0.30/0.46 thf(fact_104_lprefix__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_lappend
% 0.30/0.46 thf(fact_105_lprefix__lappend__sameI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_lappend_sameI
% 0.30/0.46 thf(fact_106_not__lfinite__lprefix__conv__eq,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 = ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_lfinite_lprefix_conv_eq
% 0.30/0.46 thf(fact_107_lappend__eq__LNil__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_eq_LNil_iff
% 0.30/0.46 thf(fact_108_LNil__eq__lappend__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu1598213697e_LNil @ A )
% 0.30/0.46 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LNil_eq_lappend_iff
% 0.30/0.46 thf(fact_109_lappend__LNil__LNil,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_LNil_LNil
% 0.30/0.46 thf(fact_110_unfold__llist_Osimps_I4_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.30/0.46 = ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.simps(4)
% 0.30/0.46 thf(fact_111_lfinite__LConsI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_LConsI
% 0.30/0.46 thf(fact_112_lfinite__LNil,axiom,
% 0.30/0.46 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_LNil
% 0.30/0.46 thf(fact_113_llist_Ocorec_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 )
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ ( G21 @ A2 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ ( G2223 @ A2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec(2)
% 0.30/0.46 thf(fact_114_llist_Ocorec_I1_J,axiom,
% 0.30/0.46 ! [C: $tType,A: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/0.46 ( ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 )
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec(1)
% 0.30/0.46 thf(fact_115_llist_Orel__distinct_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.30/0.46 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_distinct(2)
% 0.30/0.46 thf(fact_116_lhd__LCons__ltl,axiom,
% 0.30/0.46 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.30/0.46 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 0.30/0.46 = Llist ) ) ).
% 0.30/0.46
% 0.30/0.46 % lhd_LCons_ltl
% 0.30/0.46 thf(fact_117_llist_Oexhaust__sel,axiom,
% 0.30/0.46 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Llist
% 0.30/0.46 != ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ( Llist
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.exhaust_sel
% 0.30/0.46 thf(fact_118_eq__LConsD,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 => ( ( Xs
% 0.30/0.46 != ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.30/0.46 = Y )
% 0.30/0.46 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 0.30/0.46 = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_LConsD
% 0.30/0.46 thf(fact_119_llist_Orel__coinduct,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,R: A > B > $o] :
% 0.30/0.46 ( ( P @ X @ Y )
% 0.30/0.46 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( P @ Llist3 @ Llist4 )
% 0.30/0.46 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/0.46 = ( coindu335574135_lnull @ B @ Llist4 ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ B @ Llist4 )
% 0.30/0.46 => ( ( R @ ( coindu1046438764le_lhd @ A @ Llist3 ) @ ( coindu1046438764le_lhd @ B @ Llist4 ) )
% 0.30/0.46 & ( P @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ B @ Llist4 ) ) ) ) ) ) )
% 0.30/0.46 => ( coindu987187967t_all2 @ A @ B @ R @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_coinduct
% 0.30/0.46 thf(fact_120_llist_Orel__sel,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( coindu987187967t_all2 @ A @ B )
% 0.30/0.46 = ( ^ [R2: A > B > $o,A3: coindu1593790203_llist @ A,B3: coindu1593790203_llist @ B] :
% 0.30/0.46 ( ( ( coindu335574135_lnull @ A @ A3 )
% 0.30/0.46 = ( coindu335574135_lnull @ B @ B3 ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ A3 )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ B @ B3 )
% 0.30/0.46 => ( ( R2 @ ( coindu1046438764le_lhd @ A @ A3 ) @ ( coindu1046438764le_lhd @ B @ B3 ) )
% 0.30/0.46 & ( coindu987187967t_all2 @ A @ B @ R2 @ ( coindu1047225960le_ltl @ A @ A3 ) @ ( coindu1047225960le_ltl @ B @ B3 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_sel
% 0.30/0.46 thf(fact_121_lprefix__expand,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.30/0.46 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.30/0.46 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_expand
% 0.30/0.46 thf(fact_122_lprefix__coinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( P @ Xs @ Ys )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.30/0.46 => ( ( ( coindu335574135_lnull @ A @ Ys3 )
% 0.30/0.46 => ( coindu335574135_lnull @ A @ Xs2 ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Ys3 )
% 0.30/0.46 => ( ( ( coindu1046438764le_lhd @ A @ Xs2 )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Ys3 ) )
% 0.30/0.46 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) )
% 0.30/0.46 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) ) ) ) ) ) ) )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_coinduct
% 0.30/0.46 thf(fact_123_split__llist,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ? [Ys3: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 0.30/0.46 & ( coindu1213758845finite @ A @ Ys3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_llist
% 0.30/0.46 thf(fact_124_unfold__llist__id,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist_id
% 0.30/0.46 thf(fact_125_lhd__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lhd_lappend
% 0.30/0.46 thf(fact_126_llist_Oset__sel_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.30/0.46 => ( member @ A @ ( coindu1046438764le_lhd @ A @ A2 ) @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_sel(1)
% 0.30/0.46 thf(fact_127_llist__set__induct,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/0.46 => ( P @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ Xs2 ) )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A,Y2: A] :
% 0.30/0.46 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/0.46 => ( ( member @ A @ Y2 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.30/0.46 => ( ( P @ Y2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.30/0.46 => ( P @ Y2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ X @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_set_induct
% 0.30/0.46 thf(fact_128_llist_Oset__induct,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A2: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.30/0.46 => ( ! [Z1: A,Z22: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z22 ) )
% 0.30/0.46 => ( ! [Z1: A,Z22: coindu1593790203_llist @ A,Xa2: A] :
% 0.30/0.46 ( ( member @ A @ Xa2 @ ( coindu1112613586e_lset @ A @ Z22 ) )
% 0.30/0.46 => ( ( P @ Xa2 @ Z22 )
% 0.30/0.46 => ( P @ Xa2 @ ( coindu1121789889_LCons @ A @ Z1 @ Z22 ) ) ) )
% 0.30/0.46 => ( P @ X @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_induct
% 0.30/0.46 thf(fact_129_llist_Oset__cases,axiom,
% 0.30/0.46 ! [A: $tType,E: A,A2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.30/0.46 => ( ! [Z22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( A2
% 0.30/0.46 != ( coindu1121789889_LCons @ A @ E @ Z22 ) )
% 0.30/0.46 => ~ ! [Z1: A,Z22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ Z1 @ Z22 ) )
% 0.30/0.46 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z22 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_cases
% 0.30/0.46 thf(fact_130_lset__induct_H,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.30/0.46 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_induct'
% 0.30/0.46 thf(fact_131_lset__induct,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.30/0.46 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.30/0.46 => ( ( X != X6 )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_induct
% 0.30/0.46 thf(fact_132_lset__cases,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs6: coindu1593790203_llist @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 != ( coindu1121789889_LCons @ A @ X @ Xs6 ) )
% 0.30/0.46 => ~ ! [X6: A,Xs6: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X6 @ Xs6 ) )
% 0.30/0.46 => ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_cases
% 0.30/0.46 thf(fact_133_llist_Oset__intros_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: coindu1593790203_llist @ A] : ( member @ A @ A1 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_intros(1)
% 0.30/0.46 thf(fact_134_llist_Oset__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A22: coindu1593790203_llist @ A,A1: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A22 ) )
% 0.30/0.46 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_intros(2)
% 0.30/0.46 thf(fact_135_lset__intros_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_intros(1)
% 0.30/0.46 thf(fact_136_lset__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,X5: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_intros(2)
% 0.30/0.46 thf(fact_137_llist_Orel__cong,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: coindu1593790203_llist @ A,Ya: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,Xa: coindu1593790203_llist @ B,R: A > B > $o,Ra: A > B > $o] :
% 0.30/0.46 ( ( X = Ya )
% 0.30/0.46 => ( ( Y = Xa )
% 0.30/0.46 => ( ! [Z3: A,Yb: B] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ Ya ) )
% 0.30/0.46 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Xa ) )
% 0.30/0.46 => ( ( R @ Z3 @ Yb )
% 0.30/0.46 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.30/0.46 => ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 0.30/0.46 = ( coindu987187967t_all2 @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_cong
% 0.30/0.46 thf(fact_138_llist_Orel__mono__strong,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,R: A > B > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,Ra: A > B > $o] :
% 0.30/0.46 ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 0.30/0.46 => ( ! [Z3: A,Yb: B] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.30/0.46 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Y ) )
% 0.30/0.46 => ( ( R @ Z3 @ Yb )
% 0.30/0.46 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.30/0.46 => ( coindu987187967t_all2 @ A @ B @ Ra @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_mono_strong
% 0.30/0.46 thf(fact_139_llist_Orel__refl__strong,axiom,
% 0.30/0.46 ! [A: $tType,X: coindu1593790203_llist @ A,Ra: A > A > $o] :
% 0.30/0.46 ( ! [Z3: A] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.30/0.46 => ( Ra @ Z3 @ Z3 ) )
% 0.30/0.46 => ( coindu987187967t_all2 @ A @ A @ Ra @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.rel_refl_strong
% 0.30/0.46 thf(fact_140_in__lset__ltlD,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) )
% 0.30/0.46 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_lset_ltlD
% 0.30/0.46 thf(fact_141_lhd__LCons,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/0.46 = X21 ) ).
% 0.30/0.46
% 0.30/0.46 % lhd_LCons
% 0.30/0.46 thf(fact_142_llist_Opred__cong,axiom,
% 0.30/0.46 ! [A: $tType,X: coindu1593790203_llist @ A,Ya: coindu1593790203_llist @ A,P: A > $o,Pa: A > $o] :
% 0.30/0.46 ( ( X = Ya )
% 0.30/0.46 => ( ! [Z3: A] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ Ya ) )
% 0.30/0.46 => ( ( P @ Z3 )
% 0.30/0.46 = ( Pa @ Z3 ) ) )
% 0.30/0.46 => ( ( coindu44415597_llist @ A @ P @ X )
% 0.30/0.46 = ( coindu44415597_llist @ A @ Pa @ Ya ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.pred_cong
% 0.30/0.46 thf(fact_143_llist_Opred__mono__strong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,X: coindu1593790203_llist @ A,Pa: A > $o] :
% 0.30/0.46 ( ( coindu44415597_llist @ A @ P @ X )
% 0.30/0.46 => ( ! [Z3: A] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.30/0.46 => ( ( P @ Z3 )
% 0.30/0.46 => ( Pa @ Z3 ) ) )
% 0.30/0.46 => ( coindu44415597_llist @ A @ Pa @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.pred_mono_strong
% 0.30/0.46 thf(fact_144_Coinductive__List__Mirabelle__kmikjhschf_Olset__into__lsetp,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ( coindu1055736764_lsetp @ A @ Xs @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % Coinductive_List_Mirabelle_kmikjhschf.lset_into_lsetp
% 0.30/0.46 thf(fact_145_lsetp__into__lset,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.30/0.46 ( ( coindu1055736764_lsetp @ A @ Xs @ X )
% 0.30/0.46 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lsetp_into_lset
% 0.30/0.46 thf(fact_146_unfold__llist_Osimps_I3_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.30/0.46 = ( G21 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % unfold_llist.simps(3)
% 0.30/0.46 thf(fact_147_llist_Ocorec__sel_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/0.46 ( ~ ( P2 @ A2 )
% 0.30/0.46 => ( ( coindu1046438764le_lhd @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/0.46 = ( G21 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.corec_sel(1)
% 0.30/0.46 thf(fact_148_lset__lmember,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 = ( coindu567634248member @ A @ X @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_lmember
% 0.30/0.46 thf(fact_149_llist_Oset__sel_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,A2: coindu1593790203_llist @ A,X: A] :
% 0.30/0.46 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.30/0.46 => ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ A2 ) ) )
% 0.30/0.46 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_sel(2)
% 0.30/0.46 thf(fact_150_in__lset__lappend__iff,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.30/0.46 = ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 | ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 & ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_lset_lappend_iff
% 0.30/0.46 thf(fact_151_lprefix__lhdD,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefix_lhdD
% 0.30/0.46 thf(fact_152_llist_Oexpand,axiom,
% 0.30/0.46 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu335574135_lnull @ A @ Llist )
% 0.30/0.46 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.30/0.46 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.30/0.46 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.30/0.46 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 0.30/0.46 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) )
% 0.30/0.46 => ( Llist = Llist5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.expand
% 0.30/0.46 thf(fact_153_llist_Ocoinduct,axiom,
% 0.30/0.46 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( R @ Llist @ Llist5 )
% 0.30/0.46 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( R @ Llist3 @ Llist4 )
% 0.30/0.46 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/0.46 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.30/0.46 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.30/0.46 & ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) )
% 0.30/0.46 => ( Llist = Llist5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.coinduct
% 0.30/0.46 thf(fact_154_llist_Ocoinduct__strong,axiom,
% 0.30/0.46 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( R @ Llist @ Llist5 )
% 0.30/0.46 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( R @ Llist3 @ Llist4 )
% 0.30/0.46 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/0.46 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.30/0.46 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/0.46 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.30/0.46 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.30/0.46 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.30/0.46 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) )
% 0.30/0.46 | ( ( coindu1047225960le_ltl @ A @ Llist3 )
% 0.30/0.46 = ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) ) )
% 0.30/0.46 => ( Llist = Llist5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.coinduct_strong
% 0.30/0.46 thf(fact_155_split__llist__first,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/0.46 => ? [Ys3: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 0.30/0.46 & ( coindu1213758845finite @ A @ Ys3 )
% 0.30/0.46 & ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_llist_first
% 0.30/0.46 thf(fact_156_llist_Osplit__sel,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F22 @ Llist ) )
% 0.30/0.46 = ( ( ( Llist
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 => ( P @ F1 ) )
% 0.30/0.46 & ( ( Llist
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.30/0.46 => ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.split_sel
% 0.30/0.46 thf(fact_157_llist_Osplit__sel__asm,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F22 @ Llist ) )
% 0.30/0.46 = ( ~ ( ( ( Llist
% 0.30/0.46 = ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 & ~ ( P @ F1 ) )
% 0.30/0.46 | ( ( Llist
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.30/0.46 & ~ ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.split_sel_asm
% 0.30/0.46 thf(fact_158_llist_Ocase__eq__if,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( coindu882539134_llist @ B @ A )
% 0.30/0.46 = ( ^ [F12: B,F23: A > ( coindu1593790203_llist @ A ) > B,Llist2: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist2 ) @ F12 @ ( F23 @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.case_eq_if
% 0.30/0.46 thf(fact_159_lset__lappend__lfinite,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_lappend_lfinite
% 0.30/0.46 thf(fact_160_llist_Osimps_I5_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( coindu882539134_llist @ B @ A @ F1 @ F22 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/0.46 = ( F22 @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.simps(5)
% 0.30/0.46 thf(fact_161_llist_Osimps_I4_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B] :
% 0.30/0.46 ( ( coindu882539134_llist @ B @ A @ F1 @ F22 @ ( coindu1598213697e_LNil @ A ) )
% 0.30/0.46 = F1 ) ).
