%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT115^1 : 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 : n016.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 2.88s 1.72s
% Output : Refutation 2.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT115^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n016.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 06:08:06 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : DAT115^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.38 % Domain : Data Structures
% 0.18/0.38 % Problem : Coinductive list 557
% 0.18/0.38 % Version : [Bla16] axioms : Especial.
% 0.18/0.38 % English :
% 0.18/0.38
% 0.18/0.38 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.18/0.38 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.18/0.38 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.18/0.38 % Source : [Bla16]
% 0.18/0.38 % Names : coinductive_list__557.p [Bla16]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.18/0.38 % Syntax : Number of formulae : 302 ( 118 unt; 36 typ; 0 def)
% 0.18/0.38 % Number of atoms : 671 ( 249 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 8 ( 2 avg)
% 0.18/0.38 % Number of connectives : 4088 ( 111 ~; 19 |; 55 &;3592 @)
% 0.18/0.38 % ( 0 <=>; 311 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 28 ( 9 avg)
% 0.18/0.38 % Number of types : 2 ( 1 usr)
% 0.18/0.38 % Number of type conns : 241 ( 241 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 38 ( 35 usr; 5 con; 0-8 aty)
% 0.18/0.38 % Number of variables : 1178 ( 59 ^;1053 !; 29 ?;1178 :)
% 0.18/0.38 % ( 37 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.38 % SPC : TH1_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.18/0.38 % 2016-07-13 14:45:01.574
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 %----Could-be-implicit typings (5)
% 0.18/0.38 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.18/0.38 coindu1593790203_llist: $tType > $tType ).
% 0.18/0.38
% 0.18/0.38 thf(ty_t_Product__Type_Oprod,type,
% 0.18/0.38 product_prod: $tType > $tType > $tType ).
% 0.18/0.38
% 0.18/0.38 thf(ty_t_Set_Oset,type,
% 0.18/0.38 set: $tType > $tType ).
% 0.18/0.38
% 0.18/0.38 thf(ty_t_itself,type,
% 0.18/0.38 itself: $tType > $tType ).
% 0.18/0.38
% 0.18/0.38 thf(ty_tf_a,type,
% 0.18/0.38 a: $tType ).
% 0.18/0.38
% 0.18/0.38 %----Explicit typings (31)
% 0.18/0.38 thf(sy_cl_HOL_Otype,type,
% 0.18/0.38 type:
% 0.18/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_cl_Lattices_Olattice,type,
% 0.18/0.38 lattice:
% 0.18/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_cl_Orderings_Olinorder,type,
% 0.18/0.38 linorder:
% 0.18/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.18/0.38 semilattice_sup:
% 0.18/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset,type,
% 0.18/0.38 coindu1928975208n_lset:
% 0.18/0.38 !>[A: $tType] : ( ( set @ A ) > ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.18/0.38 coindu268472904append:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.18/0.38 coindu1213758845finite:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.18/0.38 coindu1121789889_LCons:
% 0.18/0.38 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.18/0.38 coindu1598213697e_LNil:
% 0.18/0.38 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 0.18/0.38 coindu882539134_llist:
% 0.18/0.38 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist,type,
% 0.18/0.38 coindu1244876290_llist:
% 0.18/0.38 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coindu1593790203_llist @ A ) ) > ( C > C ) > C > ( coindu1593790203_llist @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.18/0.38 coindu1046438764le_lhd:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 0.18/0.38 coindu987187967t_all2:
% 0.18/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.18/0.38 coindu335574135_lnull:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 0.18/0.38 coindu1112613586e_lset:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.18/0.38 coindu1047225960le_ltl:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.18/0.38 coindu567634248member:
% 0.18/0.38 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.18/0.38 coindu1696667936prefix:
% 0.18/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.18/0.38 coindu1599971794_llist:
% 0.18/0.38 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_If,type,
% 0.18/0.38 if:
% 0.18/0.38 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.18/0.38 sup_sup:
% 0.18/0.38 !>[A: $tType] : ( A > A > A ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.18/0.38 ord_less_eq:
% 0.18/0.38 !>[A: $tType] : ( A > A > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Product__Type_OPair,type,
% 0.18/0.38 product_Pair:
% 0.18/0.38 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.18/0.38 produc2004651681e_prod:
% 0.18/0.38 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.18/0.38 product_rec_prod:
% 0.18/0.38 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Pure_Otype,type,
% 0.18/0.38 type2:
% 0.18/0.38 !>[A: $tType] : ( itself @ A ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_Set_OCollect,type,
% 0.18/0.38 collect:
% 0.18/0.38 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_c_member,type,
% 0.18/0.38 member:
% 0.18/0.38 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.18/0.38
% 0.18/0.38 thf(sy_v_xs,type,
% 0.18/0.38 xs: coindu1593790203_llist @ a ).