% 0.30/0.46
% 0.30/0.46 % llist.simps(4)
% 0.30/0.46 thf(fact_162_gen__lset__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu1928975208n_lset @ A )
% 0.30/0.46 = ( ^ [A5: set @ A,Xs3: coindu1593790203_llist @ A] : ( sup_sup @ ( set @ A ) @ A5 @ ( coindu1112613586e_lset @ A @ Xs3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gen_lset_def
% 0.30/0.46 thf(fact_163_lset__lappend__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) )
% 0.30/0.46 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.30/0.46 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coindu1112613586e_lset @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_lappend_conv
% 0.30/0.46 thf(fact_164_Un__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/0.46 = ( ( member @ A @ C2 @ A4 )
% 0.30/0.46 | ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_165_UnCI,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,B4: set @ A,A4: set @ A] :
% 0.30/0.46 ( ( ~ ( member @ A @ C2 @ B4 )
% 0.30/0.46 => ( member @ A @ C2 @ A4 ) )
% 0.30/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_166_sup_Oright__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 0.30/0.46 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.right_idem
% 0.30/0.46 thf(fact_167_sup__apply,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.30/0.46 => ( ( sup_sup @ ( A > B ) )
% 0.30/0.46 = ( ^ [F2: A > B,G2: A > B,X3: A] : ( sup_sup @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_apply
% 0.30/0.46 thf(fact_168_sup_Oidem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ A2 @ A2 )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.idem
% 0.30/0.46 thf(fact_169_sup__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ X )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_idem
% 0.30/0.46 thf(fact_170_sup_Oleft__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.left_idem
% 0.30/0.46 thf(fact_171_sup__left__idem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.30/0.46 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_left_idem
% 0.30/0.46 thf(fact_172_inf__sup__aci_I8_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.30/0.46 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(8)
% 0.30/0.46 thf(fact_173_inf__sup__aci_I7_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A,Z: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.30/0.46 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(7)
% 0.30/0.46 thf(fact_174_inf__sup__aci_I6_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A,Z: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/0.46 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(6)
% 0.30/0.46 thf(fact_175_inf__sup__aci_I5_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( sup_sup @ A )
% 0.30/0.46 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_aci(5)
% 0.30/0.46 thf(fact_176_sup__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.30/0.46 => ( ( sup_sup @ ( A > B ) )
% 0.30/0.46 = ( ^ [F2: A > B,G2: A > B,X3: A] : ( sup_sup @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_fun_def
% 0.30/0.46 thf(fact_177_sup_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,C2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ C2 )
% 0.30/0.46 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.assoc
% 0.30/0.46 thf(fact_178_sup__assoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A,Z: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/0.46 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_assoc
% 0.30/0.46 thf(fact_179_sup_Ocommute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( sup_sup @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] : ( sup_sup @ A @ B3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.commute
% 0.30/0.46 thf(fact_180_sup__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( sup_sup @ A )
% 0.30/0.46 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_commute
% 0.30/0.46 thf(fact_181_sup_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A2 @ C2 ) )
% 0.30/0.46 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.left_commute
% 0.30/0.46 thf(fact_182_sup__left__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A,Z: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.30/0.46 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_left_commute
% 0.30/0.46 thf(fact_183_UnE,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/0.46 => ( ~ ( member @ A @ C2 @ A4 )
% 0.30/0.46 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_184_UnI1,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ A4 )
% 0.30/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_185_UnI2,axiom,
% 0.30/0.46 ! [A: $tType,C2: A,B4: set @ A,A4: set @ A] :
% 0.30/0.46 ( ( member @ A @ C2 @ B4 )
% 0.30/0.46 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_186_bex__Un,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 = ( ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 & ( P @ X3 ) )
% 0.30/0.46 | ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ B4 )
% 0.30/0.46 & ( P @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bex_Un
% 0.30/0.46 thf(fact_187_ball__Un,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/0.46 => ( P @ X3 ) ) )
% 0.30/0.46 = ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A4 )
% 0.30/0.46 => ( P @ X3 ) )
% 0.30/0.46 & ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ B4 )
% 0.30/0.46 => ( P @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ball_Un
% 0.30/0.46 thf(fact_188_Un__assoc,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ C3 )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_assoc
% 0.30/0.46 thf(fact_189_Un__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb
% 0.30/0.46 thf(fact_190_Un__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_commute
% 0.30/0.46 thf(fact_191_Un__left__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_absorb
% 0.30/0.46 thf(fact_192_Un__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_commute
% 0.30/0.46 thf(fact_193_lset__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) @ ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_lappend
% 0.30/0.46 thf(fact_194_lprefixI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 0.30/0.46 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs2 @ Ys3 ) @ X4 )
% 0.30/0.46 => ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/0.46 | ? [X8: A,Xs7: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X8 @ Xs7 ) )
% 0.30/0.46 & ( Ys3
% 0.30/0.46 = ( coindu1121789889_LCons @ A @ X8 @ Ys6 ) )
% 0.30/0.46 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs7 @ Ys6 ) @ X4 )
% 0.30/0.46 | ( coindu1696667936prefix @ A @ Xs7 @ Ys6 ) ) ) ) )
% 0.30/0.46 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lprefixI
% 0.30/0.46 thf(fact_195_lset__eq__empty,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/0.46 ( ( ( coindu1112613586e_lset @ A @ Xs )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_eq_empty
% 0.30/0.46 thf(fact_196_empty__iff,axiom,
% 0.30/0.46 ! [A: $tType,C2: A] :
% 0.30/0.46 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_197_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ! [X3: A] :
% 0.30/0.46 ~ ( member @ A @ X3 @ A4 ) )
% 0.30/0.46 = ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_198_Collect__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X3: A] :
% 0.30/0.46 ~ ( P @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_199_empty__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ P ) )
% 0.30/0.46 = ( ! [X3: A] :
% 0.30/0.46 ~ ( P @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_200_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A4 )
% 0.30/0.46 => ( member @ A @ X2 @ B4 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_201_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 0.30/0.46 => ( A4 = B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_202_sup_Obounded__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,C2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 0.30/0.46 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.bounded_iff
% 0.30/0.46 thf(fact_203_le__sup__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A,Z: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/0.46 = ( ( ord_less_eq @ A @ X @ Z )
% 0.30/0.46 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_sup_iff
% 0.30/0.46 thf(fact_204_subset__empty,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_empty
% 0.30/0.46 thf(fact_205_empty__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.30/0.46
% 0.30/0.46 % empty_subsetI
% 0.30/0.46 thf(fact_206_sup__bot_Oright__neutral,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.right_neutral
% 0.30/0.46 thf(fact_207_sup__bot_Oleft__neutral,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.left_neutral
% 0.30/0.46 thf(fact_208_sup__eq__bot__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ( sup_sup @ A @ X @ Y )
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 = ( ( X
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 & ( Y
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_eq_bot_iff
% 0.30/0.46 thf(fact_209_bot__eq__sup__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ( bot_bot @ A )
% 0.30/0.46 = ( sup_sup @ A @ X @ Y ) )
% 0.30/0.46 = ( ( X
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 & ( Y
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_eq_sup_iff
% 0.30/0.46 thf(fact_210_Un__empty,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty
% 0.30/0.46 thf(fact_211_Un__subset__iff,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ C3 )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_subset_iff
% 0.30/0.46 thf(fact_212_sup__bot__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot_right
% 0.30/0.46 thf(fact_213_sup__bot__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot_left
% 0.30/0.46 thf(fact_214_sup_OcoboundedI2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [C2: A,B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.coboundedI2
% 0.30/0.46 thf(fact_215_sup_OcoboundedI1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [C2: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.coboundedI1
% 0.30/0.46 thf(fact_216_sup_Oabsorb__iff2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( sup_sup @ A @ A3 @ B3 )
% 0.30/0.46 = B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb_iff2
% 0.30/0.46 thf(fact_217_sup_Oabsorb__iff1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [B3: A,A3: A] :
% 0.30/0.46 ( ( sup_sup @ A @ A3 @ B3 )
% 0.30/0.46 = A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb_iff1
% 0.30/0.46 thf(fact_218_sup_Ocobounded2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.cobounded2
% 0.30/0.46 thf(fact_219_sup_Ocobounded1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.cobounded1
% 0.30/0.46 thf(fact_220_sup_Oorder__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [B3: A,A3: A] :
% 0.30/0.46 ( A3
% 0.30/0.46 = ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.order_iff
% 0.30/0.46 thf(fact_221_sup_OboundedI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,A2: A,C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.boundedI
% 0.30/0.46 thf(fact_222_sup_OboundedE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,C2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.boundedE
% 0.30/0.46 thf(fact_223_sup__absorb2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( sup_sup @ A @ X @ Y )
% 0.30/0.46 = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_absorb2
% 0.30/0.46 thf(fact_224_sup__absorb1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( ( sup_sup @ A @ X @ Y )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_absorb1
% 0.30/0.46 thf(fact_225_sup_Oabsorb2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.30/0.46 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb2
% 0.30/0.46 thf(fact_226_sup_Oabsorb1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.30/0.46 = A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.absorb1
% 0.30/0.46 thf(fact_227_sup__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [F: A > A > A,X: A,Y: A] :
% 0.30/0.46 ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y2 ) )
% 0.30/0.46 => ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.30/0.46 => ( ! [X2: A,Y2: A,Z3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ Y2 @ Z3 ) @ X2 ) ) )
% 0.30/0.46 => ( ( sup_sup @ A @ X @ Y )
% 0.30/0.46 = ( F @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_unique
% 0.30/0.46 thf(fact_228_sup_OorderI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.orderI
% 0.30/0.46 thf(fact_229_sup_OorderE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.orderE
% 0.30/0.46 thf(fact_230_le__iff__sup,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [X3: A,Y3: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X3 @ Y3 )
% 0.30/0.46 = Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_sup
% 0.30/0.46 thf(fact_231_sup__least,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [Y: A,X: A,Z: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Z @ X )
% 0.30/0.46 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_least
% 0.30/0.46 thf(fact_232_sup__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,C2: A,B2: A,D: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.30/0.46 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C2 @ D ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_mono
% 0.30/0.46 thf(fact_233_sup_Omono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [C2: A,A2: A,D: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ D @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( sup_sup @ A @ C2 @ D ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup.mono
% 0.30/0.46 thf(fact_234_le__supI2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI2
% 0.30/0.46 thf(fact_235_le__supI1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ A2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI1
% 0.30/0.46 thf(fact_236_sup__ge2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_ge2
% 0.30/0.46 thf(fact_237_sup__ge1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_ge1
% 0.30/0.46 thf(fact_238_le__supI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,X: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ X )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ X )
% 0.30/0.46 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supI
% 0.30/0.46 thf(fact_239_le__supE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ A2 @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ B2 @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_supE
% 0.30/0.46 thf(fact_240_Un__empty__right,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = A4 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_right
% 0.30/0.46 thf(fact_241_Un__empty__left,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.30/0.46 = B4 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_left
% 0.30/0.46 thf(fact_242_subset__Un__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A5 @ B5 )
% 0.30/0.46 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Un_eq
% 0.30/0.46 thf(fact_243_Un__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A,A4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 0.30/0.46 => ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 = A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb2
% 0.30/0.46 thf(fact_244_Un__absorb1,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 => ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 = B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb1
% 0.30/0.46 thf(fact_245_Un__upper2,axiom,
% 0.30/0.46 ! [A: $tType,B4: set @ A,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper2
% 0.30/0.46 thf(fact_246_Un__upper1,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper1
% 0.30/0.46 thf(fact_247_Un__least,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,C3: set @ A,B4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_least
% 0.30/0.46 thf(fact_248_Un__mono,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,C3: set @ A,B4: set @ A,D2: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ D2 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ ( sup_sup @ ( set @ A ) @ C3 @ D2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_mono
% 0.30/0.46 thf(fact_249_inf__sup__ord_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(3)
% 0.30/0.46 thf(fact_250_inf__sup__ord_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/0.46 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inf_sup_ord(4)
% 0.30/0.46 thf(fact_251_emptyE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] :
% 0.30/0.46 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_252_set__mp,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 => ( ( member @ A @ X @ A4 )
% 0.30/0.46 => ( member @ A @ X @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_mp
% 0.30/0.46 thf(fact_253_in__mono,axiom,
% 0.30/0.46 ! [A: $tType,A4: set @ A,B4: set @ A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/0.46 => ( ( member @ A @ X @ A4 )
% 0.30/0.46 => ( member @ A @ X @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_mono
% 0.30/0.46
% 0.30/0.46 %----Type constructors (15)
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.46 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.46 ! [A6: $tType] : ( bounded_lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.46 ! [A6: $tType,A7: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/0.46 => ( bounded_lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.30/0.46 ! [A6: $tType,A7: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/0.46 => ( bounde1808546759up_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.30/0.46 ! [A6: $tType,A7: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/0.46 => ( bounded_lattice_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.30/0.46 ! [A6: $tType,A7: $tType] :
% 0.30/0.46 ( ( semilattice_sup @ A7 @ ( type2 @ A7 ) )
% 0.30/0.46 => ( semilattice_sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/0.46 ! [A6: $tType,A7: $tType] :
% 0.30/0.46 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/0.46 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.30/0.46 ! [A6: $tType] : ( bounde1808546759up_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_4,axiom,
% 0.30/0.46 ! [A6: $tType] : ( bounded_lattice_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_5,axiom,
% 0.30/0.46 ! [A6: $tType] : ( semilattice_sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Olattice_6,axiom,
% 0.30/0.46 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.30/0.46 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_8,axiom,
% 0.30/0.46 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_9,axiom,
% 0.30/0.46 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 0.30/0.46 lattice @ $o @ ( type2 @ $o ) ).
% 0.30/0.46
% 0.30/0.46 %----Helper facts (3)
% 0.30/0.46 thf(help_If_3_1_T,axiom,
% 0.30/0.46 ! [P: $o] :
% 0.30/0.46 ( ( P = $true )
% 0.30/0.46 | ( P = $false ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_2_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $false @ X @ Y )
% 0.30/0.46 = Y ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_1_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $true @ X @ Y )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 %----Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 comple1396247847notone @ ( coindu1593790203_llist @ a ) @ ( coindu1593790203_llist @ a ) @ ( coindu1696667936prefix @ a ) @ ( coindu1696667936prefix @ a ) @ ( coindu1121789889_LCons @ a @ x ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.30/1.50 ---- Embedded in THF ---
% 0.30/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.50 %%% Generated on Tue Feb 24 06:07:24 EST 2026
% 0.30/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.50 %%% Logic specification used:
% 0.30/1.50 %%% thf(spec, logic, $$dhol).
% 0.30/1.50
% 0.30/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DnhfbxsEpZ/DTF2DTF6414.p
% 0.30/1.50 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 0.30/1.50 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.30/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.30/1.50 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.30/1.50 thf(ty_tf_a, type, a: $tType).
% 0.30/1.50 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset, type, coindu1928975208n_lset: (!> [A:$tType]: (((set @ A) > ((coindu1593790203_llist @ A) > (set @ A)))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist, type, coindu882539134_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coindu1593790203_llist @ A) > B)) > ((coindu1593790203_llist @ A) > B)))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist, type, coindu1244876290_llist: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (coindu1593790203_llist @ A)) > ((C > C) > (C > (coindu1593790203_llist @ A)))))))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd, type, coindu1046438764le_lhd: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 0.30/1.50 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) > $o)))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset, type, coindu1112613586e_lset: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (set @ A))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl, type, coindu1047225960le_ltl: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Opred__llist, type, coindu44415597_llist: (!> [A:$tType]: (((A > $o) > ((coindu1593790203_llist @ A) > $o))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olsetp, type, coindu1055736764_lsetp: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (A > $o))))).
% 0.30/1.50 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist, type, coindu1599971794_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coindu1593790203_llist @ B)))))))).
% 0.30/1.50 thf(sy_c_Complete__Partial__Order_Omonotone, type, comple1396247847notone: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((B > (B > $o)) > ((A > B) > $o)))))).
% 0.30/1.50 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.30/1.50 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 0.30/1.50 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 0.30/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.30/1.50 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.30/1.50 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.30/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.30/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.30/1.50 thf(sy_v_x, type, x: a).
% 0.30/1.50 thf(fact_0_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 0.30/1.50 thf(fact_1_llist_Oleq__refl, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ X) @ X)))).
% 0.30/1.50 thf(fact_2_llist_Oinject, axiom, (! [A:$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)))))).
% 0.30/1.50 thf(fact_3_LCons__lprefix__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) & (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 0.30/1.50 thf(fact_4_lprefix__trans, axiom, (! [A:$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)))))).
% 0.30/1.50 thf(fact_5_llist_Oleq__trans, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A),Z:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ Z) => (((coindu1696667936prefix @ A) @ X) @ Z)))))).
% 0.30/1.50 thf(fact_6_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 0.30/1.50 thf(fact_7_Le__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 0.30/1.50 thf(fact_8_llist_Oleq__antisym, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ X) => (X = Y)))))).
% 0.30/1.50 thf(fact_9_LCons__lprefix__conv, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Ys2:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ X) @ Ys2)) & (((coindu1696667936prefix @ A) @ Xs) @ Ys2)))))))).
% 0.30/1.50 thf(fact_10_lprefix__down__linear, axiom, (! [A:$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))))))).
% 0.30/1.50 thf(fact_11_llist_Omonotone__if__bot, axiom, (! [B:$tType,A:$tType,Bound:(coindu1593790203_llist @ A),G:((coindu1593790203_llist @ A) > B),Bot:B,F:((coindu1593790203_llist @ A) > B),Ord:(B > (B > $o))]: (((! [X2:(coindu1593790203_llist @ A)]: ((((((coindu1696667936prefix @ A) @ X2) @ Bound) => ((G @ X2) = Bot)) & ((~ ((((coindu1696667936prefix @ A) @ X2) @ Bound))) => ((G @ X2) = (F @ X2)))))) => ((! [X2:(coindu1593790203_llist @ A),Y2:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X2) @ Y2) => ((~ ((((coindu1696667936prefix @ A) @ X2) @ Bound))) => ((Ord @ (F @ X2)) @ (F @ Y2)))))) => ((! [X2:(coindu1593790203_llist @ A)]: (((~ ((((coindu1696667936prefix @ A) @ X2) @ Bound))) => ((Ord @ Bot) @ (F @ X2))))) => (((Ord @ Bot) @ Bot) => (((((comple1396247847notone @ (coindu1593790203_llist @ A)) @ B) @ (coindu1696667936prefix @ A)) @ Ord) @ G)))))))).
% 0.30/1.50 thf(fact_12_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 0.30/1.50 thf(fact_13_monotoneD, axiom, (! [B:$tType,A:$tType,Orda:(A > (A > $o)),Ordb:(B > (B > $o)),F:(A > B),X:A,Y:A]: (((((((comple1396247847notone @ A) @ B) @ Orda) @ Ordb) @ F) => (((Orda @ X) @ Y) => ((Ordb @ (F @ X)) @ (F @ Y))))))).
% 0.30/1.50 thf(fact_14_monotoneI, axiom, (! [B:$tType,A:$tType,Orda:(A > (A > $o)),Ordb:(B > (B > $o)),F:(A > B)]: (((! [X2:A,Y2:A]: ((((Orda @ X2) @ Y2) => ((Ordb @ (F @ X2)) @ (F @ Y2))))) => (((((comple1396247847notone @ A) @ B) @ Orda) @ Ordb) @ F))))).
% 0.30/1.50 thf(fact_15_monotone__def, axiom, (! [B:$tType,A:$tType]: ((((comple1396247847notone @ A) @ B) = (^ [Orda2:(A > (A > $o)),Ordb2:(B > (B > $o)),F2:(A > B)]: ((! [X3:A,Y3:A]: ((((Orda2 @ X3) @ Y3) => ((Ordb2 @ (F2 @ X3)) @ (F2 @ Y3))))))))))).
% 0.30/1.50 thf(fact_16_llist_Opred__inject_I2_J, axiom, (! [A:$tType,P:(A > $o),A2:A,Aa:(coindu1593790203_llist @ A)]: (((((coindu44415597_llist @ A) @ P) @ (((coindu1121789889_LCons @ A) @ A2) @ Aa)) = ((P @ A2) & (((coindu44415597_llist @ A) @ P) @ Aa)))))).
% 0.30/1.50 thf(fact_17_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((~ ((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 0.30/1.50 thf(fact_18_lprefix_Ocases, axiom, (! [A:$tType,A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ A1) @ A22) => (((A1 = (coindu1598213697e_LNil @ A)) => (! [Xs2:(coindu1593790203_llist @ A)]: ((A22 != Xs2)))) => (~ ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X2:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) => ((A22 = (((coindu1121789889_LCons @ A) @ X2) @ Ys3)) => (~ ((((coindu1696667936prefix @ A) @ Xs2) @ Ys3)))))))))))))).
% 0.30/1.50 thf(fact_19_lprefix_Osimps, axiom, (! [A:$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),Ys4:(coindu1593790203_llist @ A),X3:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ X3) @ Ys4)) & (((coindu1696667936prefix @ A) @ Xs3) @ Ys4)))))))))))).
% 0.30/1.50 thf(fact_20_lprefix_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A)]: ((((X4 @ X) @ Xa) => ((! [X2:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X4 @ X2) @ Xa2) => ((? [Xs4:(coindu1593790203_llist @ A)]: (((X2 = (coindu1598213697e_LNil @ A)) & (Xa2 = Xs4)))) | (? [Xs4:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ A),Xb:A]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys5)) & (((X4 @ Xs4) @ Ys5) | (((coindu1696667936prefix @ A) @ Xs4) @ Ys5)))))))))) => (((coindu1696667936prefix @ A) @ X) @ Xa)))))).
% 0.30/1.50 thf(fact_21_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs5:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs5)) & (((coindu1696667936prefix @ A) @ Xs5) @ Ys))))))))).
% 0.30/1.50 thf(fact_22_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B2:B,X:A,Xs:(coindu1593790203_llist @ A)]: (((((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B2) = (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((~ ((IS_LNIL @ B2))) & ((X = (LHD @ B2)) & (Xs = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B2))))))))).
% 0.30/1.50 thf(fact_23_lsetp_Ointros_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A,X5:A]: (((((coindu1055736764_lsetp @ A) @ Xs) @ X) => (((coindu1055736764_lsetp @ A) @ (((coindu1121789889_LCons @ A) @ X5) @ Xs)) @ X))))).
% 0.30/1.50 thf(fact_24_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 0.30/1.50 thf(fact_25_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 0.30/1.50 thf(fact_26_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P2 @ A2) => (((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2) = (coindu1598213697e_LNil @ B)))))).
% 0.30/1.50 thf(fact_27_llist_Opred__inject_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((((coindu44415597_llist @ A) @ P) @ (coindu1598213697e_LNil @ A))))).
% 0.30/1.50 thf(fact_28_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1599971794_llist @ A) @ B) = (^ [P3:(A > $o),G212:(A > B),G222:(A > A),A3:A]: (((((if @ (coindu1593790203_llist @ B)) @ (P3 @ A3)) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ (G212 @ A3)) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G222) @ (G222 @ A3)))))))))).
% 0.30/1.50 thf(fact_29_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 0.30/1.50 thf(fact_30_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X3:A,Xs5:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)))))))).
% 0.30/1.50 thf(fact_31_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 0.30/1.50 thf(fact_32_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 0.30/1.50 thf(fact_33_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2) = (((coindu1121789889_LCons @ B) @ (G21 @ A2)) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A2)))))))).
% 0.30/1.50 thf(fact_34_lsetp_Oinducts, axiom, (! [A:$tType,X1:(coindu1593790203_llist @ A),X23:A,P:((coindu1593790203_llist @ A) > (A > $o))]: (((((coindu1055736764_lsetp @ A) @ X1) @ X23) => ((! [X2:A,Xs2:(coindu1593790203_llist @ A)]: (((P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) @ X2))) => ((! [Xs2:(coindu1593790203_llist @ A),X2:A,X6:A]: (((((coindu1055736764_lsetp @ A) @ Xs2) @ X2) => (((P @ Xs2) @ X2) => ((P @ (((coindu1121789889_LCons @ A) @ X6) @ Xs2)) @ X2))))) => ((P @ X1) @ X23))))))).
% 0.30/1.50 thf(fact_35_lsetp_Osimps, axiom, (! [A:$tType]: (((coindu1055736764_lsetp @ A) = (^ [A12:(coindu1593790203_llist @ A),A23:A]: (((? [X3:A,Xs3:(coindu1593790203_llist @ A)]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & (A23 = X3)))) | (? [Xs3:(coindu1593790203_llist @ A),X3:A,X7:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X7) @ Xs3)) & ((A23 = X3) & (((coindu1055736764_lsetp @ A) @ Xs3) @ X3)))))))))))).