% 0.18/0.38
% 0.18/0.38 thf(sy_v_ys,type,
% 0.18/0.38 ys: coindu1593790203_llist @ a ).
% 0.18/0.38
% 0.18/0.38 thf(sy_v_zs,type,
% 0.18/0.38 zs: coindu1593790203_llist @ a ).
% 0.18/0.38
% 0.18/0.38 %----Relevant facts (255)
% 0.18/0.38 thf(fact_0_lprefix__refl,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_refl
% 0.18/0.38 thf(fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062,axiom,
% 0.18/0.38 ( ( coindu1213758845finite @ a @ xs )
% 0.18/0.38 => ( coindu1696667936prefix @ a @ ys @ zs ) ) ).
% 0.18/0.38
% 0.18/0.38 % \<open>lfinite xs \<longrightarrow> ys \<sqsubseteq> zs\<close>
% 0.18/0.38 thf(fact_2_lappend__assoc,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.18/0.38 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_assoc
% 0.18/0.38 thf(fact_3_lprefix__trans,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_trans
% 0.18/0.38 thf(fact_4_lprefix__antisym,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.18/0.38 => ( Xs = Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_antisym
% 0.18/0.38 thf(fact_5_lprefix__lappend,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_lappend
% 0.18/0.38 thf(fact_6_lprefix__down__linear,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.18/0.38 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.18/0.38 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_down_linear
% 0.18/0.38 thf(fact_7_lprefix__lappend__sameI,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_lappend_sameI
% 0.18/0.38 thf(fact_8_lfinite__lappend,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_lappend
% 0.18/0.38 thf(fact_9_lappend__code_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.18/0.38 = Ys ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_code(1)
% 0.18/0.38 thf(fact_10_lprefix__code_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_code(1)
% 0.18/0.38 thf(fact_11_lappend__LNil2,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = Xs ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_LNil2
% 0.18/0.38 thf(fact_12_lappend__inf,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.18/0.38 = Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_inf
% 0.18/0.38 thf(fact_13_not__lfinite__lprefix__conv__eq,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 = ( Xs = Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % not_lfinite_lprefix_conv_eq
% 0.18/0.38 thf(fact_14_lappend__code_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_code(2)
% 0.18/0.38 thf(fact_15_LCons__lprefix__LCons,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.18/0.38 = ( ( X = Y )
% 0.18/0.38 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % LCons_lprefix_LCons
% 0.18/0.38 thf(fact_16_lappend_Odisc__iff_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.18/0.38 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend.disc_iff(2)
% 0.18/0.38 thf(fact_17_lnull__lappend,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lnull_lappend
% 0.18/0.38 thf(fact_18_lappend__LNil__LNil,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_LNil_LNil
% 0.18/0.38 thf(fact_19_LNil__eq__lappend__iff,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu1598213697e_LNil @ A )
% 0.18/0.38 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( ( Xs
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 & ( Ys
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % LNil_eq_lappend_iff
% 0.18/0.38 thf(fact_20_llist_Oinject,axiom,
% 0.18/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.18/0.38 = ( ( X21 = Y21 )
% 0.18/0.38 & ( X22 = Y22 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.inject
% 0.18/0.38 thf(fact_21_lfinite__code_I2_J,axiom,
% 0.18/0.38 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.18/0.38 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.18/0.38 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_code(2)
% 0.18/0.38 thf(fact_22_lfinite__LCons,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.18/0.38 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_LCons
% 0.18/0.38 thf(fact_23_lfinite__code_I1_J,axiom,
% 0.18/0.38 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_code(1)
% 0.18/0.38 thf(fact_24_lprefix__LNil,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_LNil
% 0.18/0.38 thf(fact_25_llist_Odisc_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.18/0.38 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.disc(2)
% 0.18/0.38 thf(fact_26_llist_Odisc_I1_J,axiom,
% 0.18/0.38 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.disc(1)
% 0.18/0.38 thf(fact_27_llist_OdiscI_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Llist
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.18/0.38 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.discI(2)
% 0.18/0.38 thf(fact_28_llist_OdiscI_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Llist
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.discI(1)
% 0.18/0.38 thf(fact_29_llist_Ocollapse_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Llist )
% 0.18/0.38 => ( Llist
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.collapse(1)
% 0.18/0.38 thf(fact_30_llist_Odistinct_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1598213697e_LNil @ A )
% 0.18/0.38 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.distinct(1)
% 0.18/0.38 thf(fact_31_lfinite_Ocases,axiom,
% 0.18/0.38 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ A2 )
% 0.18/0.38 => ( ( A2
% 0.18/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ? [X2: A] :
% 0.18/0.38 ( A2
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.18/0.38 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite.cases
% 0.18/0.38 thf(fact_32_lfinite_Osimps,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( coindu1213758845finite @ A )
% 0.18/0.38 = ( ^ [A3: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( A3
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 | ? [Xs3: coindu1593790203_llist @ A,X3: A] :
% 0.18/0.38 ( ( A3
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.18/0.38 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite.simps
% 0.18/0.38 thf(fact_33_llist_Oexhaust,axiom,
% 0.18/0.38 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Y
% 0.18/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.exhaust