% 0.30/1.50 thf(fact_36_lsetp_Ocases, axiom, (! [A:$tType,A1:(coindu1593790203_llist @ A),A22:A]: (((((coindu1055736764_lsetp @ A) @ A1) @ A22) => ((! [X2:A]: (((? [Xs2:(coindu1593790203_llist @ A)]: ((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (A22 != X2)))) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X6:A]: ((A1 = (((coindu1121789889_LCons @ A) @ X6) @ Xs2)))) => (~ ((((coindu1055736764_lsetp @ A) @ Xs2) @ A22))))))))))))).
% 0.30/1.50 thf(fact_37_lsetp_Ointros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1055736764_lsetp @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ X)))).
% 0.30/1.50 thf(fact_38_gen__lset__code_I1_J, axiom, (! [A:$tType,A4:(set @ A)]: (((((coindu1928975208n_lset @ A) @ A4) @ (coindu1598213697e_LNil @ A)) = A4)))).
% 0.30/1.50 thf(fact_39_llist_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((coindu1244876290_llist @ C) @ A) = (^ [P3:(C > $o),G212:(C > A),Q22:(C > $o),G221:(C > (coindu1593790203_llist @ A)),G2222:(C > C),A3:C]: (((((if @ (coindu1593790203_llist @ A)) @ (P3 @ A3)) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ (G212 @ A3)) @ ((((if @ (coindu1593790203_llist @ A)) @ (Q22 @ A3)) @ (G221 @ A3)) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q22) @ G221) @ G2222) @ (G2222 @ A3))))))))))).
% 0.30/1.50 thf(fact_40_lfinite_Oinducts, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs2:(coindu1593790203_llist @ A),X2:A]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))) => (P @ X))))))).
% 0.30/1.50 thf(fact_41_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A3:(coindu1593790203_llist @ A)]: (((A3 = (coindu1598213697e_LNil @ A)) | (? [Xs3:(coindu1593790203_llist @ A),X3:A]: (((A3 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((coindu1213758845finite @ A) @ Xs3))))))))))).
% 0.30/1.50 thf(fact_42_lfinite_Ocases, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ A2) => ((A2 != (coindu1598213697e_LNil @ A)) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X2:A]: ((A2 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (~ (((coindu1213758845finite @ A) @ Xs2))))))))))))).
% 0.30/1.50 thf(fact_43_lappend__snocL1__conv__LCons2, axiom, (! [A:$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)))))).
% 0.30/1.50 thf(fact_44_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 0.30/1.50 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.30/1.50 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) = A4)))).
% 0.30/1.50 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.30/1.50 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 0.30/1.50 thf(fact_49_ltl__unfold__llist, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),A2:B,LHD:(B > A),LTL:(B > B)]: ((((IS_LNIL @ A2) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = (coindu1598213697e_LNil @ A))) & ((~ ((IS_LNIL @ A2))) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ A2)))))))).
% 0.30/1.50 thf(fact_50_llist_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(coindu1593790203_llist @ A),B2:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ A2) @ B2) => (((A2 = (coindu1598213697e_LNil @ A)) => (B2 != (coindu1598213697e_LNil @ B))) => (~ ((! [X12:A,X24:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X12) @ X24)) => (! [Y1:B,Y23:(coindu1593790203_llist @ B)]: (((B2 = (((coindu1121789889_LCons @ B) @ Y1) @ Y23)) => (((R @ X12) @ Y1) => (~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X24) @ Y23))))))))))))))))).
% 0.30/1.50 thf(fact_51_llist_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:B,Y22:(coindu1593790203_llist @ B)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 0.30/1.50 thf(fact_52_llist_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,X22:(coindu1593790203_llist @ A),Y21:B,Y22:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22)) = (((R @ X21) @ Y21) & (((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22)))))).
% 0.30/1.50 thf(fact_53_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 0.30/1.50 thf(fact_54_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 0.30/1.50 thf(fact_55_lappend__code_I2_J, axiom, (! [A:$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)))))).
% 0.30/1.50 thf(fact_56_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 0.30/1.50 thf(fact_57_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 0.30/1.50 thf(fact_58_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 0.30/1.50 thf(fact_59_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 0.30/1.50 thf(fact_60_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.30/1.50 thf(fact_61_lfinite__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 0.30/1.50 thf(fact_62_unfold__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),G21:(A > B),G22:(A > A),A2:A]: ((((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)) = (P2 @ A2))))).
% 0.30/1.50 thf(fact_63_unfold__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),G21:(A > B),G22:(A > A),A2:A]: (((~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)))) = (~ ((P2 @ A2))))))).
% 0.30/1.50 thf(fact_64_lfinite__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & ((coindu1213758845finite @ A) @ Ys)))))).
% 0.30/1.50 thf(fact_65_llist_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C),A2:C]: ((((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)) = (P2 @ A2))))).
% 0.30/1.50 thf(fact_66_llist_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C),A2:C]: (((~ (((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)))) = (~ ((P2 @ A2))))))).
% 0.30/1.50 thf(fact_67_ltl__lappend, axiom, (! [A:$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))))))).
% 0.30/1.50 thf(fact_68_lprefix__lappend__same, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs)) = (((coindu1213758845finite @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Ys) @ Zs)))))).
% 0.30/1.50 thf(fact_69_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(coindu1593790203_llist @ B)]: (((! [X2:B]: (((Ra @ X2) @ X2))) => (((((coindu987187967t_all2 @ B) @ B) @ Ra) @ X) @ X))))).
% 0.30/1.50 thf(fact_70_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu987187967t_all2 @ A) @ A) @ (^ [Y4:A,Z2:A]: ((Y4 = Z2)))) = (^ [Y4:(coindu1593790203_llist @ A),Z2:(coindu1593790203_llist @ A)]: ((Y4 = Z2))))))).
% 0.30/1.50 thf(fact_71_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 0.30/1.50 thf(fact_72_lappend_Oexhaust, axiom, (! [A:$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)))))))).
% 0.30/1.50 thf(fact_73_lfinite__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs2) => (P @ Xs2)))) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((P @ ((coindu1047225960le_ltl @ A) @ Xs2)) => (P @ Xs2)))))) => (P @ Xs))))))).
% 0.30/1.50 thf(fact_74_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 0.30/1.50 thf(fact_75_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 0.30/1.50 thf(fact_76_lappend__assoc, axiom, (! [A:$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)))))).
% 0.30/1.50 thf(fact_77_lappend__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((((coindu268472904append @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ Ys) = ((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 0.30/1.50 thf(fact_78_lappend__inf, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 0.30/1.50 thf(fact_79_lnull__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu335574135_lnull @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))))).
% 0.30/1.50 thf(fact_80_llist_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A2:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((P2 @ A2) => ((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)))))).
% 0.30/1.50 thf(fact_81_llist_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A2:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((~ ((P2 @ A2))) => (~ (((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)))))))).
% 0.30/1.50 thf(fact_82_llist_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A2:C,Q222:(C > $o),G21:(C > A),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((~ ((P2 @ A2))) => (((Q222 @ A2) => (((coindu1047225960le_ltl @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)) = (G2212 @ A2))) & ((~ ((Q222 @ A2))) => (((coindu1047225960le_ltl @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)) = ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ (G2223 @ A2))))))))).
% 0.30/1.50 thf(fact_83_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 0.30/1.50 thf(fact_84_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 0.30/1.50 thf(fact_85_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 0.30/1.50 thf(fact_86_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 0.30/1.50 thf(fact_87_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 0.30/1.50 thf(fact_88_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 0.30/1.50 thf(fact_89_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 0.30/1.50 thf(fact_90_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 0.30/1.50 thf(fact_91_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist))))))).
% 0.30/1.50 thf(fact_92_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X3:A,Xs5:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)))))))).
% 0.30/1.50 thf(fact_93_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist2:(coindu1593790203_llist @ A)]: ((Llist2 = (coindu1598213697e_LNil @ A)))))))).
% 0.30/1.50 thf(fact_94_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 0.30/1.50 thf(fact_95_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 0.30/1.50 thf(fact_96_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.30/1.50 thf(fact_97_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,Y21:B,X22:(coindu1593790203_llist @ A),Y22:(coindu1593790203_llist @ B)]: ((((R @ X21) @ Y21) => ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22) => (((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 0.30/1.50 thf(fact_98_llist_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ B))))).
% 0.30/1.50 thf(fact_99_lprefix__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys)))))).
% 0.30/1.50 thf(fact_100_ltl__simps_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1047225960le_ltl @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X22)))).
% 0.30/1.50 thf(fact_101_unfold__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P2 @ A2) => ((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)))))).
% 0.30/1.50 thf(fact_102_unfold__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)))))))).
% 0.30/1.50 thf(fact_103_ltl__simps_I1_J, axiom, (! [A:$tType]: ((((coindu1047225960le_ltl @ A) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 0.30/1.50 thf(fact_104_lprefix__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 0.30/1.50 thf(fact_105_lprefix__lappend__sameI, axiom, (! [A:$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)))))).
% 0.30/1.50 thf(fact_106_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 0.30/1.50 thf(fact_107_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 0.30/1.50 thf(fact_108_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 0.30/1.50 thf(fact_109_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 0.30/1.50 thf(fact_110_unfold__llist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (((coindu1047225960le_ltl @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)) = ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A2))))))).
% 0.30/1.50 thf(fact_111_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 0.30/1.50 thf(fact_112_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.30/1.50 thf(fact_113_llist_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A2:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((~ ((P2 @ A2))) => (((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2) = (((coindu1121789889_LCons @ A) @ (G21 @ A2)) @ ((((if @ (coindu1593790203_llist @ A)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ (G2223 @ A2))))))))).
% 0.30/1.50 thf(fact_114_llist_Ocorec_I1_J, axiom, (! [C:$tType,A:$tType,P2:(C > $o),A2:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((P2 @ A2) => (((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2) = (coindu1598213697e_LNil @ A)))))).
% 0.30/1.50 thf(fact_115_llist_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) @ (coindu1598213697e_LNil @ B))))))).
% 0.30/1.50 thf(fact_116_lhd__LCons__ltl, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist)) = Llist))))).
% 0.30/1.50 thf(fact_117_llist_Oexhaust__sel, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist != (coindu1598213697e_LNil @ A)) => (Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))).
% 0.30/1.50 thf(fact_118_eq__LConsD, axiom, (! [A:$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))))))).
% 0.30/1.50 thf(fact_119_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 > $o))]: ((((P @ X) @ Y) => ((! [Llist3:(coindu1593790203_llist @ A),Llist4:(coindu1593790203_llist @ B)]: ((((P @ Llist3) @ Llist4) => ((((coindu335574135_lnull @ A) @ Llist3) = ((coindu335574135_lnull @ B) @ Llist4)) & ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((~ (((coindu335574135_lnull @ B) @ Llist4))) => (((R @ ((coindu1046438764le_lhd @ A) @ Llist3)) @ ((coindu1046438764le_lhd @ B) @ Llist4)) & ((P @ ((coindu1047225960le_ltl @ A) @ Llist3)) @ ((coindu1047225960le_ltl @ B) @ Llist4))))))))) => (((((coindu987187967t_all2 @ A) @ B) @ R) @ X) @ Y)))))).
% 0.30/1.50 thf(fact_120_llist_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((coindu987187967t_all2 @ A) @ B) = (^ [R2:(A > (B > $o)),A3:(coindu1593790203_llist @ A),B3:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ A3) = ((coindu335574135_lnull @ B) @ B3)) & ((~ (((coindu335574135_lnull @ A) @ A3))) => ((~ (((coindu335574135_lnull @ B) @ B3))) => (((R2 @ ((coindu1046438764le_lhd @ A) @ A3)) @ ((coindu1046438764le_lhd @ B) @ B3)) & (((((coindu987187967t_all2 @ A) @ B) @ R2) @ ((coindu1047225960le_ltl @ A) @ A3)) @ ((coindu1047225960le_ltl @ B) @ B3)))))))))))).
% 0.30/1.50 thf(fact_121_lprefix__expand, axiom, (! [A:$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))))).
% 0.30/1.50 thf(fact_122_lprefix__coinduct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((P @ Xs) @ Ys) => ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: ((((P @ Xs2) @ Ys3) => ((((coindu335574135_lnull @ A) @ Ys3) => ((coindu335574135_lnull @ A) @ Xs2)) & ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((~ (((coindu335574135_lnull @ A) @ Ys3))) => ((((coindu1046438764le_lhd @ A) @ Xs2) = ((coindu1046438764le_lhd @ A) @ Ys3)) & (((P @ ((coindu1047225960le_ltl @ A) @ Xs2)) @ ((coindu1047225960le_ltl @ A) @ Ys3)) | (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2)) @ ((coindu1047225960le_ltl @ A) @ Ys3)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 0.30/1.50 thf(fact_123_split__llist, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (? [Ys3:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: (((Xs = (((coindu268472904append @ A) @ Ys3) @ (((coindu1121789889_LCons @ A) @ X) @ Zs2))) & ((coindu1213758845finite @ A) @ Ys3)))))))).
% 0.30/1.50 thf(fact_124_unfold__llist__id, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((((((coindu1599971794_llist @ (coindu1593790203_llist @ A)) @ A) @ (coindu335574135_lnull @ A)) @ (coindu1046438764le_lhd @ A)) @ (coindu1047225960le_ltl @ A)) @ Xs) = Xs)))).
% 0.30/1.50 thf(fact_125_lhd__lappend, axiom, (! [A:$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))))))).
% 0.30/1.50 thf(fact_126_llist_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ A2))) => (((member @ A) @ ((coindu1046438764le_lhd @ A) @ A2)) @ ((coindu1112613586e_lset @ A) @ A2)))))).
% 0.30/1.50 thf(fact_127_llist__set__induct, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs2)) @ Xs2)))) => ((! [Xs2:(coindu1593790203_llist @ A),Y2:A]: (((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((((member @ A) @ Y2) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2))) => (((P @ Y2) @ ((coindu1047225960le_ltl @ A) @ Xs2)) => ((P @ Y2) @ Xs2)))))) => ((P @ X) @ Xs))))))).
% 0.30/1.50 thf(fact_128_llist_Oset__induct, axiom, (! [A:$tType,X:A,A2:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A2)) => ((! [Z1:A,Z22:(coindu1593790203_llist @ A)]: (((P @ Z1) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z22)))) => ((! [Z1:A,Z22:(coindu1593790203_llist @ A),Xa2:A]: (((((member @ A) @ Xa2) @ ((coindu1112613586e_lset @ A) @ Z22)) => (((P @ Xa2) @ Z22) => ((P @ Xa2) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z22)))))) => ((P @ X) @ A2))))))).
% 0.30/1.50 thf(fact_129_llist_Oset__cases, axiom, (! [A:$tType,E:A,A2:(coindu1593790203_llist @ A)]: (((((member @ A) @ E) @ ((coindu1112613586e_lset @ A) @ A2)) => ((! [Z22:(coindu1593790203_llist @ A)]: ((A2 != (((coindu1121789889_LCons @ A) @ E) @ Z22)))) => (~ ((! [Z1:A,Z22:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ Z1) @ Z22)) => (~ ((((member @ A) @ E) @ ((coindu1112613586e_lset @ A) @ Z22)))))))))))))).
% 0.30/1.50 thf(fact_130_lset__induct_H, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X) @ Xs2)))) => ((! [X6:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X6) @ Xs2)))))) => (P @ Xs))))))).
% 0.30/1.50 thf(fact_131_lset__induct, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X) @ Xs2)))) => ((! [X6:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((X != X6) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X6) @ Xs2))))))) => (P @ Xs))))))).
% 0.30/1.50 thf(fact_132_lset__cases, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs6:(coindu1593790203_llist @ A)]: ((Xs != (((coindu1121789889_LCons @ A) @ X) @ Xs6)))) => (~ ((! [X6:A,Xs6:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ X6) @ Xs6)) => (~ ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs6)))))))))))))).
% 0.30/1.50 thf(fact_133_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coindu1593790203_llist @ A)]: ((((member @ A) @ A1) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A1) @ A22)))))).
% 0.30/1.50 thf(fact_134_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(coindu1593790203_llist @ A),A1:A]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A22)) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A1) @ A22))))))).
% 0.30/1.50 thf(fact_135_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 0.30/1.50 thf(fact_136_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),X5:A]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X5) @ Xs))))))).
% 0.30/1.50 thf(fact_137_llist_Orel__cong, axiom, (! [A:$tType,B:$tType,X:(coindu1593790203_llist @ A),Ya:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ B),Xa:(coindu1593790203_llist @ B),R:(A > (B > $o)),Ra:(A > (B > $o))]: (((X = Ya) => ((Y = Xa) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ Ya)) => ((((member @ B) @ Yb) @ ((coindu1112613586e_lset @ B) @ Xa)) => (((R @ Z3) @ Yb) = ((Ra @ Z3) @ Yb)))))) => ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X) @ Y) = (((((coindu987187967t_all2 @ A) @ B) @ Ra) @ Ya) @ Xa)))))))).
% 0.30/1.50 thf(fact_138_llist_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ B),Ra:(A > (B > $o))]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ X) @ Y) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ X)) => ((((member @ B) @ Yb) @ ((coindu1112613586e_lset @ B) @ Y)) => (((R @ Z3) @ Yb) => ((Ra @ Z3) @ Yb)))))) => (((((coindu987187967t_all2 @ A) @ B) @ Ra) @ X) @ Y)))))).
% 0.30/1.50 thf(fact_139_llist_Orel__refl__strong, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Ra:(A > (A > $o))]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ X)) => ((Ra @ Z3) @ Z3)))) => (((((coindu987187967t_all2 @ A) @ A) @ Ra) @ X) @ X))))).
% 0.30/1.50 thf(fact_140_in__lset__ltlD, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs))) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)))))).
% 0.30/1.50 thf(fact_141_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1046438764le_lhd @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X21)))).
% 0.30/1.50 thf(fact_142_llist_Opred__cong, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Ya:(coindu1593790203_llist @ A),P:(A > $o),Pa:(A > $o)]: (((X = Ya) => ((! [Z3:A]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ Ya)) => ((P @ Z3) = (Pa @ Z3))))) => ((((coindu44415597_llist @ A) @ P) @ X) = (((coindu44415597_llist @ A) @ Pa) @ Ya))))))).
% 0.30/1.50 thf(fact_143_llist_Opred__mono__strong, axiom, (! [A:$tType,P:(A > $o),X:(coindu1593790203_llist @ A),Pa:(A > $o)]: (((((coindu44415597_llist @ A) @ P) @ X) => ((! [Z3:A]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ X)) => ((P @ Z3) => (Pa @ Z3))))) => (((coindu44415597_llist @ A) @ Pa) @ X)))))).
% 0.30/1.50 thf(fact_144_Coinductive__List__Mirabelle__kmikjhschf_Olset__into__lsetp, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (((coindu1055736764_lsetp @ A) @ Xs) @ X))))).
% 0.30/1.50 thf(fact_145_lsetp__into__lset, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: (((((coindu1055736764_lsetp @ A) @ Xs) @ X) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)))))).
% 0.30/1.50 thf(fact_146_unfold__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (((coindu1046438764le_lhd @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)) = (G21 @ A2)))))).
% 0.30/1.50 thf(fact_147_llist_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A2:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((~ ((P2 @ A2))) => (((coindu1046438764le_lhd @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A2)) = (G21 @ A2)))))).
% 0.30/1.50 thf(fact_148_lset__lmember, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) = (((coindu567634248member @ A) @ X) @ Xs))))).
% 0.30/1.50 thf(fact_149_llist_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A),X:A]: (((~ (((coindu335574135_lnull @ A) @ A2))) => ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ A2))) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A2))))))).
% 0.30/1.50 thf(fact_150_in__lset__lappend__iff, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))) = ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) | (((coindu1213758845finite @ A) @ Xs) & (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Ys)))))))).
% 0.30/1.50 thf(fact_151_lprefix__lhdD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys))))))).
% 0.30/1.50 thf(fact_152_llist_Oexpand, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Llist) = ((coindu335574135_lnull @ A) @ Llist5)) => (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist) = ((coindu1046438764le_lhd @ A) @ Llist5)) & (((coindu1047225960le_ltl @ A) @ Llist) = ((coindu1047225960le_ltl @ A) @ Llist5))))) => (Llist = Llist5)))))).
% 0.30/1.50 thf(fact_153_llist_Ocoinduct, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist5) => ((! [Llist3:(coindu1593790203_llist @ A),Llist4:(coindu1593790203_llist @ A)]: ((((R @ Llist3) @ Llist4) => ((((coindu335574135_lnull @ A) @ Llist3) = ((coindu335574135_lnull @ A) @ Llist4)) & ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((((coindu1046438764le_lhd @ A) @ Llist3) = ((coindu1046438764le_lhd @ A) @ Llist4)) & ((R @ ((coindu1047225960le_ltl @ A) @ Llist3)) @ ((coindu1047225960le_ltl @ A) @ Llist4))))))))) => (Llist = Llist5)))))).
% 0.30/1.50 thf(fact_154_llist_Ocoinduct__strong, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist5) => ((! [Llist3:(coindu1593790203_llist @ A),Llist4:(coindu1593790203_llist @ A)]: ((((R @ Llist3) @ Llist4) => ((((coindu335574135_lnull @ A) @ Llist3) = ((coindu335574135_lnull @ A) @ Llist4)) & ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((((coindu1046438764le_lhd @ A) @ Llist3) = ((coindu1046438764le_lhd @ A) @ Llist4)) & (((R @ ((coindu1047225960le_ltl @ A) @ Llist3)) @ ((coindu1047225960le_ltl @ A) @ Llist4)) | (((coindu1047225960le_ltl @ A) @ Llist3) = ((coindu1047225960le_ltl @ A) @ Llist4)))))))))) => (Llist = Llist5)))))).
% 0.30/1.50 thf(fact_155_split__llist__first, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (? [Ys3:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: (((Xs = (((coindu268472904append @ A) @ Ys3) @ (((coindu1121789889_LCons @ A) @ X) @ Zs2))) & (((coindu1213758845finite @ A) @ Ys3) & (~ ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Ys3)))))))))))).
% 0.30/1.50 thf(fact_156_llist_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F1) @ F22) @ Llist)) = (((Llist = (coindu1598213697e_LNil @ A)) => (P @ F1)) & ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) => (P @ ((F22 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))).
% 0.30/1.50 thf(fact_157_llist_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F1) @ F22) @ Llist)) = (~ ((((Llist = (coindu1598213697e_LNil @ A)) & (~ ((P @ F1)))) | ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) & (~ ((P @ ((F22 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))))))).
% 0.30/1.50 thf(fact_158_llist_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((coindu882539134_llist @ B) @ A) = (^ [F12:B,F23:(A > ((coindu1593790203_llist @ A) > B)),Llist2:(coindu1593790203_llist @ A)]: (((((if @ B) @ ((coindu335574135_lnull @ A) @ Llist2)) @ F12) @ ((F23 @ ((coindu1046438764le_lhd @ A) @ Llist2)) @ ((coindu1047225960le_ltl @ A) @ Llist2))))))))).
% 0.30/1.50 thf(fact_159_lset__lappend__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coindu1112613586e_lset @ A) @ Xs)) @ ((coindu1112613586e_lset @ A) @ Ys))))))).
% 0.30/1.50 thf(fact_160_llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > ((coindu1593790203_llist @ A) > B)),X21:A,X22:(coindu1593790203_llist @ A)]: (((((((coindu882539134_llist @ B) @ A) @ F1) @ F22) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = ((F22 @ X21) @ X22))))).
% 0.30/1.50 thf(fact_161_llist_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > ((coindu1593790203_llist @ A) > B))]: (((((((coindu882539134_llist @ B) @ A) @ F1) @ F22) @ (coindu1598213697e_LNil @ A)) = F1)))).
% 0.30/1.50 thf(fact_162_gen__lset__def, axiom, (! [A:$tType]: (((coindu1928975208n_lset @ A) = (^ [A5:(set @ A),Xs3:(coindu1593790203_llist @ A)]: ((((sup_sup @ (set @ A)) @ A5) @ ((coindu1112613586e_lset @ A) @ Xs3)))))))).
% 0.30/1.50 thf(fact_163_lset__lappend__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1213758845finite @ A) @ Xs) => (((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coindu1112613586e_lset @ A) @ Xs)) @ ((coindu1112613586e_lset @ A) @ Ys)))) & ((~ (((coindu1213758845finite @ A) @ Xs))) => (((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1112613586e_lset @ A) @ Xs))))))).
% 0.30/1.50 thf(fact_164_Un__iff, axiom, (! [A:$tType,C2:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) = ((((member @ A) @ C2) @ A4) | (((member @ A) @ C2) @ B4)))))).
% 0.30/1.50 thf(fact_165_UnCI, axiom, (! [A:$tType,C2:A,B4:(set @ A),A4:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ A4)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B4)))))).
% 0.30/1.50 thf(fact_166_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ B2) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 0.30/1.50 thf(fact_167_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X3:A]: ((((sup_sup @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 0.30/1.50 thf(fact_168_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 0.30/1.50 thf(fact_169_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 0.30/1.50 thf(fact_170_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 0.30/1.50 thf(fact_171_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_172_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_173_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 0.30/1.50 thf(fact_174_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 0.30/1.50 thf(fact_175_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X3:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X3)))))))).
% 0.30/1.50 thf(fact_176_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X3:A]: ((((sup_sup @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 0.30/1.50 thf(fact_177_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ C2) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B2) @ C2))))))))).
% 0.30/1.50 thf(fact_178_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 0.30/1.50 thf(fact_179_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A3:A,B3:A]: ((((sup_sup @ A) @ B3) @ A3)))))))).
% 0.30/1.50 thf(fact_180_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X3:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X3)))))))).
% 0.30/1.50 thf(fact_181_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: (((((sup_sup @ A) @ B2) @ (((sup_sup @ A) @ A2) @ C2)) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B2) @ C2))))))))).
% 0.30/1.50 thf(fact_182_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 0.30/1.50 thf(fact_183_UnE, axiom, (! [A:$tType,C2:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) => ((~ ((((member @ A) @ C2) @ A4))) => (((member @ A) @ C2) @ B4)))))).
% 0.30/1.50 thf(fact_184_UnI1, axiom, (! [A:$tType,C2:A,A4:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A4) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B4)))))).
% 0.30/1.50 thf(fact_185_UnI2, axiom, (! [A:$tType,C2:A,B4:(set @ A),A4:(set @ A)]: (((((member @ A) @ C2) @ B4) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A4) @ B4)))))).
% 0.30/1.50 thf(fact_186_bex__Un, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) & (P @ X3)))) = ((? [X3:A]: (((((member @ A) @ X3) @ A4) & (P @ X3)))) | (? [X3:A]: (((((member @ A) @ X3) @ B4) & (P @ X3))))))))).
% 0.30/1.50 thf(fact_187_ball__Un, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) => (P @ X3)))) = ((! [X3:A]: (((((member @ A) @ X3) @ A4) => (P @ X3)))) & (! [X3:A]: (((((member @ A) @ X3) @ B4) => (P @ X3))))))))).
% 0.30/1.50 thf(fact_188_Un__assoc, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) @ C3) = (((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B4) @ C3)))))).
% 0.30/1.50 thf(fact_189_Un__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ A4) = A4)))).
% 0.30/1.50 thf(fact_190_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A5))))))).
% 0.30/1.50 thf(fact_191_Un__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) = (((sup_sup @ (set @ A)) @ A4) @ B4))))).
% 0.30/1.50 thf(fact_192_Un__left__commute, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B4) @ C3)) = (((sup_sup @ (set @ A)) @ B4) @ (((sup_sup @ (set @ A)) @ A4) @ C3)))))).
% 0.30/1.50 thf(fact_193_lset__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((ord_less_eq @ (set @ A)) @ ((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))) @ (((sup_sup @ (set @ A)) @ ((coindu1112613586e_lset @ A) @ Xs)) @ ((coindu1112613586e_lset @ A) @ Ys)))))).
% 0.30/1.50 thf(fact_194_lprefixI, axiom, (! [A:$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) => ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs2) @ Ys3)) @ X4) => (((coindu335574135_lnull @ A) @ Xs2) | (? [X8:A,Xs7:(coindu1593790203_llist @ A),Ys6:(coindu1593790203_llist @ A)]: (((Xs2 = (((coindu1121789889_LCons @ A) @ X8) @ Xs7)) & ((Ys3 = (((coindu1121789889_LCons @ A) @ X8) @ Ys6)) & ((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs7) @ Ys6)) @ X4) | (((coindu1696667936prefix @ A) @ Xs7) @ Ys6)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 0.30/1.50 thf(fact_195_lset__eq__empty, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1112613586e_lset @ A) @ Xs) = (bot_bot @ (set @ A))) = ((coindu335574135_lnull @ A) @ Xs))))).
% 0.30/1.50 thf(fact_196_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_197_all__not__in__conv, axiom, (! [A:$tType,A4:(set @ A)]: (((! [X3:A]: ((~ ((((member @ A) @ X3) @ A4))))) = (A4 = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_198_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X3:A]: ((~ ((P @ X3))))))))).
% 0.30/1.50 thf(fact_199_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X3:A]: ((~ ((P @ X3))))))))).
% 0.30/1.50 thf(fact_200_subsetI, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B4))))).
% 0.30/1.50 thf(fact_201_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A4) => (A4 = B4)))))).
% 0.30/1.50 thf(fact_202_sup_Obounded__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C2)) @ A2) = ((((ord_less_eq @ A) @ B2) @ A2) & (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 0.30/1.50 thf(fact_203_le__sup__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = ((((ord_less_eq @ A) @ X) @ Z) & (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 0.30/1.50 thf(fact_204_subset__empty, axiom, (! [A:$tType,A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = (A4 = (bot_bot @ (set @ A))))))).
% 0.30/1.50 thf(fact_205_empty__subsetI, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A4)))).
% 0.30/1.50 thf(fact_206_sup__bot_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 0.30/1.50 thf(fact_207_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 0.30/1.50 thf(fact_208_sup__eq__bot__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 0.30/1.50 thf(fact_209_bot__eq__sup__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 0.30/1.50 thf(fact_210_Un__empty, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A4) @ B4) = (bot_bot @ (set @ A))) = ((A4 = (bot_bot @ (set @ A))) & (B4 = (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_211_Un__subset__iff, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) @ C3) = ((((ord_less_eq @ (set @ A)) @ A4) @ C3) & (((ord_less_eq @ (set @ A)) @ B4) @ C3)))))).
% 0.30/1.50 thf(fact_212_sup__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 0.30/1.50 thf(fact_213_sup__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 0.30/1.50 thf(fact_214_sup_OcoboundedI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ C2) @ B2) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.30/1.50 thf(fact_215_sup_OcoboundedI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C2) @ A2) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.30/1.50 thf(fact_216_sup_Oabsorb__iff2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: (((((sup_sup @ A) @ A3) @ B3) = B3)))))))).
% 0.30/1.50 thf(fact_217_sup_Oabsorb__iff1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B3:A,A3:A]: (((((sup_sup @ A) @ A3) @ B3) = A3)))))))).
% 0.30/1.50 thf(fact_218_sup_Ocobounded2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: ((((ord_less_eq @ A) @ B2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 0.30/1.50 thf(fact_219_sup_Ocobounded1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 0.30/1.50 thf(fact_220_sup_Oorder__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B3:A,A3:A]: ((A3 = (((sup_sup @ A) @ A3) @ B3))))))))).
% 0.30/1.50 thf(fact_221_sup_OboundedI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C2) @ A2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C2)) @ A2))))))))).
% 0.30/1.50 thf(fact_222_sup_OboundedE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C2)) @ A2) => (~ (((((ord_less_eq @ A) @ B2) @ A2) => (~ ((((ord_less_eq @ A) @ C2) @ A2))))))))))))).
% 0.30/1.50 thf(fact_223_sup__absorb2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((sup_sup @ A) @ X) @ Y) = Y)))))))).
% 0.30/1.50 thf(fact_224_sup__absorb1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((sup_sup @ A) @ X) @ Y) = X)))))))).
% 0.30/1.50 thf(fact_225_sup_Oabsorb2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((sup_sup @ A) @ A2) @ B2) = B2)))))))).
% 0.30/1.50 thf(fact_226_sup_Oabsorb1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((sup_sup @ A) @ A2) @ B2) = A2)))))))).
% 0.30/1.50 thf(fact_227_sup__unique, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [F:(A > (A > A)),X:A,Y:A]: (((! [X2:A,Y2:A]: ((((ord_less_eq @ A) @ X2) @ ((F @ X2) @ Y2)))) => ((! [X2:A,Y2:A]: ((((ord_less_eq @ A) @ Y2) @ ((F @ X2) @ Y2)))) => ((! [X2:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ Z3) @ X2) => (((ord_less_eq @ A) @ ((F @ Y2) @ Z3)) @ X2))))) => ((((sup_sup @ A) @ X) @ Y) = ((F @ X) @ Y))))))))))).
% 0.30/1.50 thf(fact_228_sup_OorderI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = (((sup_sup @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 0.30/1.50 thf(fact_229_sup_OorderE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => (A2 = (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.30/1.50 thf(fact_230_le__iff__sup, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X3:A,Y3:A]: (((((sup_sup @ A) @ X3) @ Y3) = Y3)))))))).
% 0.30/1.50 thf(fact_231_sup__least, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A,Z:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ Z) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y) @ Z)) @ X))))))))).
% 0.30/1.50 thf(fact_232_sup__mono, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,C2:A,B2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ C2) => ((((ord_less_eq @ A) @ B2) @ D) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ (((sup_sup @ A) @ C2) @ D)))))))))).
% 0.30/1.50 thf(fact_233_sup_Omono, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,A2:A,D:A,B2:A]: (((((ord_less_eq @ A) @ C2) @ A2) => ((((ord_less_eq @ A) @ D) @ B2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C2) @ D)) @ (((sup_sup @ A) @ A2) @ B2)))))))))).
% 0.30/1.50 thf(fact_234_le__supI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ X) @ B2) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.30/1.50 thf(fact_235_le__supI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X) @ A2) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 0.30/1.50 thf(fact_236_sup__ge2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_237_sup__ge1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_238_le__supI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,X:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ X) => ((((ord_less_eq @ A) @ B2) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X))))))))).
% 0.30/1.50 thf(fact_239_le__supE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A,X:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X) => (~ (((((ord_less_eq @ A) @ A2) @ X) => (~ ((((ord_less_eq @ A) @ B2) @ X))))))))))))).
% 0.30/1.50 thf(fact_240_Un__empty__right, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (bot_bot @ (set @ A))) = A4)))).
% 0.30/1.50 thf(fact_241_Un__empty__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B4) = B4)))).
% 0.30/1.50 thf(fact_242_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ B5) = B5))))))).
% 0.30/1.50 thf(fact_243_Un__absorb2, axiom, (! [A:$tType,B4:(set @ A),A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B4) @ A4) => ((((sup_sup @ (set @ A)) @ A4) @ B4) = A4))))).
% 0.30/1.50 thf(fact_244_Un__absorb1, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((sup_sup @ (set @ A)) @ A4) @ B4) = B4))))).
% 0.30/1.50 thf(fact_245_Un__upper2, axiom, (! [A:$tType,B4:(set @ A),A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B4) @ (((sup_sup @ (set @ A)) @ A4) @ B4))))).
% 0.30/1.50 thf(fact_246_Un__upper1, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B4))))).
% 0.30/1.50 thf(fact_247_Un__least, axiom, (! [A:$tType,A4:(set @ A),C3:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C3) => ((((ord_less_eq @ (set @ A)) @ B4) @ C3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) @ C3)))))).
% 0.30/1.50 thf(fact_248_Un__mono, axiom, (! [A:$tType,A4:(set @ A),C3:(set @ A),B4:(set @ A),D2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C3) => ((((ord_less_eq @ (set @ A)) @ B4) @ D2) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B4)) @ (((sup_sup @ (set @ A)) @ C3) @ D2))))))).
% 0.30/1.50 thf(fact_249_inf__sup__ord_I3_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_250_inf__sup__ord_I4_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 0.30/1.50 thf(fact_251_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 0.30/1.50 thf(fact_252_set__mp, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B4)))))).
% 0.30/1.50 thf(fact_253_in__mono, axiom, (! [A:$tType,A4:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B4) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B4)))))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A6:$tType]: (((bounded_lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounded_lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounde1808546759up_bot @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounded_lattice_bot @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A6:$tType,A7:$tType]: ((((semilattice_sup @ A7) @ (type2 @ A7)) => ((semilattice_sup @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.30/1.50 thf(tcon_fun___Lattices_Olattice, axiom, (! [A6:$tType,A7:$tType]: ((((lattice @ A7) @ (type2 @ A7)) => ((lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3, axiom, (! [A6:$tType]: (((bounde1808546759up_bot @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_4, axiom, (! [A6:$tType]: (((bounded_lattice_bot @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_5, axiom, (! [A6:$tType]: (((semilattice_sup @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.30/1.50 thf(tcon_Set_Oset___Lattices_Olattice_6, axiom, (! [A6:$tType]: (((lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_7, axiom, ((bounde1808546759up_bot @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_8, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_9, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(tcon_HOL_Obool___Lattices_Olattice_10, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 0.30/1.50 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.30/1.50 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 0.30/1.50 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 0.30/1.50 thf(conj_0, conjecture, (((((comple1396247847notone @ (coindu1593790203_llist @ a)) @ (coindu1593790203_llist @ a)) @ (coindu1696667936prefix @ a)) @ (coindu1696667936prefix @ a)) @ ((coindu1121789889_LCons @ a) @ x))).
% 0.30/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.DnhfbxsEpZ/DTF2DTF6414.p
% 0.30/1.50 ------------------------
% 0.30/1.53 ---- Cleaned THF ---
% 0.30/1.53 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.30/1.53 coindu1593790203_llist: $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_t_Product__Type_Oprod,type,
% 0.30/1.53 product_prod: $tType > $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_t_Set_Oset,type,
% 0.30/1.53 set: $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_t_itself,type,
% 0.30/1.53 itself: $tType > $tType ).
% 0.30/1.53
% 0.30/1.53 thf(ty_tf_a,type,
% 0.30/1.53 a: $tType ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/1.53 bounded_lattice:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_HOL_Otype,type,
% 0.30/1.53 type:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Olattice,type,
% 0.30/1.53 lattice:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.30/1.53 semilattice_sup:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.30/1.53 bounded_lattice_bot:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.30/1.53 bounde1808546759up_bot:
% 0.30/1.53 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset,type,
% 0.30/1.53 coindu1928975208n_lset:
% 0.30/1.53 !>[A: $tType] : ( ( set @ A ) > ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.30/1.53 coindu268472904append:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.30/1.53 coindu1213758845finite:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.30/1.53 coindu1121789889_LCons:
% 0.30/1.53 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.30/1.53 coindu1598213697e_LNil:
% 0.30/1.53 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 0.30/1.53 coindu882539134_llist:
% 0.30/1.53 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist,type,
% 0.30/1.53 coindu1244876290_llist:
% 0.30/1.53 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coindu1593790203_llist @ A ) ) > ( C > C ) > C > ( coindu1593790203_llist @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.30/1.53 coindu1046438764le_lhd:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 0.30/1.53 coindu987187967t_all2:
% 0.30/1.53 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.30/1.53 coindu335574135_lnull:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 0.30/1.53 coindu1112613586e_lset:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.30/1.53 coindu1047225960le_ltl:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Opred__llist,type,
% 0.30/1.53 coindu44415597_llist:
% 0.30/1.53 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.30/1.53 coindu567634248member:
% 0.30/1.53 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.30/1.53 coindu1696667936prefix:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olsetp,type,
% 0.30/1.53 coindu1055736764_lsetp:
% 0.30/1.53 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.30/1.53 coindu1599971794_llist:
% 0.30/1.53 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Complete__Partial__Order_Omonotone,type,
% 0.30/1.53 comple1396247847notone:
% 0.30/1.53 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( B > B > $o ) > ( A > B ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_If,type,
% 0.30/1.53 if:
% 0.30/1.53 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/1.53 sup_sup:
% 0.30/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/1.53 bot_bot:
% 0.30/1.53 !>[A: $tType] : A ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/1.53 ord_less_eq:
% 0.30/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Product__Type_OPair,type,
% 0.30/1.53 product_Pair:
% 0.30/1.53 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Pure_Otype,type,
% 0.30/1.53 type2:
% 0.30/1.53 !>[A: $tType] : ( itself @ A ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_Set_OCollect,type,
% 0.30/1.53 collect:
% 0.30/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_c_member,type,
% 0.30/1.53 member:
% 0.30/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(sy_v_x,type,
% 0.30/1.53 x: a ).