% 0.18/0.38 thf(fact_34_neq__LNil__conv,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs
% 0.18/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = ( ? [X3: A,Xs4: coindu1593790203_llist @ A] :
% 0.18/0.38 ( Xs
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % neq_LNil_conv
% 0.18/0.38 thf(fact_35_not__lnull__conv,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.18/0.38 = ( ? [X3: A,Xs4: coindu1593790203_llist @ A] :
% 0.18/0.38 ( Xs
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % not_lnull_conv
% 0.18/0.38 thf(fact_36_lappend_Oexhaust,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend.exhaust
% 0.18/0.38 thf(fact_37_lfinite_Oinducts,axiom,
% 0.18/0.38 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ X )
% 0.18/0.38 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.18/0.38 => ( ( P @ Xs2 )
% 0.18/0.38 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.18/0.38 => ( P @ X ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite.inducts
% 0.18/0.38 thf(fact_38_lnull__def,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A )
% 0.18/0.38 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( Llist2
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lnull_def
% 0.18/0.38 thf(fact_39_lnull__imp__lfinite,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lnull_imp_lfinite
% 0.18/0.38 thf(fact_40_lfinite__LNil,axiom,
% 0.18/0.38 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_LNil
% 0.18/0.38 thf(fact_41_lfinite__LConsI,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_LConsI
% 0.18/0.38 thf(fact_42_lappend_Octr_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.18/0.38 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend.ctr(1)
% 0.18/0.38 thf(fact_43_lappend__snocL1__conv__LCons2,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.18/0.38 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_snocL1_conv_LCons2
% 0.18/0.38 thf(fact_44_mem__Collect__eq,axiom,
% 0.18/0.38 ! [A: $tType,A2: A,P: A > $o] :
% 0.18/0.38 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.18/0.38 = ( P @ A2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % mem_Collect_eq
% 0.18/0.38 thf(fact_45_Collect__mem__eq,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A] :
% 0.18/0.38 ( ( collect @ A
% 0.18/0.38 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.18/0.38 = A4 ) ).
% 0.18/0.38
% 0.18/0.38 % Collect_mem_eq
% 0.18/0.38 thf(fact_46_Collect__cong,axiom,
% 0.18/0.38 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.18/0.38 ( ! [X2: A] :
% 0.18/0.38 ( ( P @ X2 )
% 0.18/0.38 = ( Q @ X2 ) )
% 0.18/0.38 => ( ( collect @ A @ P )
% 0.18/0.38 = ( collect @ A @ Q ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Collect_cong
% 0.18/0.38 thf(fact_47_ext,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.18/0.38 ( ! [X2: A] :
% 0.18/0.38 ( ( F @ X2 )
% 0.18/0.38 = ( G @ X2 ) )
% 0.18/0.38 => ( F = G ) ) ).
% 0.18/0.38
% 0.18/0.38 % ext
% 0.18/0.38 thf(fact_48_lprefix__LCons__conv,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.18/0.38 = ( ( Xs
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 | ? [Xs4: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Y @ Xs4 ) )
% 0.18/0.38 & ( coindu1696667936prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_LCons_conv
% 0.18/0.38 thf(fact_49_lprefix_Ocoinduct,axiom,
% 0.18/0.38 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( X4 @ X @ Xa )
% 0.18/0.38 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( X4 @ X2 @ Xa2 )
% 0.18/0.38 => ( ? [Xs5: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( X2
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 & ( Xa2 = Xs5 ) )
% 0.18/0.38 | ? [Xs5: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,Xb: A] :
% 0.18/0.38 ( ( X2
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 0.18/0.38 & ( Xa2
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Xb @ Ys2 ) )
% 0.18/0.38 & ( ( X4 @ Xs5 @ Ys2 )
% 0.18/0.38 | ( coindu1696667936prefix @ A @ Xs5 @ Ys2 ) ) ) ) )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix.coinduct
% 0.18/0.38 thf(fact_50_lprefix_Osimps,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A )
% 0.18/0.38 = ( ^ [A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( A1
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 & ( A22 = Xs3 ) )
% 0.18/0.38 | ? [Xs3: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X3: A] :
% 0.18/0.38 ( ( A1
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.18/0.38 & ( A22
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Ys3 ) )
% 0.18/0.38 & ( coindu1696667936prefix @ A @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix.simps
% 0.18/0.38 thf(fact_51_lprefix_Ocases,axiom,
% 0.18/0.38 ! [A: $tType,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ A12 @ A23 )
% 0.18/0.38 => ( ( ( A12
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ! [Xs2: coindu1593790203_llist @ A] : ( A23 != Xs2 ) )
% 0.18/0.38 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X2: A] :
% 0.18/0.38 ( ( A12
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.18/0.38 => ( ( A23
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Ys4 ) )
% 0.18/0.38 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys4 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix.cases
% 0.18/0.38 thf(fact_52_lprefix__code_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_code(2)
% 0.18/0.38 thf(fact_53_lprefix__not__lnullD,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_not_lnullD
% 0.18/0.38 thf(fact_54_lprefix__lnullD,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.18/0.38 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_lnullD
% 0.18/0.38 thf(fact_55_lappend__lnull2,axiom,
% 0.18/0.38 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Ys )
% 0.18/0.38 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.18/0.38 = Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_lnull2
% 0.18/0.38 thf(fact_56_lappend__lnull1,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.18/0.38 = Ys ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_lnull1
% 0.18/0.38 thf(fact_57_lprefix__lnull,axiom,
% 0.18/0.38 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Ys )
% 0.18/0.38 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_lnull
% 0.18/0.38 thf(fact_58_lnull__lprefix,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.18/0.38
% 0.18/0.38 % lnull_lprefix
% 0.18/0.38 thf(fact_59_lappend_Odisc_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.18/0.38 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend.disc(1)
% 0.18/0.38 thf(fact_60_lappend_Odisc_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.18/0.38 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend.disc(2)
% 0.18/0.38 thf(fact_61_LCons__lprefix__conv,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.18/0.38 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Ys
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X @ Ys5 ) )
% 0.18/0.38 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % LCons_lprefix_conv
% 0.18/0.38 thf(fact_62_Le__LCons,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Le_LCons
% 0.18/0.38 thf(fact_63_LNil__lprefix,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.18/0.38
% 0.18/0.38 % LNil_lprefix
% 0.18/0.38 thf(fact_64_lappend__eq__LNil__iff,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = ( ( Xs
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 & ( Ys
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_eq_LNil_iff
% 0.18/0.38 thf(fact_65_lmember__code_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,X: A] :
% 0.18/0.38 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % lmember_code(1)
% 0.18/0.38 thf(fact_66_lmember__code_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.18/0.38 = ( ( X = Y )
% 0.18/0.38 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lmember_code(2)
% 0.18/0.38 thf(fact_67_lprefixI,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 0.18/0.38 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs2 @ Ys4 ) @ X4 )
% 0.18/0.38 => ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.18/0.38 | ? [X5: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs2
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X5 @ Xs6 ) )
% 0.18/0.38 & ( Ys4
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X5 @ Ys6 ) )
% 0.18/0.38 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 0.18/0.38 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefixI
% 0.18/0.38 thf(fact_68_split__llist,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ? [Ys4: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs
% 0.18/0.38 = ( coindu268472904append @ A @ Ys4 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 0.18/0.38 & ( coindu1213758845finite @ A @ Ys4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % split_llist
% 0.18/0.38 thf(fact_69_split__llist__first,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ? [Ys4: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs
% 0.18/0.38 = ( coindu268472904append @ A @ Ys4 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 0.18/0.38 & ( coindu1213758845finite @ A @ Ys4 )
% 0.18/0.38 & ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys4 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % split_llist_first
% 0.18/0.38 thf(fact_70_lhd__lappend,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 0.18/0.38 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lhd_lappend
% 0.18/0.38 thf(fact_71_gen__lset__code_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A] :
% 0.18/0.38 ( ( coindu1928975208n_lset @ A @ A4 @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = A4 ) ).
% 0.18/0.38
% 0.18/0.38 % gen_lset_code(1)
% 0.18/0.38 thf(fact_72_llist_Ocorec__code,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType] :
% 0.18/0.38 ( ( coindu1244876290_llist @ C @ A )
% 0.18/0.38 = ( ^ [P2: C > $o,G21: C > A,Q22: C > $o,G221: C > ( coindu1593790203_llist @ A ),G222: C > C,A3: C] : ( if @ ( coindu1593790203_llist @ A ) @ ( P2 @ A3 ) @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ A @ ( G21 @ A3 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_code
% 0.18/0.38 thf(fact_73_unfold__llist_Ocode,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType] :
% 0.18/0.38 ( ( coindu1599971794_llist @ A @ B )
% 0.18/0.38 = ( ^ [P2: A > $o,G21: A > B,G22: A > A,A3: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P2 @ A3 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G21 @ A3 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.code
% 0.18/0.38 thf(fact_74_ltl__lappend,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 0.18/0.38 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % ltl_lappend
% 0.18/0.38 thf(fact_75_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,G212: A > B,G223: A > A,A2: A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) )
% 0.18/0.38 = ( P3 @ A2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.disc_iff(1)
% 0.18/0.38 thf(fact_76_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,G212: A > B,G223: A > A,A2: A] :
% 0.18/0.38 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) ) )
% 0.18/0.38 = ( ~ ( P3 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.disc_iff(2)
% 0.18/0.38 thf(fact_77_lfinite__ltl,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.18/0.38 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_ltl
% 0.18/0.38 thf(fact_78_unfold__llist__eq__LCons,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.18/0.38 = ( ~ ( IS_LNIL @ B2 )
% 0.18/0.38 & ( X
% 0.18/0.38 = ( LHD @ B2 ) )
% 0.18/0.38 & ( Xs
% 0.18/0.38 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist_eq_LCons
% 0.18/0.38 thf(fact_79_llist_Ocorec__disc__iff_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C,A2: C] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.18/0.38 = ( P3 @ A2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_disc_iff(1)
% 0.18/0.38 thf(fact_80_llist_Ocorec__disc__iff_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C,A2: C] :
% 0.18/0.38 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) )
% 0.18/0.38 = ( ~ ( P3 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_disc_iff(2)
% 0.18/0.38 thf(fact_81_unfold__llist__id,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 0.18/0.38 = Xs ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist_id
% 0.18/0.38 thf(fact_82_lhd__LCons__ltl,axiom,
% 0.18/0.38 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.18/0.38 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 0.18/0.38 = Llist ) ) ).