% 0.30/1.53
% 0.30/1.53 thf(fact_0_lprefix__refl,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_1_llist_Oleq__refl,axiom,
% 0.30/1.53 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_2_llist_Oinject,axiom,
% 0.30/1.53 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.30/1.53 = ( ( X21 = Y21 )
% 0.30/1.53 & ( X22 = Y22 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_3_LCons__lprefix__LCons,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/1.53 = ( ( X = Y )
% 0.30/1.53 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_4_lprefix__trans,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_5_llist_Oleq__trans,axiom,
% 0.30/1.53 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_6_lprefix__antisym,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.30/1.53 => ( Xs = Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_7_Le__LCons,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_8_llist_Oleq__antisym,axiom,
% 0.30/1.53 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 0.30/1.53 => ( X = Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_9_LCons__lprefix__conv,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.30/1.53 = ( ? [Ys2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Ys
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X @ Ys2 ) )
% 0.30/1.53 & ( coindu1696667936prefix @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_10_lprefix__down__linear,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_11_llist_Omonotone__if__bot,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,Bound: coindu1593790203_llist @ A,G: ( coindu1593790203_llist @ A ) > B,Bot: B,F: ( coindu1593790203_llist @ A ) > B,Ord: B > B > $o] :
% 0.30/1.53 ( ! [X2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/1.53 => ( ( G @ X2 )
% 0.30/1.53 = Bot ) )
% 0.30/1.53 & ( ~ ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/1.53 => ( ( G @ X2 )
% 0.30/1.53 = ( F @ X2 ) ) ) )
% 0.30/1.53 => ( ! [X2: coindu1593790203_llist @ A,Y2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ X2 @ Y2 )
% 0.30/1.53 => ( ~ ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/1.53 => ( Ord @ ( F @ X2 ) @ ( F @ Y2 ) ) ) )
% 0.30/1.53 => ( ! [X2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu1696667936prefix @ A @ X2 @ Bound )
% 0.30/1.53 => ( Ord @ Bot @ ( F @ X2 ) ) )
% 0.30/1.53 => ( ( Ord @ Bot @ Bot )
% 0.30/1.53 => ( comple1396247847notone @ ( coindu1593790203_llist @ A ) @ B @ ( coindu1696667936prefix @ A ) @ Ord @ G ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_12_lmember__code_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/1.53 = ( ( X = Y )
% 0.30/1.53 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_13_monotoneD,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,Orda: A > A > $o,Ordb: B > B > $o,F: A > B,X: A,Y: A] :
% 0.30/1.53 ( ( comple1396247847notone @ A @ B @ Orda @ Ordb @ F )
% 0.30/1.53 => ( ( Orda @ X @ Y )
% 0.30/1.53 => ( Ordb @ ( F @ X ) @ ( F @ Y ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_14_monotoneI,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,Orda: A > A > $o,Ordb: B > B > $o,F: A > B] :
% 0.30/1.53 ( ! [X2: A,Y2: A] :
% 0.30/1.53 ( ( Orda @ X2 @ Y2 )
% 0.30/1.53 => ( Ordb @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.30/1.53 => ( comple1396247847notone @ A @ B @ Orda @ Ordb @ F ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_15_monotone__def,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( comple1396247847notone @ A @ B )
% 0.30/1.53 = ( ^ [Orda2: A > A > $o,Ordb2: B > B > $o,F2: A > B] :
% 0.30/1.53 ! [X3: A,Y3: A] :
% 0.30/1.53 ( ( Orda2 @ X3 @ Y3 )
% 0.30/1.53 => ( Ordb2 @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_16_llist_Opred__inject_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,A2: A,Aa: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu44415597_llist @ A @ P @ ( coindu1121789889_LCons @ A @ A2 @ Aa ) )
% 0.30/1.53 = ( ( P @ A2 )
% 0.30/1.53 & ( coindu44415597_llist @ A @ P @ Aa ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_17_lprefix__code_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_18_lprefix_Ocases,axiom,
% 0.30/1.53 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 0.30/1.53 => ( ( ( A1
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ! [Xs2: coindu1593790203_llist @ A] : ( A22 != Xs2 ) )
% 0.30/1.53 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 0.30/1.53 ( ( A1
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.30/1.53 => ( ( A22
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 0.30/1.53 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_19_lprefix_Osimps,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A )
% 0.30/1.53 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( A12
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 & ( A23 = Xs3 ) )
% 0.30/1.53 | ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 0.30/1.53 ( ( A12
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.30/1.53 & ( A23
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 0.30/1.53 & ( coindu1696667936prefix @ A @ Xs3 @ Ys4 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_20_lprefix_Ocoinduct,axiom,
% 0.30/1.53 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( X4 @ X @ Xa )
% 0.30/1.53 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( X4 @ X2 @ Xa2 )
% 0.30/1.53 => ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( X2
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 & ( Xa2 = Xs4 ) )
% 0.30/1.53 | ? [Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 0.30/1.53 ( ( X2
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.30/1.53 & ( Xa2
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 0.30/1.53 & ( ( X4 @ Xs4 @ Ys5 )
% 0.30/1.53 | ( coindu1696667936prefix @ A @ Xs4 @ Ys5 ) ) ) ) )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_21_lprefix__LCons__conv,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/1.53 = ( ( Xs
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.30/1.53 & ( coindu1696667936prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_22_unfold__llist__eq__LCons,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.30/1.53 = ( ~ ( IS_LNIL @ B2 )
% 0.30/1.53 & ( X
% 0.30/1.53 = ( LHD @ B2 ) )
% 0.30/1.53 & ( Xs
% 0.30/1.53 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_23_lsetp_Ointros_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A,X5: A] :
% 0.30/1.53 ( ( coindu1055736764_lsetp @ A @ Xs @ X )
% 0.30/1.53 => ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) @ X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_24_lprefix__code_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_25_lmember__code_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A] :
% 0.30/1.53 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_26_unfold__llist_Octr_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/1.53 ( ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.30/1.53 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_27_llist_Opred__inject_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o] : ( coindu44415597_llist @ A @ P @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_28_unfold__llist_Ocode,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( coindu1599971794_llist @ A @ B )
% 0.30/1.53 = ( ^ [P3: A > $o,G212: A > B,G222: A > A,A3: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P3 @ A3 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A3 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_29_LNil__lprefix,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_30_neq__LNil__conv,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs
% 0.30/1.53 != ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.30/1.53 ( Xs
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_31_llist_Oexhaust,axiom,
% 0.30/1.53 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Y
% 0.30/1.53 != ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.30/1.53 ( Y
% 0.30/1.53 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_32_llist_Odistinct_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1598213697e_LNil @ A )
% 0.30/1.53 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_33_unfold__llist_Octr_I2_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.30/1.53 = ( coindu1121789889_LCons @ B @ ( G21 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_34_lsetp_Oinducts,axiom,
% 0.30/1.53 ! [A: $tType,X1: coindu1593790203_llist @ A,X23: A,P: ( coindu1593790203_llist @ A ) > A > $o] :
% 0.30/1.53 ( ( coindu1055736764_lsetp @ A @ X1 @ X23 )
% 0.30/1.53 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) @ X2 )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A,X6: A] :
% 0.30/1.53 ( ( coindu1055736764_lsetp @ A @ Xs2 @ X2 )
% 0.30/1.53 => ( ( P @ Xs2 @ X2 )
% 0.30/1.53 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) @ X2 ) ) )
% 0.30/1.53 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_35_lsetp_Osimps,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu1055736764_lsetp @ A )
% 0.30/1.53 = ( ^ [A12: coindu1593790203_llist @ A,A23: A] :
% 0.30/1.53 ( ? [X3: A,Xs3: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( A12
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.30/1.53 & ( A23 = X3 ) )
% 0.30/1.53 | ? [Xs3: coindu1593790203_llist @ A,X3: A,X7: A] :
% 0.30/1.53 ( ( A12
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X7 @ Xs3 ) )
% 0.30/1.53 & ( A23 = X3 )
% 0.30/1.53 & ( coindu1055736764_lsetp @ A @ Xs3 @ X3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_36_lsetp_Ocases,axiom,
% 0.30/1.53 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: A] :
% 0.30/1.53 ( ( coindu1055736764_lsetp @ A @ A1 @ A22 )
% 0.30/1.53 => ( ! [X2: A] :
% 0.30/1.53 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( A1
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.30/1.53 => ( A22 != X2 ) )
% 0.30/1.53 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ? [X6: A] :
% 0.30/1.53 ( A1
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) )
% 0.30/1.53 => ~ ( coindu1055736764_lsetp @ A @ Xs2 @ A22 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_37_lsetp_Ointros_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ X ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_38_gen__lset__code_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( coindu1928975208n_lset @ A @ A4 @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_39_llist_Ocorec__code,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType] :
% 0.30/1.53 ( ( coindu1244876290_llist @ C @ A )
% 0.30/1.53 = ( ^ [P3: C > $o,G212: C > A,Q22: C > $o,G221: C > ( coindu1593790203_llist @ A ),G2222: C > C,A3: C] : ( if @ ( coindu1593790203_llist @ A ) @ ( P3 @ A3 ) @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ A @ ( G212 @ A3 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q22 @ G221 @ G2222 @ ( G2222 @ A3 ) ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_40_lfinite_Oinducts,axiom,
% 0.30/1.53 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ X )
% 0.30/1.53 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.30/1.53 => ( ( P @ Xs2 )
% 0.30/1.53 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.30/1.53 => ( P @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_41_lfinite_Osimps,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu1213758845finite @ A )
% 0.30/1.53 = ( ^ [A3: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 | ? [Xs3: coindu1593790203_llist @ A,X3: A] :
% 0.30/1.53 ( ( A3
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.30/1.53 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_42_lfinite_Ocases,axiom,
% 0.30/1.53 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ A2 )
% 0.30/1.53 => ( ( A2
% 0.30/1.53 != ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ? [X2: A] :
% 0.30/1.53 ( A2
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.30/1.53 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_43_lappend__snocL1__conv__LCons2,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.30/1.53 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_44_lprefix__LNil,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/1.53 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/1.53 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/1.53 = ( P @ A2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( collect @ A
% 0.30/1.53 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_47_Collect__cong,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/1.53 ( ! [X2: A] :
% 0.30/1.53 ( ( P @ X2 )
% 0.30/1.53 = ( Q @ X2 ) )
% 0.30/1.53 => ( ( collect @ A @ P )
% 0.30/1.53 = ( collect @ A @ Q ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_48_ext,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/1.53 ( ! [X2: A] :
% 0.30/1.53 ( ( F @ X2 )
% 0.30/1.53 = ( G @ X2 ) )
% 0.30/1.53 => ( F = G ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_49_ltl__unfold__llist,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.30/1.53 ( ( ( IS_LNIL @ A2 )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) )
% 0.30/1.53 & ( ~ ( IS_LNIL @ A2 )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.30/1.53 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_50_llist_Orel__cases,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 0.30/1.53 => ( ( ( A2
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ( B2
% 0.30/1.53 != ( coindu1598213697e_LNil @ B ) ) )
% 0.30/1.53 => ~ ! [X12: A,X24: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( A2
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X12 @ X24 ) )
% 0.30/1.53 => ! [Y1: B,Y23: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( B2
% 0.30/1.53 = ( coindu1121789889_LCons @ B @ Y1 @ Y23 ) )
% 0.30/1.53 => ( ( R @ X12 @ Y1 )
% 0.30/1.53 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X24 @ Y23 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_51_llist_Orel__distinct_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.30/1.53 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_52_llist_Orel__inject_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 0.30/1.53 = ( ( R @ X21 @ Y21 )
% 0.30/1.53 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_53_lnull__lappend,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_54_lappend_Odisc__iff_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.30/1.53 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_55_lappend__code_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_56_lfinite__code_I2_J,axiom,
% 0.30/1.53 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.30/1.53 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_57_lfinite__LCons,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.30/1.53 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_58_lappend__LNil2,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = Xs ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_59_lappend__code_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.30/1.53 = Ys ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_60_lfinite__code_I1_J,axiom,
% 0.30/1.53 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_61_lfinite__ltl,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.30/1.53 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_62_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.30/1.53 = ( P2 @ A2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_63_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.30/1.53 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) )
% 0.30/1.53 = ( ~ ( P2 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_64_lfinite__lappend,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_65_llist_Ocorec__disc__iff_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A2: C] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/1.53 = ( P2 @ A2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_66_llist_Ocorec__disc__iff_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A2: C] :
% 0.30/1.53 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) ) )
% 0.30/1.53 = ( ~ ( P2 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_67_ltl__lappend,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_68_lprefix__lappend__same,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) )
% 0.30/1.53 = ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ Ys @ Zs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_69_llist_Orel__refl,axiom,
% 0.30/1.53 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ! [X2: B] : ( Ra @ X2 @ X2 )
% 0.30/1.53 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_70_llist_Orel__eq,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu987187967t_all2 @ A @ A
% 0.30/1.53 @ ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.30/1.53 = ( ^ [Y4: coindu1593790203_llist @ A,Z2: coindu1593790203_llist @ A] : ( Y4 = Z2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_71_lnull__imp__lfinite,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_72_lappend_Oexhaust,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_73_lfinite__induct,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/1.53 => ( P @ Xs2 ) )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/1.53 => ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.30/1.53 => ( P @ Xs2 ) ) ) )
% 0.30/1.53 => ( P @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_74_lappend__lnull2,axiom,
% 0.30/1.53 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/1.53 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/1.53 = Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_75_lappend__lnull1,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/1.53 = Ys ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_76_lappend__assoc,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.30/1.53 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_77_lappend__ltl,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys )
% 0.30/1.53 = ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_78_lappend__inf,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/1.53 = Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_79_lnull__ltlI,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_80_llist_Ocorec__disc_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/1.53 ( ( P2 @ A2 )
% 0.30/1.53 => ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_81_llist_Ocorec__disc_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_82_llist_Ocorec__sel_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,A2: C,Q222: C > $o,G21: C > A,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ( ( ( Q222 @ A2 )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/1.53 = ( G2212 @ A2 ) ) )
% 0.30/1.53 & ( ~ ( Q222 @ A2 )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/1.53 = ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ ( G2223 @ A2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_83_lappend_Odisc_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/1.53 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_84_lappend_Odisc_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.30/1.53 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_85_lappend_Octr_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/1.53 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_86_lnull__lprefix,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_87_lprefix__lnull,axiom,
% 0.30/1.53 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_88_lprefix__lnullD,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.30/1.53 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_89_lprefix__not__lnullD,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_90_llist_Odisc_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/1.53 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_91_llist_OdiscI_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Llist
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/1.53 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_92_not__lnull__conv,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.30/1.53 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.30/1.53 ( Xs
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_93_lnull__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A )
% 0.30/1.53 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( Llist2
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_94_llist_Ocollapse_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu335574135_lnull @ A @ Llist )
% 0.30/1.53 => ( Llist
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_95_llist_OdiscI_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Llist
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_96_llist_Odisc_I1_J,axiom,
% 0.30/1.53 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_97_llist_Orel__intros_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( R @ X21 @ Y21 )
% 0.30/1.53 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 0.30/1.53 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_98_llist_Octr__transfer_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_99_lprefix__ltlI,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_100_ltl__simps_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/1.53 = X22 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_101_unfold__llist_Odisc_I1_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/1.53 ( ( P2 @ A2 )
% 0.30/1.53 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_102_unfold__llist_Odisc_I2_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_103_ltl__simps_I1_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_104_lprefix__lappend,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_105_lprefix__lappend__sameI,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_106_not__lfinite__lprefix__conv__eq,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 = ( Xs = Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_107_lappend__eq__LNil__iff,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = ( ( Xs
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 & ( Ys
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_108_LNil__eq__lappend__iff,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu1598213697e_LNil @ A )
% 0.30/1.53 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( ( Xs
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 & ( Ys
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_109_lappend__LNil__LNil,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_110_unfold__llist_Osimps_I4_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.30/1.53 = ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_111_lfinite__LConsI,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_112_lfinite__LNil,axiom,
% 0.30/1.53 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_113_llist_Ocorec_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 )
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ ( G21 @ A2 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ ( G2223 @ A2 ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_114_llist_Ocorec_I1_J,axiom,
% 0.30/1.53 ! [C: $tType,A: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/1.53 ( ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 )
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_115_llist_Orel__distinct_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.30/1.53 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_116_lhd__LCons__ltl,axiom,
% 0.30/1.53 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.30/1.53 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 0.30/1.53 = Llist ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_117_llist_Oexhaust__sel,axiom,
% 0.30/1.53 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Llist
% 0.30/1.53 != ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ( Llist
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_118_eq__LConsD,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.30/1.53 => ( ( Xs
% 0.30/1.53 != ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.30/1.53 = Y )
% 0.30/1.53 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 0.30/1.53 = Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_119_llist_Orel__coinduct,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,R: A > B > $o] :
% 0.30/1.53 ( ( P @ X @ Y )
% 0.30/1.53 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( P @ Llist3 @ Llist4 )
% 0.30/1.53 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/1.53 = ( coindu335574135_lnull @ B @ Llist4 ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ B @ Llist4 )
% 0.30/1.53 => ( ( R @ ( coindu1046438764le_lhd @ A @ Llist3 ) @ ( coindu1046438764le_lhd @ B @ Llist4 ) )
% 0.30/1.53 & ( P @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ B @ Llist4 ) ) ) ) ) ) )
% 0.30/1.53 => ( coindu987187967t_all2 @ A @ B @ R @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_120_llist_Orel__sel,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( coindu987187967t_all2 @ A @ B )
% 0.30/1.53 = ( ^ [R2: A > B > $o,A3: coindu1593790203_llist @ A,B3: coindu1593790203_llist @ B] :
% 0.30/1.53 ( ( ( coindu335574135_lnull @ A @ A3 )
% 0.30/1.53 = ( coindu335574135_lnull @ B @ B3 ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ A3 )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ B @ B3 )
% 0.30/1.53 => ( ( R2 @ ( coindu1046438764le_lhd @ A @ A3 ) @ ( coindu1046438764le_lhd @ B @ B3 ) )
% 0.30/1.53 & ( coindu987187967t_all2 @ A @ B @ R2 @ ( coindu1047225960le_ltl @ A @ A3 ) @ ( coindu1047225960le_ltl @ B @ B3 ) ) ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_121_lprefix__expand,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.30/1.53 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.30/1.53 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_122_lprefix__coinduct,axiom,
% 0.30/1.53 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( P @ Xs @ Ys )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( P @ Xs2 @ Ys3 )
% 0.30/1.53 => ( ( ( coindu335574135_lnull @ A @ Ys3 )
% 0.30/1.53 => ( coindu335574135_lnull @ A @ Xs2 ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Ys3 )
% 0.30/1.53 => ( ( ( coindu1046438764le_lhd @ A @ Xs2 )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Ys3 ) )
% 0.30/1.53 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) )
% 0.30/1.53 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys3 ) ) ) ) ) ) ) )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_123_split__llist,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ? [Ys3: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs
% 0.30/1.53 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 0.30/1.53 & ( coindu1213758845finite @ A @ Ys3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_124_unfold__llist__id,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 0.30/1.53 = Xs ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_125_lhd__lappend,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_126_llist_Oset__sel_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.30/1.53 => ( member @ A @ ( coindu1046438764le_lhd @ A @ A2 ) @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_127_llist__set__induct,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/1.53 => ( P @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ Xs2 ) )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A,Y2: A] :
% 0.30/1.53 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/1.53 => ( ( member @ A @ Y2 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.30/1.53 => ( ( P @ Y2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.30/1.53 => ( P @ Y2 @ Xs2 ) ) ) )
% 0.30/1.53 => ( P @ X @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_128_llist_Oset__induct,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A2: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.30/1.53 => ( ! [Z1: A,Z22: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z22 ) )
% 0.30/1.53 => ( ! [Z1: A,Z22: coindu1593790203_llist @ A,Xa2: A] :
% 0.30/1.53 ( ( member @ A @ Xa2 @ ( coindu1112613586e_lset @ A @ Z22 ) )
% 0.30/1.53 => ( ( P @ Xa2 @ Z22 )
% 0.30/1.53 => ( P @ Xa2 @ ( coindu1121789889_LCons @ A @ Z1 @ Z22 ) ) ) )
% 0.30/1.53 => ( P @ X @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_129_llist_Oset__cases,axiom,
% 0.30/1.53 ! [A: $tType,E: A,A2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.30/1.53 => ( ! [Z22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( A2
% 0.30/1.53 != ( coindu1121789889_LCons @ A @ E @ Z22 ) )
% 0.30/1.53 => ~ ! [Z1: A,Z22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( A2
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ Z1 @ Z22 ) )
% 0.30/1.53 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z22 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_130_lset__induct_H,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.30/1.53 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.30/1.53 => ( ( P @ Xs2 )
% 0.30/1.53 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) )
% 0.30/1.53 => ( P @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_131_lset__induct,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.30/1.53 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.30/1.53 => ( ( X != X6 )
% 0.30/1.53 => ( ( P @ Xs2 )
% 0.30/1.53 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) ) )
% 0.30/1.53 => ( P @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_132_lset__cases,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ( ! [Xs6: coindu1593790203_llist @ A] :
% 0.30/1.53 ( Xs
% 0.30/1.53 != ( coindu1121789889_LCons @ A @ X @ Xs6 ) )