% 0.18/0.38
% 0.18/0.38 % lhd_LCons_ltl
% 0.18/0.38 thf(fact_83_llist__set__induct,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.18/0.38 => ( P @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ Xs2 ) )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A,Y2: A] :
% 0.18/0.38 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.18/0.38 => ( ( member @ A @ Y2 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.18/0.38 => ( ( P @ Y2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.18/0.38 => ( P @ Y2 @ Xs2 ) ) ) )
% 0.18/0.38 => ( P @ X @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist_set_induct
% 0.18/0.38 thf(fact_84_lset__lmember,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 = ( coindu567634248member @ A @ X @ Xs ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_lmember
% 0.18/0.38 thf(fact_85_in__lset__ltlD,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) )
% 0.18/0.38 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % in_lset_ltlD
% 0.18/0.38 thf(fact_86_unfold__llist_Osimps_I3_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) )
% 0.18/0.38 = ( G212 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.simps(3)
% 0.18/0.38 thf(fact_87_unfold__llist_Osimps_I4_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) )
% 0.18/0.38 = ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.simps(4)
% 0.18/0.38 thf(fact_88_llist_Ocorec__sel_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1046438764le_lhd @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.18/0.38 = ( G212 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_sel(1)
% 0.18/0.38 thf(fact_89_llist_Ocorec__sel_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,A2: C,Q222: C > $o,G212: C > A,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ( ( ( Q222 @ A2 )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.18/0.38 = ( G2212 @ A2 ) ) )
% 0.18/0.38 & ( ~ ( Q222 @ A2 )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 0.18/0.38 = ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_sel(2)
% 0.18/0.38 thf(fact_90_llist_Oset__sel_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,A2: coindu1593790203_llist @ A,X: A] :
% 0.18/0.38 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.18/0.38 => ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ A2 ) ) )
% 0.18/0.38 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.set_sel(2)
% 0.18/0.38 thf(fact_91_llist_Oset__sel_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.18/0.38 => ( member @ A @ ( coindu1046438764le_lhd @ A @ A2 ) @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.set_sel(1)
% 0.18/0.38 thf(fact_92_llist_Ocoinduct__strong,axiom,
% 0.18/0.38 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( R @ Llist @ Llist3 )
% 0.18/0.38 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( R @ Llist4 @ Llist5 )
% 0.18/0.38 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.18/0.38 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.18/0.38 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.18/0.38 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.18/0.38 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) )
% 0.18/0.38 | ( ( coindu1047225960le_ltl @ A @ Llist4 )
% 0.18/0.38 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 0.18/0.38 => ( Llist = Llist3 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.coinduct_strong
% 0.18/0.38 thf(fact_93_llist_Ocoinduct,axiom,
% 0.18/0.38 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( R @ Llist @ Llist3 )
% 0.18/0.38 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( R @ Llist4 @ Llist5 )
% 0.18/0.38 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.18/0.38 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.18/0.38 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.18/0.38 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.18/0.38 & ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 0.18/0.38 => ( Llist = Llist3 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.coinduct
% 0.18/0.38 thf(fact_94_llist_Oexpand,axiom,
% 0.18/0.38 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu335574135_lnull @ A @ Llist )
% 0.18/0.38 = ( coindu335574135_lnull @ A @ Llist3 ) )
% 0.18/0.38 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.18/0.38 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Llist3 ) )
% 0.18/0.38 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 0.18/0.38 = ( coindu1047225960le_ltl @ A @ Llist3 ) ) ) ) )
% 0.18/0.38 => ( Llist = Llist3 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.expand
% 0.18/0.38 thf(fact_95_ltl__unfold__llist,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.18/0.38 ( ( ( IS_LNIL @ A2 )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) )
% 0.18/0.38 & ( ~ ( IS_LNIL @ A2 )
% 0.18/0.38 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.18/0.38 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % ltl_unfold_llist
% 0.18/0.38 thf(fact_96_llist_Oexhaust__sel,axiom,
% 0.18/0.38 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Llist
% 0.18/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ( Llist