% 0.30/1.53 => ~ ! [X6: A,Xs6: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X6 @ Xs6 ) )
% 0.30/1.53 => ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs6 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_133_llist_Oset__intros_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,A1: A,A22: coindu1593790203_llist @ A] : ( member @ A @ A1 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_134_llist_Oset__intros_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,A22: coindu1593790203_llist @ A,A1: A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A22 ) )
% 0.30/1.53 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_135_lset__intros_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_136_lset__intros_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,X5: A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_137_llist_Orel__cong,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,X: coindu1593790203_llist @ A,Ya: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,Xa: coindu1593790203_llist @ B,R: A > B > $o,Ra: A > B > $o] :
% 0.30/1.53 ( ( X = Ya )
% 0.30/1.53 => ( ( Y = Xa )
% 0.30/1.53 => ( ! [Z3: A,Yb: B] :
% 0.30/1.53 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ Ya ) )
% 0.30/1.53 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Xa ) )
% 0.30/1.53 => ( ( R @ Z3 @ Yb )
% 0.30/1.53 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.30/1.53 => ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 0.30/1.53 = ( coindu987187967t_all2 @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_138_llist_Orel__mono__strong,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,R: A > B > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,Ra: A > B > $o] :
% 0.30/1.53 ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 0.30/1.53 => ( ! [Z3: A,Yb: B] :
% 0.30/1.53 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.30/1.53 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Y ) )
% 0.30/1.53 => ( ( R @ Z3 @ Yb )
% 0.30/1.53 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.30/1.53 => ( coindu987187967t_all2 @ A @ B @ Ra @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_139_llist_Orel__refl__strong,axiom,
% 0.30/1.53 ! [A: $tType,X: coindu1593790203_llist @ A,Ra: A > A > $o] :
% 0.30/1.53 ( ! [Z3: A] :
% 0.30/1.53 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.30/1.53 => ( Ra @ Z3 @ Z3 ) )
% 0.30/1.53 => ( coindu987187967t_all2 @ A @ A @ Ra @ X @ X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_140_in__lset__ltlD,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) )
% 0.30/1.53 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_141_lhd__LCons,axiom,
% 0.30/1.53 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/1.53 = X21 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_142_llist_Opred__cong,axiom,
% 0.30/1.53 ! [A: $tType,X: coindu1593790203_llist @ A,Ya: coindu1593790203_llist @ A,P: A > $o,Pa: A > $o] :
% 0.30/1.53 ( ( X = Ya )
% 0.30/1.53 => ( ! [Z3: A] :
% 0.30/1.53 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ Ya ) )
% 0.30/1.53 => ( ( P @ Z3 )
% 0.30/1.53 = ( Pa @ Z3 ) ) )
% 0.30/1.53 => ( ( coindu44415597_llist @ A @ P @ X )
% 0.30/1.53 = ( coindu44415597_llist @ A @ Pa @ Ya ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_143_llist_Opred__mono__strong,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o,X: coindu1593790203_llist @ A,Pa: A > $o] :
% 0.30/1.53 ( ( coindu44415597_llist @ A @ P @ X )
% 0.30/1.53 => ( ! [Z3: A] :
% 0.30/1.53 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.30/1.53 => ( ( P @ Z3 )
% 0.30/1.53 => ( Pa @ Z3 ) ) )
% 0.30/1.53 => ( coindu44415597_llist @ A @ Pa @ X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_144_Coinductive__List__Mirabelle__kmikjhschf_Olset__into__lsetp,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ( coindu1055736764_lsetp @ A @ Xs @ X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_145_lsetp__into__lset,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.30/1.53 ( ( coindu1055736764_lsetp @ A @ Xs @ X )
% 0.30/1.53 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_146_unfold__llist_Osimps_I3_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.30/1.53 = ( G21 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_147_llist_Ocorec__sel_I1_J,axiom,
% 0.30/1.53 ! [A: $tType,C: $tType,P2: C > $o,A2: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.30/1.53 ( ~ ( P2 @ A2 )
% 0.30/1.53 => ( ( coindu1046438764le_lhd @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A2 ) )
% 0.30/1.53 = ( G21 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_148_lset__lmember,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 = ( coindu567634248member @ A @ X @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_149_llist_Oset__sel_I2_J,axiom,
% 0.30/1.53 ! [A: $tType,A2: coindu1593790203_llist @ A,X: A] :
% 0.30/1.53 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.30/1.53 => ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ A2 ) ) )
% 0.30/1.53 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_150_in__lset__lappend__iff,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.30/1.53 = ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 | ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 & ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_151_lprefix__lhdD,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.30/1.53 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_152_llist_Oexpand,axiom,
% 0.30/1.53 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu335574135_lnull @ A @ Llist )
% 0.30/1.53 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.30/1.53 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.30/1.53 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.30/1.53 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 0.30/1.53 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) )
% 0.30/1.53 => ( Llist = Llist5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_153_llist_Ocoinduct,axiom,
% 0.30/1.53 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( R @ Llist @ Llist5 )
% 0.30/1.53 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( R @ Llist3 @ Llist4 )
% 0.30/1.53 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/1.53 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.30/1.53 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.30/1.53 & ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) )
% 0.30/1.53 => ( Llist = Llist5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_154_llist_Ocoinduct__strong,axiom,
% 0.30/1.53 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( R @ Llist @ Llist5 )
% 0.30/1.53 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( R @ Llist3 @ Llist4 )
% 0.30/1.53 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/1.53 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.30/1.53 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.30/1.53 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.30/1.53 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.30/1.53 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.30/1.53 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) )
% 0.30/1.53 | ( ( coindu1047225960le_ltl @ A @ Llist3 )
% 0.30/1.53 = ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) ) )
% 0.30/1.53 => ( Llist = Llist5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_155_split__llist__first,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.30/1.53 => ? [Ys3: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs
% 0.30/1.53 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 0.30/1.53 & ( coindu1213758845finite @ A @ Ys3 )
% 0.30/1.53 & ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_156_llist_Osplit__sel,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F22 @ Llist ) )
% 0.30/1.53 = ( ( ( Llist
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 => ( P @ F1 ) )
% 0.30/1.53 & ( ( Llist
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.30/1.53 => ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_157_llist_Osplit__sel__asm,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F22 @ Llist ) )
% 0.30/1.53 = ( ~ ( ( ( Llist
% 0.30/1.53 = ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 & ~ ( P @ F1 ) )
% 0.30/1.53 | ( ( Llist
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.30/1.53 & ~ ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_158_llist_Ocase__eq__if,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType] :
% 0.30/1.53 ( ( coindu882539134_llist @ B @ A )
% 0.30/1.53 = ( ^ [F12: B,F23: A > ( coindu1593790203_llist @ A ) > B,Llist2: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist2 ) @ F12 @ ( F23 @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_159_lset__lappend__lfinite,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_160_llist_Osimps_I5_J,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( coindu882539134_llist @ B @ A @ F1 @ F22 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.30/1.53 = ( F22 @ X21 @ X22 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_161_llist_Osimps_I4_J,axiom,
% 0.30/1.53 ! [A: $tType,B: $tType,F1: B,F22: A > ( coindu1593790203_llist @ A ) > B] :
% 0.30/1.53 ( ( coindu882539134_llist @ B @ A @ F1 @ F22 @ ( coindu1598213697e_LNil @ A ) )
% 0.30/1.53 = F1 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_162_gen__lset__def,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( coindu1928975208n_lset @ A )
% 0.30/1.53 = ( ^ [A5: set @ A,Xs3: coindu1593790203_llist @ A] : ( sup_sup @ ( set @ A ) @ A5 @ ( coindu1112613586e_lset @ A @ Xs3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_163_lset__lappend__conv,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) )
% 0.30/1.53 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.30/1.53 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.30/1.53 = ( coindu1112613586e_lset @ A @ Xs ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_164_Un__iff,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/1.53 = ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 | ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_165_UnCI,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,B4: set @ A,A4: set @ A] :
% 0.30/1.53 ( ( ~ ( member @ A @ C2 @ B4 )
% 0.30/1.53 => ( member @ A @ C2 @ A4 ) )
% 0.30/1.53 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_166_sup_Oright__idem,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 0.30/1.53 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_167_sup__apply,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.30/1.53 => ( ( sup_sup @ ( A > B ) )
% 0.30/1.53 = ( ^ [F2: A > B,G2: A > B,X3: A] : ( sup_sup @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_168_sup_Oidem,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ A2 @ A2 )
% 0.30/1.53 = A2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_169_sup__idem,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X @ X )
% 0.30/1.53 = X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_170_sup_Oleft__idem,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/1.53 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_171_sup__left__idem,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.30/1.53 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_172_inf__sup__aci_I8_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.30/1.53 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_173_inf__sup__aci_I7_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.30/1.53 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_174_inf__sup__aci_I6_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/1.53 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_175_inf__sup__aci_I5_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( sup_sup @ A )
% 0.30/1.53 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_176_sup__fun__def,axiom,
% 0.30/1.53 ! [B: $tType,A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.30/1.53 => ( ( sup_sup @ ( A > B ) )
% 0.30/1.53 = ( ^ [F2: A > B,G2: A > B,X3: A] : ( sup_sup @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_177_sup_Oassoc,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A,C2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ C2 )
% 0.30/1.53 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_178_sup__assoc,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/1.53 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_179_sup_Ocommute,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( sup_sup @ A )
% 0.30/1.53 = ( ^ [A3: A,B3: A] : ( sup_sup @ A @ B3 @ A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_180_sup__commute,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( sup_sup @ A )
% 0.30/1.53 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_181_sup_Oleft__commute,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,A2: A,C2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A2 @ C2 ) )
% 0.30/1.53 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_182_sup__left__commute,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.30/1.53 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_183_UnE,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/1.53 => ( ~ ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_184_UnI1,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ A4 )
% 0.30/1.53 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_185_UnI2,axiom,
% 0.30/1.53 ! [A: $tType,C2: A,B4: set @ A,A4: set @ A] :
% 0.30/1.53 ( ( member @ A @ C2 @ B4 )
% 0.30/1.53 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_186_bex__Un,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,P: A > $o] :
% 0.30/1.53 ( ( ? [X3: A] :
% 0.30/1.53 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/1.53 & ( P @ X3 ) ) )
% 0.30/1.53 = ( ? [X3: A] :
% 0.30/1.53 ( ( member @ A @ X3 @ A4 )
% 0.30/1.53 & ( P @ X3 ) )
% 0.30/1.53 | ? [X3: A] :
% 0.30/1.53 ( ( member @ A @ X3 @ B4 )
% 0.30/1.53 & ( P @ X3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_187_ball__Un,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,P: A > $o] :
% 0.30/1.53 ( ( ! [X3: A] :
% 0.30/1.53 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/1.53 => ( P @ X3 ) ) )
% 0.30/1.53 = ( ! [X3: A] :
% 0.30/1.53 ( ( member @ A @ X3 @ A4 )
% 0.30/1.53 => ( P @ X3 ) )
% 0.30/1.53 & ! [X3: A] :
% 0.30/1.53 ( ( member @ A @ X3 @ B4 )
% 0.30/1.53 => ( P @ X3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_188_Un__assoc,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ C3 )
% 0.30/1.53 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_189_Un__absorb,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_190_Un__commute,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) )
% 0.30/1.53 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_191_Un__left__absorb,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) )
% 0.30/1.53 = ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_192_Un__left__commute,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) )
% 0.30/1.53 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A4 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_193_lset__lappend,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) @ ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_194_lprefixI,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 0.30/1.53 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 0.30/1.53 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs2 @ Ys3 ) @ X4 )
% 0.30/1.53 => ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.30/1.53 | ? [X8: A,Xs7: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( Xs2
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X8 @ Xs7 ) )
% 0.30/1.53 & ( Ys3
% 0.30/1.53 = ( coindu1121789889_LCons @ A @ X8 @ Ys6 ) )
% 0.30/1.53 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs7 @ Ys6 ) @ X4 )
% 0.30/1.53 | ( coindu1696667936prefix @ A @ Xs7 @ Ys6 ) ) ) ) )
% 0.30/1.53 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_195_lset__eq__empty,axiom,
% 0.30/1.53 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.30/1.53 ( ( ( coindu1112613586e_lset @ A @ Xs )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_196_empty__iff,axiom,
% 0.30/1.53 ! [A: $tType,C2: A] :
% 0.30/1.53 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_197_all__not__in__conv,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( ! [X3: A] :
% 0.30/1.53 ~ ( member @ A @ X3 @ A4 ) )
% 0.30/1.53 = ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_198_Collect__empty__eq,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o] :
% 0.30/1.53 ( ( ( collect @ A @ P )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ! [X3: A] :
% 0.30/1.53 ~ ( P @ X3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_199_empty__Collect__eq,axiom,
% 0.30/1.53 ! [A: $tType,P: A > $o] :
% 0.30/1.53 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/1.53 = ( collect @ A @ P ) )
% 0.30/1.53 = ( ! [X3: A] :
% 0.30/1.53 ~ ( P @ X3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_200_subsetI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ! [X2: A] :
% 0.30/1.53 ( ( member @ A @ X2 @ A4 )
% 0.30/1.53 => ( member @ A @ X2 @ B4 ) )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_201_subset__antisym,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 0.30/1.53 => ( A4 = B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_202_sup_Obounded__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,C2: A,A2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 0.30/1.53 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/1.53 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_203_le__sup__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A,Z: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.30/1.53 = ( ( ord_less_eq @ A @ X @ Z )
% 0.30/1.53 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_204_subset__empty,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_205_empty__subsetI,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_206_sup__bot_Oright__neutral,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/1.53 = A2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_207_sup__bot_Oleft__neutral,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A] :
% 0.30/1.53 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.30/1.53 = A2 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_208_sup__eq__bot__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ( sup_sup @ A @ X @ Y )
% 0.30/1.53 = ( bot_bot @ A ) )
% 0.30/1.53 = ( ( X
% 0.30/1.53 = ( bot_bot @ A ) )
% 0.30/1.53 & ( Y
% 0.30/1.53 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_209_bot__eq__sup__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ( bot_bot @ A )
% 0.30/1.53 = ( sup_sup @ A @ X @ Y ) )
% 0.30/1.53 = ( ( X
% 0.30/1.53 = ( bot_bot @ A ) )
% 0.30/1.53 & ( Y
% 0.30/1.53 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_210_Un__empty,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = ( ( A4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 & ( B4
% 0.30/1.53 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_211_Un__subset__iff,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,C3: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ C3 )
% 0.30/1.53 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/1.53 & ( ord_less_eq @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_212_sup__bot__right,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.30/1.53 = X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_213_sup__bot__left,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A] :
% 0.30/1.53 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.30/1.53 = X ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_214_sup_OcoboundedI2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [C2: A,B2: A,A2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/1.53 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_215_sup_OcoboundedI1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [C2: A,A2: A,B2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.30/1.53 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_216_sup_Oabsorb__iff2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( ord_less_eq @ A )
% 0.30/1.53 = ( ^ [A3: A,B3: A] :
% 0.30/1.53 ( ( sup_sup @ A @ A3 @ B3 )
% 0.30/1.53 = B3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_217_sup_Oabsorb__iff1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( ord_less_eq @ A )
% 0.30/1.53 = ( ^ [B3: A,A3: A] :
% 0.30/1.53 ( ( sup_sup @ A @ A3 @ B3 )
% 0.30/1.53 = A3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_218_sup_Ocobounded2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_219_sup_Ocobounded1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_220_sup_Oorder__iff,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( ord_less_eq @ A )
% 0.30/1.53 = ( ^ [B3: A,A3: A] :
% 0.30/1.53 ( A3
% 0.30/1.53 = ( sup_sup @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_221_sup_OboundedI,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,A2: A,C2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_222_sup_OboundedE,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,C2: A,A2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C2 ) @ A2 )
% 0.30/1.53 => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_223_sup__absorb2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/1.53 => ( ( sup_sup @ A @ X @ Y )
% 0.30/1.53 = Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_224_sup__absorb1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/1.53 => ( ( sup_sup @ A @ X @ Y )
% 0.30/1.53 = X ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_225_sup_Oabsorb2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/1.53 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.30/1.53 = B2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_226_sup_Oabsorb1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,A2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/1.53 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.30/1.53 = A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_227_sup__unique,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [F: A > A > A,X: A,Y: A] :
% 0.30/1.53 ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y2 ) )
% 0.30/1.53 => ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.30/1.53 => ( ! [X2: A,Y2: A,Z3: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( F @ Y2 @ Z3 ) @ X2 ) ) )
% 0.30/1.53 => ( ( sup_sup @ A @ X @ Y )
% 0.30/1.53 = ( F @ X @ Y ) ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_228_sup_OorderI,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A] :
% 0.30/1.53 ( ( A2
% 0.30/1.53 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/1.53 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_229_sup_OorderE,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [B2: A,A2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/1.53 => ( A2
% 0.30/1.53 = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_230_le__iff__sup,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ( ( ord_less_eq @ A )
% 0.30/1.53 = ( ^ [X3: A,Y3: A] :
% 0.30/1.53 ( ( sup_sup @ A @ X3 @ Y3 )
% 0.30/1.53 = Y3 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_231_sup__least,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A,Z: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/1.53 => ( ( ord_less_eq @ A @ Z @ X )
% 0.30/1.53 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_232_sup__mono,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,C2: A,B2: A,D: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.30/1.53 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C2 @ D ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_233_sup_Omono,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [C2: A,A2: A,D: A,B2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.30/1.53 => ( ( ord_less_eq @ A @ D @ B2 )
% 0.30/1.53 => ( ord_less_eq @ A @ ( sup_sup @ A @ C2 @ D ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_234_le__supI2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,B2: A,A2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ B2 )
% 0.30/1.53 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_235_le__supI1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,A2: A,B2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ X @ A2 )
% 0.30/1.53 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_236_sup__ge2,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_237_sup__ge1,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_238_le__supI,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,X: A,B2: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ A2 @ X )
% 0.30/1.53 => ( ( ord_less_eq @ A @ B2 @ X )
% 0.30/1.53 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_239_le__supE,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [A2: A,B2: A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X )
% 0.30/1.53 => ~ ( ( ord_less_eq @ A @ A2 @ X )
% 0.30/1.53 => ~ ( ord_less_eq @ A @ B2 @ X ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_240_Un__empty__right,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ A4 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/1.53 = A4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_241_Un__empty__left,axiom,
% 0.30/1.53 ! [A: $tType,B4: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.30/1.53 = B4 ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_242_subset__Un__eq,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/1.53 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.30/1.53 ( ( sup_sup @ ( set @ A ) @ A5 @ B5 )
% 0.30/1.53 = B5 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_243_Un__absorb2,axiom,
% 0.30/1.53 ! [A: $tType,B4: set @ A,A4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ B4 @ A4 )
% 0.30/1.53 => ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 = A4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_244_Un__absorb1,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 => ( ( sup_sup @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 = B4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_245_Un__upper2,axiom,
% 0.30/1.53 ! [A: $tType,B4: set @ A,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_246_Un__upper1,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_247_Un__least,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,C3: set @ A,B4: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C3 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ C3 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_248_Un__mono,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,C3: set @ A,B4: set @ A,D2: set @ A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C3 )
% 0.30/1.53 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ D2 )
% 0.30/1.53 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B4 ) @ ( sup_sup @ ( set @ A ) @ C3 @ D2 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_249_inf__sup__ord_I3_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_250_inf__sup__ord_I4_J,axiom,
% 0.30/1.53 ! [A: $tType] :
% 0.30/1.53 ( ( lattice @ A @ ( type2 @ A ) )
% 0.30/1.53 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_251_emptyE,axiom,
% 0.30/1.53 ! [A: $tType,A2: A] :
% 0.30/1.53 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_252_set__mp,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 => ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( member @ A @ X @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(fact_253_in__mono,axiom,
% 0.30/1.53 ! [A: $tType,A4: set @ A,B4: set @ A,X: A] :
% 0.30/1.53 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B4 )
% 0.30/1.53 => ( ( member @ A @ X @ A4 )
% 0.30/1.53 => ( member @ A @ X @ B4 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/1.53 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/1.53 ! [A6: $tType] : ( bounded_lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/1.53 ! [A6: $tType,A7: $tType] :
% 0.30/1.53 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/1.53 => ( bounded_lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.30/1.53 ! [A6: $tType,A7: $tType] :
% 0.30/1.53 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/1.53 => ( bounde1808546759up_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.30/1.53 ! [A6: $tType,A7: $tType] :
% 0.30/1.53 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/1.53 => ( bounded_lattice_bot @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.30/1.53 ! [A6: $tType,A7: $tType] :
% 0.30/1.53 ( ( semilattice_sup @ A7 @ ( type2 @ A7 ) )
% 0.30/1.53 => ( semilattice_sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.30/1.53 ! [A6: $tType,A7: $tType] :
% 0.30/1.53 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.30/1.53 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.30/1.53 ! [A6: $tType] : ( bounde1808546759up_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_4,axiom,
% 0.30/1.53 ! [A6: $tType] : ( bounded_lattice_bot @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_5,axiom,
% 0.30/1.53 ! [A6: $tType] : ( semilattice_sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_Set_Oset___Lattices_Olattice_6,axiom,
% 0.30/1.53 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.30/1.53 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_8,axiom,
% 0.30/1.53 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_9,axiom,
% 0.30/1.53 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 0.30/1.53 lattice @ $o @ ( type2 @ $o ) ).