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.exhaust_sel
% 0.18/0.38 thf(fact_97_eq__LConsD,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.18/0.38 => ( ( Xs
% 0.18/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.18/0.38 = Y )
% 0.18/0.38 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 0.18/0.38 = Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % eq_LConsD
% 0.18/0.38 thf(fact_98_lprefix__coinduct,axiom,
% 0.18/0.38 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( P @ Xs @ Ys )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( P @ Xs2 @ Ys4 )
% 0.18/0.38 => ( ( ( coindu335574135_lnull @ A @ Ys4 )
% 0.18/0.38 => ( coindu335574135_lnull @ A @ Xs2 ) )
% 0.18/0.38 & ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Ys4 )
% 0.18/0.38 => ( ( ( coindu1046438764le_lhd @ A @ Xs2 )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Ys4 ) )
% 0.18/0.38 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys4 ) )
% 0.18/0.38 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys4 ) ) ) ) ) ) ) )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_coinduct
% 0.18/0.38 thf(fact_99_lprefix__expand,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.18/0.38 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.18/0.38 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_expand
% 0.18/0.38 thf(fact_100_llist_Oset__induct,axiom,
% 0.18/0.38 ! [A: $tType,X: A,A2: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.18/0.38 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.18/0.38 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A,Xa2: A] :
% 0.18/0.38 ( ( member @ A @ Xa2 @ ( coindu1112613586e_lset @ A @ Z2 ) )
% 0.18/0.38 => ( ( P @ Xa2 @ Z2 )
% 0.18/0.38 => ( P @ Xa2 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) ) ) )
% 0.18/0.38 => ( P @ X @ A2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.set_induct
% 0.18/0.38 thf(fact_101_llist_Oset__cases,axiom,
% 0.18/0.38 ! [A: $tType,E: A,A2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.18/0.38 => ( ! [Z2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( A2
% 0.18/0.38 != ( coindu1121789889_LCons @ A @ E @ Z2 ) )
% 0.18/0.38 => ~ ! [Z1: A,Z2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( A2
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.18/0.38 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z2 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.set_cases
% 0.18/0.38 thf(fact_102_lset__induct_H,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.18/0.38 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.18/0.38 => ( ( P @ Xs2 )
% 0.18/0.38 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) )
% 0.18/0.38 => ( P @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_induct'
% 0.18/0.38 thf(fact_103_lset__induct,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.18/0.38 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.18/0.38 => ( ( X != X6 )
% 0.18/0.38 => ( ( P @ Xs2 )
% 0.18/0.38 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) ) )
% 0.18/0.38 => ( P @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_induct
% 0.18/0.38 thf(fact_104_lset__cases,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ( ! [Xs7: coindu1593790203_llist @ A] :
% 0.18/0.38 ( Xs
% 0.18/0.38 != ( coindu1121789889_LCons @ A @ X @ Xs7 ) )
% 0.18/0.38 => ~ ! [X6: A,Xs7: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( Xs
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ X6 @ Xs7 ) )
% 0.18/0.38 => ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs7 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_cases
% 0.18/0.38 thf(fact_105_llist_Oset__intros_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,A12: A,A23: coindu1593790203_llist @ A] : ( member @ A @ A12 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A12 @ A23 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.set_intros(1)
% 0.18/0.38 thf(fact_106_llist_Oset__intros_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,X: A,A23: coindu1593790203_llist @ A,A12: A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A23 ) )
% 0.18/0.38 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A12 @ A23 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.set_intros(2)
% 0.18/0.38 thf(fact_107_lset__intros_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_intros(1)
% 0.18/0.38 thf(fact_108_lset__intros_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,X7: A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X7 @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_intros(2)
% 0.18/0.38 thf(fact_109_lnull__ltlI,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lnull_ltlI
% 0.18/0.38 thf(fact_110_ltl__simps_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.18/0.38 = X22 ) ).
% 0.18/0.38
% 0.18/0.38 % ltl_simps(2)
% 0.18/0.38 thf(fact_111_ltl__simps_I1_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.18/0.38
% 0.18/0.38 % ltl_simps(1)
% 0.18/0.38 thf(fact_112_lprefix__ltlI,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_ltlI
% 0.18/0.38 thf(fact_113_lhd__LCons,axiom,
% 0.18/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.18/0.38 = X21 ) ).
% 0.18/0.38
% 0.18/0.38 % lhd_LCons
% 0.18/0.38 thf(fact_114_unfold__llist_Odisc_I1_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.18/0.38 ( ( P3 @ A2 )
% 0.18/0.38 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.disc(1)
% 0.18/0.38 thf(fact_115_unfold__llist_Odisc_I2_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.disc(2)
% 0.18/0.38 thf(fact_116_unfold__llist_Octr_I2_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 0.18/0.38 = ( coindu1121789889_LCons @ B @ ( G212 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.ctr(2)
% 0.18/0.38 thf(fact_117_unfold__llist_Octr_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.18/0.38 ( ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 0.18/0.38 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % unfold_llist.ctr(1)
% 0.18/0.38 thf(fact_118_llist_Ocorec__disc_I1_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 0.18/0.38 ( ( P3 @ A2 )
% 0.18/0.38 => ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_disc(1)
% 0.18/0.38 thf(fact_119_llist_Ocorec__disc_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec_disc(2)
% 0.18/0.38 thf(fact_120_llist_Ocorec_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 0.18/0.38 ( ~ ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ ( G212 @ A2 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec(2)
% 0.18/0.38 thf(fact_121_llist_Ocorec_I1_J,axiom,
% 0.18/0.38 ! [C: $tType,A: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 0.18/0.38 ( ( P3 @ A2 )
% 0.18/0.38 => ( ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.corec(1)
% 0.18/0.38 thf(fact_122_in__lset__lappend__iff,axiom,
% 0.18/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.18/0.38 = ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.18/0.38 | ( ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 & ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % in_lset_lappend_iff
% 0.18/0.38 thf(fact_123_lappend__ltl,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys )
% 0.18/0.38 = ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lappend_ltl
% 0.18/0.38 thf(fact_124_lfinite__induct,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.18/0.38 => ( P @ Xs2 ) )
% 0.18/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.18/0.38 => ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.18/0.38 => ( P @ Xs2 ) ) ) )
% 0.18/0.38 => ( P @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lfinite_induct
% 0.18/0.38 thf(fact_125_lprefix__lhdD,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.18/0.38 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.18/0.38 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lprefix_lhdD
% 0.18/0.38 thf(fact_126_old_Oprod_Oinject,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.18/0.38 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.18/0.38 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.18/0.38 = ( ( A2 = A5 )
% 0.18/0.38 & ( B2 = B3 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % old.prod.inject
% 0.18/0.38 thf(fact_127_prod_Oinject,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y23: B] :
% 0.18/0.38 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 0.18/0.38 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 0.18/0.38 = ( ( X1 = Y1 )
% 0.18/0.38 & ( X23 = Y23 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod.inject
% 0.18/0.38 thf(fact_128_llist_Osplit__sel__asm,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.18/0.38 = ( ~ ( ( ( Llist
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 & ~ ( P @ F1 ) )
% 0.18/0.38 | ( ( Llist
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.18/0.38 & ~ ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.split_sel_asm
% 0.18/0.38 thf(fact_129_llist_Osplit__sel,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.18/0.38 = ( ( ( Llist
% 0.18/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 => ( P @ F1 ) )
% 0.18/0.38 & ( ( Llist
% 0.18/0.38 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.18/0.38 => ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.split_sel
% 0.18/0.38 thf(fact_130_llist_Ocase__eq__if,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType] :
% 0.18/0.38 ( ( coindu882539134_llist @ B @ A )
% 0.18/0.38 = ( ^ [F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist2: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist2 ) @ F12 @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.case_eq_if
% 0.18/0.38 thf(fact_131_lset__lappend__lfinite,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_lappend_lfinite
% 0.18/0.38 thf(fact_132_llist_Osimps_I5_J,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.18/0.38 = ( F2 @ X21 @ X22 ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.simps(5)
% 0.18/0.38 thf(fact_133_llist_Osimps_I4_J,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B] :
% 0.18/0.38 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1598213697e_LNil @ A ) )
% 0.18/0.38 = F1 ) ).