% 0.30/1.53
% 0.30/1.53 thf(help_If_3_1_T,axiom,
% 0.30/1.53 ! [P: $o] :
% 0.30/1.53 ( ( P = $true )
% 0.30/1.53 | ( P = $false ) ) ).
% 0.30/1.53
% 0.30/1.53 thf(help_If_2_1_T,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A] :
% 0.30/1.53 ( ( if @ A @ $false @ X @ Y )
% 0.30/1.53 = Y ) ).
% 0.30/1.53
% 0.30/1.53 thf(help_If_1_1_T,axiom,
% 0.30/1.53 ! [A: $tType,X: A,Y: A] :
% 0.30/1.53 ( ( if @ A @ $true @ X @ Y )
% 0.30/1.53 = X ) ).
% 0.30/1.53
% 0.30/1.53 thf(conj_0,conjecture,
% 0.30/1.53 comple1396247847notone @ ( coindu1593790203_llist @ a ) @ ( coindu1593790203_llist @ a ) @ ( coindu1696667936prefix @ a ) @ ( coindu1696667936prefix @ a ) @ ( coindu1121789889_LCons @ a @ x ) ).
% 0.30/1.53 ------------------------
% 0.30/1.56 % (6623)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/183Mi)
% 0.30/1.56 % (6625)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_6414 for (2999ds/27Mi)
% 0.30/1.56 % (6629)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/18Mi)
% 0.30/1.57 % (6629)Instruction limit reached!
% 0.30/1.57 % (6629)------------------------------
% 0.30/1.57 % (6629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (6629)Termination reason: Unknown
% 0.30/1.57 % (6629)Termination phase: shuffling
% 0.30/1.57
% 0.30/1.57 % (6629)Memory used [KB]: 1663
% 0.30/1.57 % (6629)Time elapsed: 0.008 s
% 0.30/1.57 % (6629)Instructions burned: 19 (million)
% 0.30/1.57 % (6629)------------------------------
% 0.30/1.57 % (6629)------------------------------
% 0.30/1.57 % (6624)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_6414 for (2999ds/4Mi)
% 0.30/1.57 % (6626)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/2Mi)
% 0.30/1.57 % (6627)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_6414 for (2999ds/2Mi)
% 0.30/1.57 % (6628)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_6414 for (2999ds/275Mi)
% 0.30/1.57 % (6626)Instruction limit reached!
% 0.30/1.57 % (6626)------------------------------
% 0.30/1.57 % (6626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (6626)Termination reason: Unknown
% 0.30/1.57 % (6626)Termination phase: shuffling
% 0.30/1.57
% 0.30/1.57 % (6626)Memory used [KB]: 1407
% 0.30/1.57 % (6626)Time elapsed: 0.004 s
% 0.30/1.57 % (6626)Instructions burned: 3 (million)
% 0.30/1.57 % (6626)------------------------------
% 0.30/1.57 % (6626)------------------------------
% 0.30/1.57 % (6627)Instruction limit reached!
% 0.30/1.57 % (6627)------------------------------
% 0.30/1.57 % (6627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (6627)Termination reason: Unknown
% 0.30/1.57 % (6627)Termination phase: shuffling
% 0.30/1.57
% 0.30/1.57 % (6627)Memory used [KB]: 1407
% 0.30/1.57 % (6627)Time elapsed: 0.004 s
% 0.30/1.57 % (6627)Instructions burned: 3 (million)
% 0.30/1.57 % (6627)------------------------------
% 0.30/1.57 % (6627)------------------------------
% 0.30/1.57 % (6624)Instruction limit reached!
% 0.30/1.57 % (6624)------------------------------
% 0.30/1.57 % (6624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (6624)Termination reason: Unknown
% 0.30/1.57 % (6624)Termination phase: shuffling
% 0.30/1.57
% 0.30/1.57 % (6624)Memory used [KB]: 1407
% 0.30/1.57 % (6624)Time elapsed: 0.005 s
% 0.30/1.57 % (6624)Instructions burned: 5 (million)
% 0.30/1.57 % (6624)------------------------------
% 0.30/1.57 % (6624)------------------------------
% 0.30/1.57 % (6625)Instruction limit reached!
% 0.30/1.57 % (6625)------------------------------
% 0.30/1.57 % (6625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (6625)Termination reason: Unknown
% 0.30/1.57 % (6625)Termination phase: Property scanning
% 0.30/1.57
% 0.30/1.57 % (6625)Memory used [KB]: 1918
% 0.30/1.57 % (6625)Time elapsed: 0.011 s
% 0.30/1.57 % (6625)Instructions burned: 28 (million)
% 0.30/1.57 % (6625)------------------------------
% 0.30/1.57 % (6625)------------------------------
% 0.30/1.58 % (6630)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/3Mi)
% 0.30/1.58 % (6630)Instruction limit reached!
% 0.30/1.58 % (6630)------------------------------
% 0.30/1.58 % (6630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (6630)Termination reason: Unknown
% 0.30/1.58 % (6630)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (6630)Memory used [KB]: 1407
% 0.30/1.58 % (6630)Time elapsed: 0.003 s
% 0.30/1.58 % (6630)Instructions burned: 3 (million)
% 0.30/1.58 % (6630)------------------------------
% 0.30/1.58 % (6630)------------------------------
% 0.30/1.58 % (6634)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_6414 for (2999ds/1041Mi)
% 0.30/1.59 % (6631)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_6414 for (2999ds/37Mi)
% 0.30/1.59 % (6632)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_6414 for (2999ds/15Mi)
% 0.30/1.59 % (6633)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_6414 for (2999ds/3Mi)
% 0.30/1.59 % (6635)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/7Mi)
% 0.30/1.59 % (6633)Instruction limit reached!
% 0.30/1.59 % (6633)------------------------------
% 0.30/1.59 % (6633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (6633)Termination reason: Unknown
% 0.30/1.59 % (6633)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (6633)Memory used [KB]: 1407
% 0.30/1.59 % (6633)Time elapsed: 0.004 s
% 0.30/1.59 % (6633)Instructions burned: 4 (million)
% 0.30/1.59 % (6633)------------------------------
% 0.30/1.59 % (6633)------------------------------
% 2.89/1.60 % (6635)Instruction limit reached!
% 2.89/1.60 % (6635)------------------------------
% 2.89/1.60 % (6635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (6635)Termination reason: Unknown
% 2.89/1.60 % (6635)Termination phase: shuffling
% 2.89/1.60
% 2.89/1.60 % (6635)Memory used [KB]: 1535
% 2.89/1.60 % (6635)Time elapsed: 0.005 s
% 2.89/1.60 % (6635)Instructions burned: 9 (million)
% 2.89/1.60 % (6635)------------------------------
% 2.89/1.60 % (6635)------------------------------
% 2.89/1.60 % (6632)Instruction limit reached!
% 2.89/1.60 % (6632)------------------------------
% 2.89/1.60 % (6632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (6632)Termination reason: Unknown
% 2.89/1.60 % (6632)Termination phase: shuffling
% 2.89/1.60
% 2.89/1.60 % (6632)Memory used [KB]: 1663
% 2.89/1.60 % (6632)Time elapsed: 0.012 s
% 2.89/1.60 % (6632)Instructions burned: 15 (million)
% 2.89/1.60 % (6632)------------------------------
% 2.89/1.60 % (6632)------------------------------
% 2.89/1.60 % (6631)Instruction limit reached!
% 2.89/1.60 % (6631)------------------------------
% 2.89/1.60 % (6631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (6631)Termination reason: Unknown
% 2.89/1.60 % (6631)Termination phase: shuffling
% 2.89/1.60
% 2.89/1.60 % (6631)Memory used [KB]: 2174
% 2.89/1.60 % (6631)Time elapsed: 0.017 s
% 2.89/1.60 % (6631)Instructions burned: 39 (million)
% 2.89/1.60 % (6631)------------------------------
% 2.89/1.60 % (6631)------------------------------
% 2.89/1.60 % (6628)Refutation not found, incomplete strategy
% 2.89/1.60 % (6628)------------------------------
% 2.89/1.60 % (6628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.60 % (6628)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.60
% 2.89/1.60
% 2.89/1.60 % (6628)Memory used [KB]: 6524
% 2.89/1.60 % (6628)Time elapsed: 0.035 s
% 2.89/1.60 % (6628)Instructions burned: 55 (million)
% 2.89/1.60 % (6628)------------------------------
% 2.89/1.60 % (6628)------------------------------
% 2.89/1.61 % (6637)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_6414 for (2999ds/3Mi)
% 2.89/1.61 % (6637)Instruction limit reached!
% 2.89/1.61 % (6637)------------------------------
% 2.89/1.61 % (6637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.61 % (6637)Termination reason: Unknown
% 2.89/1.61 % (6637)Termination phase: shuffling
% 2.89/1.61
% 2.89/1.61 % (6637)Memory used [KB]: 1407
% 2.89/1.61 % (6637)Time elapsed: 0.003 s
% 2.89/1.61 % (6637)Instructions burned: 5 (million)
% 2.89/1.61 % (6637)------------------------------
% 2.89/1.61 % (6637)------------------------------
% 2.89/1.61 % (6636)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/16Mi)
% 2.89/1.62 % (6639)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/7Mi)
% 2.89/1.62 % (6636)Instruction limit reached!
% 2.89/1.62 % (6636)------------------------------
% 2.89/1.62 % (6636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.62 % (6636)Termination reason: Unknown
% 2.89/1.62 % (6636)Termination phase: shuffling
% 2.89/1.62
% 2.89/1.62 % (6636)Memory used [KB]: 1663
% 2.89/1.62 % (6636)Time elapsed: 0.009 s
% 2.89/1.62 % (6636)Instructions burned: 16 (million)
% 2.89/1.62 % (6636)------------------------------
% 2.89/1.62 % (6636)------------------------------
% 2.89/1.62 % (6641)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/4Mi)
% 2.89/1.62 % (6623)Instruction limit reached!
% 2.89/1.62 % (6623)------------------------------
% 2.89/1.62 % (6623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.62 % (6623)Termination reason: Unknown
% 2.89/1.62 % (6623)Termination phase: Saturation
% 2.89/1.62
% 2.89/1.62 % (6623)Memory used [KB]: 7164
% 2.89/1.62 % (6623)Time elapsed: 0.056 s
% 2.89/1.62 % (6623)Instructions burned: 183 (million)
% 2.89/1.62 % (6623)------------------------------
% 2.89/1.62 % (6623)------------------------------
% 2.89/1.62 % (6639)Instruction limit reached!
% 2.89/1.62 % (6639)------------------------------
% 2.89/1.62 % (6639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.62 % (6639)Termination reason: Unknown
% 2.89/1.62 % (6639)Termination phase: shuffling
% 2.89/1.62
% 2.89/1.62 % (6639)Memory used [KB]: 1535
% 2.89/1.62 % (6639)Time elapsed: 0.005 s
% 2.89/1.62 % (6639)Instructions burned: 9 (million)
% 2.89/1.62 % (6639)------------------------------
% 2.89/1.62 % (6639)------------------------------
% 2.89/1.62 % (6638)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_6414 for (2999ds/3Mi)
% 2.89/1.62 % (6641)Instruction limit reached!
% 2.89/1.62 % (6641)------------------------------
% 2.89/1.62 % (6641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.62 % (6641)Termination reason: Unknown
% 2.89/1.62 % (6641)Termination phase: shuffling
% 2.89/1.62
% 2.89/1.62 % (6641)Memory used [KB]: 1407
% 2.89/1.62 % (6641)Time elapsed: 0.003 s
% 2.89/1.62 % (6641)Instructions burned: 5 (million)
% 2.89/1.62 % (6641)------------------------------
% 2.89/1.62 % (6641)------------------------------
% 2.89/1.62 % (6638)Instruction limit reached!
% 2.89/1.62 % (6638)------------------------------
% 2.89/1.62 % (6638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.62 % (6638)Termination reason: Unknown
% 2.89/1.62 % (6638)Termination phase: shuffling
% 2.89/1.62
% 2.89/1.62 % (6638)Memory used [KB]: 1407
% 2.89/1.62 % (6638)Time elapsed: 0.004 s
% 2.89/1.62 % (6638)Instructions burned: 3 (million)
% 2.89/1.62 % (6638)------------------------------
% 2.89/1.62 % (6638)------------------------------
% 2.89/1.62 % (6640)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/3Mi)
% 2.89/1.63 % (6640)Instruction limit reached!
% 2.89/1.63 % (6640)------------------------------
% 2.89/1.63 % (6640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.63 % (6640)Termination reason: Unknown
% 2.89/1.63 % (6640)Termination phase: shuffling
% 2.89/1.63
% 2.89/1.63 % (6640)Memory used [KB]: 1407
% 2.89/1.63 % (6640)Time elapsed: 0.004 s
% 2.89/1.63 % (6640)Instructions burned: 3 (million)
% 2.89/1.63 % (6640)------------------------------
% 2.89/1.63 % (6640)------------------------------
% 2.89/1.63 % (6642)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/18Mi)
% 2.89/1.63 % (6643)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/710Mi)
% 2.89/1.63 % (6644)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/6Mi)
% 2.89/1.63 % (6645)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_6414 for (2999ds/902Mi)
% 2.89/1.63 % (6644)Instruction limit reached!
% 2.89/1.63 % (6644)------------------------------
% 2.89/1.63 % (6644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.63 % (6644)Termination reason: Unknown
% 2.89/1.63 % (6644)Termination phase: shuffling
% 2.89/1.63
% 2.89/1.63 % (6644)Memory used [KB]: 1407
% 2.89/1.63 % (6644)Time elapsed: 0.004 s
% 2.89/1.63 % (6644)Instructions burned: 6 (million)
% 2.89/1.63 % (6644)------------------------------
% 2.89/1.63 % (6644)------------------------------
% 2.89/1.63 % (6642)Instruction limit reached!
% 2.89/1.63 % (6642)------------------------------
% 2.89/1.63 % (6642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.63 % (6642)Termination reason: Unknown
% 2.89/1.63 % (6642)Termination phase: shuffling
% 2.89/1.63
% 2.89/1.63 % (6642)Memory used [KB]: 1663
% 2.89/1.63 % (6642)Time elapsed: 0.007 s
% 2.89/1.63 % (6642)Instructions burned: 18 (million)
% 2.89/1.63 % (6642)------------------------------
% 2.89/1.63 % (6642)------------------------------
% 2.89/1.64 % (6646)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_6414 for (2999ds/21Mi)
% 2.89/1.64 % (6648)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_6414 for (2999ds/6Mi)
% 2.89/1.64 % (6649)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/377Mi)
% 2.89/1.64 % (6648)Instruction limit reached!
% 2.89/1.64 % (6648)------------------------------
% 2.89/1.64 % (6648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.64 % (6648)Termination reason: Unknown
% 2.89/1.64 % (6648)Termination phase: shuffling
% 2.89/1.64
% 2.89/1.64 % (6648)Memory used [KB]: 1407
% 2.89/1.64 % (6648)Time elapsed: 0.004 s
% 2.89/1.64 % (6648)Instructions burned: 7 (million)
% 2.89/1.64 % (6648)------------------------------
% 2.89/1.64 % (6648)------------------------------
% 2.89/1.64 % (6647)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6414 for (2999ds/5Mi)
% 2.89/1.65 % (6647)Instruction limit reached!
% 2.89/1.65 % (6647)------------------------------
% 2.89/1.65 % (6647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.65 % (6647)Termination reason: Unknown
% 2.89/1.65 % (6647)Termination phase: shuffling
% 2.89/1.65
% 2.89/1.65 % (6647)Memory used [KB]: 1407
% 2.89/1.65 % (6647)Time elapsed: 0.005 s
% 2.89/1.65 % (6647)Instructions burned: 5 (million)
% 2.89/1.65 % (6647)------------------------------
% 2.89/1.65 % (6647)------------------------------
% 2.89/1.65 % (6646)Instruction limit reached!
% 2.89/1.65 % (6646)------------------------------
% 2.89/1.65 % (6646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.65 % (6646)Termination reason: Unknown
% 2.89/1.65 % (6646)Termination phase: shuffling
% 2.89/1.65
% 2.89/1.65 % (6646)Memory used [KB]: 1791
% 2.89/1.65 % (6646)Time elapsed: 0.015 s
% 2.89/1.65 % (6646)Instructions burned: 21 (million)
% 2.89/1.65 % (6646)------------------------------
% 2.89/1.65 % (6646)------------------------------
% 2.89/1.65 % (6650)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_6414 for (2999ds/779Mi)
% 2.89/1.66 % (6651)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_6414 for (2999ds/19Mi)
% 2.89/1.67 % (6652)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6414 for (2998ds/879Mi)
% 2.89/1.67 % (6645)Refutation not found, incomplete strategy
% 2.89/1.67 % (6645)------------------------------
% 2.89/1.67 % (6645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.67 % (6645)Termination reason: Refutation not found, incomplete strategy
% 2.89/1.67
% 2.89/1.67
% 2.89/1.67 % (6645)Memory used [KB]: 7291
% 2.89/1.67 % (6645)Time elapsed: 0.041 s
% 2.89/1.67 % (6645)Instructions burned: 135 (million)
% 2.89/1.67 % (6645)------------------------------
% 2.89/1.67 % (6645)------------------------------
% 2.89/1.67 % (6651)Instruction limit reached!
% 2.89/1.67 % (6651)------------------------------
% 2.89/1.67 % (6651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.67 % (6651)Termination reason: Unknown
% 2.89/1.67 % (6651)Termination phase: shuffling
% 2.89/1.67
% 2.89/1.67 % (6651)Memory used [KB]: 1663
% 2.89/1.67 % (6651)Time elapsed: 0.010 s
% 2.89/1.67 % (6651)Instructions burned: 20 (million)
% 2.89/1.67 % (6651)------------------------------
% 2.89/1.67 % (6651)------------------------------
% 2.89/1.68 % (6653)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6414 for (2998ds/17Mi)
% 2.89/1.68 % (6654)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6414 for (2998ds/3Mi)
% 2.89/1.68 % (6654)Instruction limit reached!
% 2.89/1.68 % (6654)------------------------------
% 2.89/1.68 % (6654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.68 % (6654)Termination reason: Unknown
% 2.89/1.68 % (6654)Termination phase: shuffling
% 2.89/1.68
% 2.89/1.68 % (6654)Memory used [KB]: 1407
% 2.89/1.68 % (6654)Time elapsed: 0.003 s
% 2.89/1.68 % (6654)Instructions burned: 4 (million)
% 2.89/1.68 % (6654)------------------------------
% 2.89/1.68 % (6654)------------------------------
% 2.89/1.68 % (6653)Instruction limit reached!
% 2.89/1.68 % (6653)------------------------------
% 2.89/1.68 % (6653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.68 % (6653)Termination reason: Unknown
% 2.89/1.68 % (6653)Termination phase: shuffling
% 2.89/1.68
% 2.89/1.68 % (6653)Memory used [KB]: 1791
% 2.89/1.68 % (6653)Time elapsed: 0.007 s
% 2.89/1.68 % (6653)Instructions burned: 19 (million)
% 2.89/1.68 % (6653)------------------------------
% 2.89/1.68 % (6653)------------------------------
% 2.89/1.69 % (6643)First to succeed.
% 2.89/1.69 % (6643)Refutation found. Thanks to Tanya!
% 2.89/1.69 % SZS status Theorem for DTF2THF_6414
% 2.89/1.69 % SZS output start Proof for DTF2THF_6414
% 2.89/1.69 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.89/1.69 thf(type_def_7, type, set: ($tType) > $tType).
% 2.89/1.69 thf(type_def_8, type, coindu1593790203_llist: ($tType) > $tType).
% 2.89/1.69 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 2.89/1.69 thf(type_def_10, type, a: $tType).
% 2.89/1.69 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 2.89/1.69 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 2.89/1.69 thf(func_def_2, type, set: ($tType) > $tType).
% 2.89/1.69 thf(func_def_3, type, itself: ($tType) > $tType).
% 2.89/1.69 thf(func_def_4, type, a: $tType).
% 2.89/1.69 thf(func_def_5, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.69 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.69 thf(func_def_7, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.69 thf(func_def_8, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.69 thf(func_def_9, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.69 thf(func_def_10, type, bounde1808546759up_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.89/1.69 thf(func_def_11, type, coindu1928975208n_lset: !>[X0: $tType]:(set @ X0 > coindu1593790203_llist @ X0 > set @ X0)).
% 2.89/1.69 thf(func_def_12, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_13, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.89/1.69 thf(func_def_14, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_15, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_16, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0)).
% 2.89/1.69 thf(func_def_17, type, coindu1244876290_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coindu1593790203_llist @ X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 2.89/1.69 thf(func_def_18, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.89/1.69 thf(func_def_19, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o)).
% 2.89/1.69 thf(func_def_20, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.89/1.69 thf(func_def_21, type, coindu1112613586e_lset: !>[X0: $tType]:(coindu1593790203_llist @ X0 > set @ X0)).
% 2.89/1.69 thf(func_def_22, type, coindu1047225960le_ltl: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_23, type, coindu44415597_llist: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > $o)).
% 2.89/1.69 thf(func_def_24, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 2.89/1.69 thf(func_def_25, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.89/1.69 thf(func_def_26, type, coindu1055736764_lsetp: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > $o)).
% 2.89/1.69 thf(func_def_27, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 2.89/1.69 thf(func_def_28, type, comple1396247847notone: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X1 > $o) > (X0 > X1) > $o)).
% 2.89/1.69 thf(func_def_29, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.89/1.69 thf(func_def_30, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.89/1.69 thf(func_def_31, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.89/1.69 thf(func_def_32, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.89/1.69 thf(func_def_33, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.89/1.69 thf(func_def_34, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.89/1.69 thf(func_def_35, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.89/1.69 thf(func_def_36, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.89/1.69 thf(func_def_37, type, x: a).
% 2.89/1.69 thf(func_def_55, type, sP0: !>[X0: $tType, X1: $tType]:(X0 > coindu1593790203_llist @ X1 > (coindu1593790203_llist @ X1 > X0) > (coindu1593790203_llist @ X1 > X0) > $o)).
% 2.89/1.69 thf(func_def_56, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.89/1.69 thf(func_def_57, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X0 > $o) > (X1 > X1 > $o) > X1)).
% 2.89/1.69 thf(func_def_58, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X0 > $o) > (X1 > X1 > $o) > X1)).
% 2.89/1.69 thf(func_def_59, type, sK4: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_60, type, sK5: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_61, type, sK6: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_62, type, sK7: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_63, type, sK8: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_64, type, sK9: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_65, type, sK10: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.89/1.69 thf(func_def_66, type, sK11: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0)).
% 2.89/1.69 thf(func_def_67, type, sK12: !>[X0: $tType, X1: $tType]:(X0 > coindu1593790203_llist @ X1 > (coindu1593790203_llist @ X1 > X0) > (coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1)).
% 2.89/1.69 thf(func_def_68, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X1 > X0) > X0 > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X1)).
% 2.89/1.69 thf(func_def_69, type, sK14: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X1)).
% 2.89/1.69 thf(func_def_70, type, sK15: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X1)).
% 2.89/1.69 thf(func_def_72, type, sK17: coindu1593790203_llist @ a).
% 2.89/1.69 thf(func_def_73, type, sK18: coindu1593790203_llist @ a).
% 2.89/1.69 thf(func_def_74, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X1 > X0) > X1)).
% 2.89/1.69 thf(func_def_75, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > (X1 > X1 > $o) > X1)).
% 2.89/1.69 thf(func_def_76, type, ph21: !>[X0: $tType]:(X0)).
% 2.89/1.69 thf(f1461,plain,(
% 2.89/1.69 $false),
% 2.89/1.69 inference(trivial_inequality_removal,[status(thm)],[f1423])).
% 2.89/1.69 thf(f1423,plain,(
% 2.89/1.69 ($false = $true)),
% 2.89/1.69 inference(superposition,[status(thm)],[f1072,f930])).
% 2.89/1.69 thf(f930,plain,(
% 2.89/1.69 ($false = (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ sK18) @ (coindu1121789889_LCons @ a @ x @ sK17)))),
% 2.89/1.69 inference(binary_proxy_clausification,[status(thm)],[f929])).
% 2.89/1.69 thf(f929,plain,(
% 2.89/1.69 ($false = ((coindu1696667936prefix @ a @ sK18 @ sK17) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ sK18) @ (coindu1121789889_LCons @ a @ x @ sK17))))),
% 2.89/1.69 inference(beta_eta_normalization,[status(thm)],[f928])).
% 2.89/1.69 thf(f928,plain,(
% 2.89/1.69 (((^[Y0 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y0 @ sK17) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y0) @ (coindu1121789889_LCons @ a @ x @ sK17)))) @ sK18) = $false)),
% 2.89/1.69 inference(sigma_clausification,[status(thm)],[f927])).
% 2.89/1.69 thf(f927,plain,(
% 2.89/1.69 ($false = (!! @ coindu1593790203_llist @ a @ (^[Y0 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y0 @ sK17) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y0) @ (coindu1121789889_LCons @ a @ x @ sK17))))))),
% 2.89/1.69 inference(beta_eta_normalization,[status(thm)],[f926])).
% 2.89/1.69 thf(f926,plain,(
% 2.89/1.69 ($false = ((^[Y0 : coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y1 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y1 @ Y0) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y1) @ (coindu1121789889_LCons @ a @ x @ Y0)))))) @ sK17))),
% 2.89/1.69 inference(sigma_clausification,[status(thm)],[f925])).
% 2.89/1.69 thf(f925,plain,(
% 2.89/1.69 ((!! @ coindu1593790203_llist @ a @ (^[Y0 : coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y1 : coindu1593790203_llist @ a]: ((coindu1696667936prefix @ a @ Y1 @ Y0) => (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x @ Y1) @ (coindu1121789889_LCons @ a @ x @ Y0))))))) != $true)),
% 2.89/1.69 inference(beta_eta_normalization,[status(thm)],[f884])).
% 2.89/1.69 thf(f884,plain,(
% 2.89/1.69 (((^[Y0 : coindu1593790203_llist @ a > coindu1593790203_llist @ a > $o]: ((^[Y1 : coindu1593790203_llist @ a > coindu1593790203_llist @ a > $o]: ((^[Y2 : coindu1593790203_llist @ a > coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y3 : coindu1593790203_llist @ a]: (!! @ coindu1593790203_llist @ a @ (^[Y4 : coindu1593790203_llist @ a]: ((Y0 @ Y4 @ Y3) => (Y1 @ (Y2 @ Y4) @ (Y2 @ Y3)))))))))))) @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x)) != $true)),
% 2.89/1.69 inference(definition_unfolding,[status(thm)],[f860,f830])).
% 2.89/1.69 thf(f830,plain,(
% 2.89/1.69 ( ! [X1 : $tType,X0 : $tType] : ((comple1396247847notone @ X1 @ X0 = (^[Y0 : X1 > X1 > $o]: ((^[Y1 : X0 > X0 > $o]: ((^[Y2 : X1 > X0]: (!! @ X1 @ (^[Y3 : X1]: (!! @ X1 @ (^[Y4 : X1]: ((Y0 @ Y4 @ Y3) => (Y1 @ (Y2 @ Y4) @ (Y2 @ Y3)))))))))))))) )),
% 2.89/1.69 inference(cnf_transformation,[status(thm)],[f303])).
% 2.89/1.69 thf(f303,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : $tType] : (comple1396247847notone @ X1 @ X0 = (^[Y0 : X1 > X1 > $o]: ((^[Y1 : X0 > X0 > $o]: ((^[Y2 : X1 > X0]: (!! @ X1 @ (^[Y3 : X1]: (!! @ X1 @ (^[Y4 : X1]: ((Y0 @ Y4 @ Y3) => (Y1 @ (Y2 @ Y4) @ (Y2 @ Y3)))))))))))))),
% 2.89/1.69 inference(fool_elimination,[status(thm)],[f302])).
% 2.89/1.69 thf(f302,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : $tType] : ((^[X2 : X1 > X1 > $o, X3 : X0 > X0 > $o, X4 : X1 > X0] : (! [X5 : X1,X6 : X1] : ((X2 @ X5 @ X6) => (X3 @ (X4 @ X5) @ (X4 @ X6))))) = comple1396247847notone @ X1 @ X0)),
% 2.89/1.69 inference(rectify,[status(thm)],[f16])).
% 2.89/1.69 thf(f16,axiom,(
% 2.89/1.69 ! [X1 : $tType,X0 : $tType] : ((^[X23 : X0 > X0 > $o, X24 : X1 > X1 > $o, X25 : X0 > X1] : (! [X26 : X0,X27 : X0] : ((X23 @ X26 @ X27) => (X24 @ (X25 @ X26) @ (X25 @ X27))))) = comple1396247847notone @ X0 @ X1)),
% 2.89/1.69 file('/export/starexec/sandbox2/tmp/tmp.DnhfbxsEpZ/DTF2THF_6414.p',fact_15_monotone__def)).
% 2.89/1.69 thf(f860,plain,(
% 2.89/1.69 ((comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x)) != $true)),
% 2.89/1.69 inference(cnf_transformation,[status(thm)],[f756])).
% 2.89/1.69 thf(f756,plain,(
% 2.89/1.69 ((comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x)) != $true)),
% 2.89/1.69 inference(flattening,[status(thm)],[f387])).
% 2.89/1.69 thf(f387,plain,(
% 2.89/1.69 ~((comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x)) = $true)),
% 2.89/1.69 inference(fool_elimination,[status(thm)],[f386])).
% 2.89/1.69 thf(f386,plain,(
% 2.89/1.69 ~(comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))),
% 2.89/1.69 inference(rectify,[status(thm)],[f274])).
% 2.89/1.69 thf(f274,negated_conjecture,(
% 2.89/1.69 ~(comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))),
% 2.89/1.69 inference(negated_conjecture,[status(cth)],[f273])).
% 2.89/1.69 thf(f273,conjecture,(
% 2.89/1.69 (comple1396247847notone @ coindu1593790203_llist @ a @ coindu1593790203_llist @ a @ coindu1696667936prefix @ a @ coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ x))),
% 2.89/1.69 file('/export/starexec/sandbox2/tmp/tmp.DnhfbxsEpZ/DTF2THF_6414.p',conj_0)).
% 2.89/1.69 thf(f1072,plain,(
% 2.89/1.69 ( ! [X0 : a] : (($true = (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ X0 @ sK18) @ (coindu1121789889_LCons @ a @ X0 @ sK17)))) )),
% 2.89/1.69 inference(trivial_inequality_removal,[status(thm)],[f1069])).
% 2.89/1.69 thf(f1069,plain,(
% 2.89/1.69 ( ! [X0 : a] : (($true != $true) | ($true = (coindu1696667936prefix @ a @ (coindu1121789889_LCons @ a @ X0 @ sK18) @ (coindu1121789889_LCons @ a @ X0 @ sK17)))) )),
% 2.89/1.69 inference(superposition,[status(thm)],[f894,f931])).
% 2.89/1.69 thf(f931,plain,(
% 2.89/1.69 ((coindu1696667936prefix @ a @ sK18 @ sK17) = $true)),
% 2.89/1.69 inference(binary_proxy_clausification,[status(thm)],[f929])).
% 2.89/1.69 thf(f894,plain,(
% 2.89/1.69 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : X0,X4 : coindu1593790203_llist @ X0] : (($true != (coindu1696667936prefix @ X0 @ X2 @ X4)) | ((coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ (coindu1121789889_LCons @ X0 @ X1 @ X4)) = $true)) )),
% 2.89/1.69 inference(equality_resolution,[status(thm)],[f845])).
% 2.89/1.69 thf(f845,plain,(
% 2.89/1.69 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : X0,X4 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3)) | ($true != (coindu1696667936prefix @ X0 @ X2 @ X4)) | ((coindu1121789889_LCons @ X0 @ X1 @ X4) != X3)) )),
% 2.89/1.69 inference(cnf_transformation,[status(thm)],[f809])).
% 2.89/1.69 thf(f809,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((($true = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3)) | ! [X4 : coindu1593790203_llist @ X0] : (($true != (coindu1696667936prefix @ X0 @ X2 @ X4)) | ((coindu1121789889_LCons @ X0 @ X1 @ X4) != X3))) & ((($true = (coindu1696667936prefix @ X0 @ X2 @ (sK7 @ X0 @ X3 @ X2 @ X1))) & ((coindu1121789889_LCons @ X0 @ X1 @ (sK7 @ X0 @ X3 @ X2 @ X1)) = X3)) | ($true != (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3))))),
% 2.89/1.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f807,f808])).
% 2.89/1.69 thf(f808,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : (? [X5 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ X2 @ X5)) & ((coindu1121789889_LCons @ X0 @ X1 @ X5) = X3)) => (($true = (coindu1696667936prefix @ X0 @ X2 @ (sK7 @ X0 @ X3 @ X2 @ X1))) & ((coindu1121789889_LCons @ X0 @ X1 @ (sK7 @ X0 @ X3 @ X2 @ X1)) = X3)))),
% 2.89/1.69 introduced(definition,[],[choice_axiom])).
% 2.89/1.69 thf(f807,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((($true = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3)) | ! [X4 : coindu1593790203_llist @ X0] : (($true != (coindu1696667936prefix @ X0 @ X2 @ X4)) | ((coindu1121789889_LCons @ X0 @ X1 @ X4) != X3))) & (? [X5 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ X2 @ X5)) & ((coindu1121789889_LCons @ X0 @ X1 @ X5) = X3)) | ($true != (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3))))),
% 2.89/1.69 inference(rectify,[status(thm)],[f806])).
% 2.89/1.69 thf(f806,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((($true = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3)) | ! [X4 : coindu1593790203_llist @ X0] : (($true != (coindu1696667936prefix @ X0 @ X2 @ X4)) | ((coindu1121789889_LCons @ X0 @ X1 @ X4) != X3))) & (? [X4 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ X2 @ X4)) & ((coindu1121789889_LCons @ X0 @ X1 @ X4) = X3)) | ($true != (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3))))),
% 2.89/1.69 inference(nnf_transformation,[status(thm)],[f379])).
% 2.89/1.69 thf(f379,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3)) <=> ? [X4 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ X2 @ X4)) & ((coindu1121789889_LCons @ X0 @ X1 @ X4) = X3)))),
% 2.89/1.69 inference(fool_elimination,[status(thm)],[f378])).
% 2.89/1.69 thf(f378,plain,(
% 2.89/1.69 ! [X0 : $tType,X1 : X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : (? [X4 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X1 @ X4) = X3) & (coindu1696667936prefix @ X0 @ X2 @ X4)) = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X1 @ X2) @ X3))),
% 2.89/1.69 inference(rectify,[status(thm)],[f10])).
% 2.89/1.69 thf(f10,axiom,(
% 2.89/1.69 ! [X0 : $tType,X4 : X0,X3 : coindu1593790203_llist @ X0,X10 : coindu1593790203_llist @ X0] : (? [X13 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X4 @ X13) = X10) & (coindu1696667936prefix @ X0 @ X3 @ X13)) = (coindu1696667936prefix @ X0 @ (coindu1121789889_LCons @ X0 @ X4 @ X3) @ X10))),
% 2.89/1.69 file('/export/starexec/sandbox2/tmp/tmp.DnhfbxsEpZ/DTF2THF_6414.p',fact_9_LCons__lprefix__conv)).
% 2.89/1.69 % SZS output end Proof for DTF2THF_6414
% 2.89/1.69 % (6643)------------------------------
% 2.89/1.69 % (6643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.69 % (6643)Termination reason: Refutation
% 2.89/1.69
% 2.89/1.69 % (6643)Memory used [KB]: 7036
% 2.89/1.69 % (6643)Time elapsed: 0.063 s
% 2.89/1.69 % (6643)Instructions burned: 192 (million)
% 2.89/1.69 % (6643)------------------------------
% 2.89/1.69 % (6643)------------------------------
% 2.89/1.69 % (6622)Success in time 0.141 s
%------------------------------------------------------------------------------