% 0.18/0.38
% 0.18/0.38 % llist.simps(4)
% 0.18/0.38 thf(fact_134_gen__lset__def,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( coindu1928975208n_lset @ A )
% 0.18/0.38 = ( ^ [A6: set @ A,Xs3: coindu1593790203_llist @ A] : ( sup_sup @ ( set @ A ) @ A6 @ ( coindu1112613586e_lset @ A @ Xs3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % gen_lset_def
% 0.18/0.38 thf(fact_135_surj__pair,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.18/0.38 ? [X2: A,Y2: B] :
% 0.18/0.38 ( P3
% 0.18/0.38 = ( product_Pair @ A @ B @ X2 @ Y2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % surj_pair
% 0.18/0.38 thf(fact_136_prod__cases,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.18/0.38 ( ! [A7: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B4 ) )
% 0.18/0.38 => ( P @ P3 ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_cases
% 0.18/0.38 thf(fact_137_Pair__inject,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 0.18/0.38 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.18/0.38 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.18/0.38 => ~ ( ( A2 = A5 )
% 0.18/0.38 => ( B2 != B3 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Pair_inject
% 0.18/0.38 thf(fact_138_prod__cases3,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.18/0.38 ~ ! [A7: A,B4: B,C2: C] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_cases3
% 0.18/0.38 thf(fact_139_prod__cases4,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.18/0.38 ~ ! [A7: A,B4: B,C2: C,D2: D] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_cases4
% 0.18/0.38 thf(fact_140_prod__cases5,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 0.18/0.38 ~ ! [A7: A,B4: B,C2: C,D2: D,E3: E2] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_cases5
% 0.18/0.38 thf(fact_141_prod__cases6,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) )] :
% 0.18/0.38 ~ ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F3 ) @ D2 @ ( product_Pair @ E2 @ F3 @ E3 @ F4 ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_cases6
% 0.18/0.38 thf(fact_142_prod__cases7,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F3: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.18/0.38 ~ ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3,G3: G2] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F3 @ G2 ) @ E3 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_cases7
% 0.18/0.38 thf(fact_143_prod__induct3,axiom,
% 0.18/0.38 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.18/0.38 ( ! [A7: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 0.18/0.38 => ( P @ X ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_induct3
% 0.18/0.38 thf(fact_144_prod__induct4,axiom,
% 0.18/0.38 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.18/0.38 ( ! [A7: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.18/0.38 => ( P @ X ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_induct4
% 0.18/0.38 thf(fact_145_prod__induct5,axiom,
% 0.18/0.38 ! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 0.18/0.38 ( ! [A7: A,B4: B,C2: C,D2: D,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
% 0.18/0.38 => ( P @ X ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_induct5
% 0.18/0.38 thf(fact_146_prod__induct6,axiom,
% 0.18/0.38 ! [F3: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) )] :
% 0.18/0.38 ( ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F3 ) @ D2 @ ( product_Pair @ E2 @ F3 @ E3 @ F4 ) ) ) ) ) )
% 0.18/0.38 => ( P @ X ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_induct6
% 0.18/0.38 thf(fact_147_prod__induct7,axiom,
% 0.18/0.38 ! [G2: $tType,F3: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.18/0.38 ( ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F3 @ G2 ) @ E3 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) )
% 0.18/0.38 => ( P @ X ) ) ).
% 0.18/0.38
% 0.18/0.38 % prod_induct7
% 0.18/0.38 thf(fact_148_old_Oprod_Oexhaust,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.18/0.38 ~ ! [A7: A,B4: B] :
% 0.18/0.38 ( Y
% 0.18/0.38 != ( product_Pair @ A @ B @ A7 @ B4 ) ) ).
% 0.18/0.38
% 0.18/0.38 % old.prod.exhaust
% 0.18/0.38 thf(fact_149_old_Oprod_Oinducts,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.18/0.38 ( ! [A7: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B4 ) )
% 0.18/0.38 => ( P @ Prod ) ) ).
% 0.18/0.38
% 0.18/0.38 % old.prod.inducts
% 0.18/0.38 thf(fact_150_lset__lappend__conv,axiom,
% 0.18/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.18/0.38 ( ( ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) )
% 0.18/0.38 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.18/0.38 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.18/0.38 = ( coindu1112613586e_lset @ A @ Xs ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_lappend_conv
% 0.18/0.38 thf(fact_151_old_Oprod_Orec,axiom,
% 0.18/0.38 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.18/0.38 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.18/0.38 = ( F1 @ A2 @ B2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % old.prod.rec
% 0.18/0.38 thf(fact_152_UnCI,axiom,
% 0.18/0.38 ! [A: $tType,C3: A,B5: set @ A,A4: set @ A] :
% 0.18/0.38 ( ( ~ ( member @ A @ C3 @ B5 )
% 0.18/0.38 => ( member @ A @ C3 @ A4 ) )
% 0.18/0.38 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % UnCI
% 0.18/0.38 thf(fact_153_Un__iff,axiom,
% 0.18/0.38 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.18/0.38 = ( ( member @ A @ C3 @ A4 )
% 0.18/0.38 | ( member @ A @ C3 @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_iff
% 0.18/0.38 thf(fact_154_sup__apply,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.18/0.38 => ( ( sup_sup @ ( A > B ) )
% 0.18/0.38 = ( ^ [F5: A > B,G4: A > B,X3: A] : ( sup_sup @ B @ ( F5 @ X3 ) @ ( G4 @ X3 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_apply
% 0.18/0.38 thf(fact_155_sup_Oright__idem,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A] :
% 0.18/0.38 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 0.18/0.38 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.right_idem
% 0.18/0.38 thf(fact_156_sup__left__idem,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A] :
% 0.18/0.38 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.18/0.38 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_left_idem
% 0.18/0.38 thf(fact_157_sup_Oleft__idem,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A] :
% 0.18/0.38 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 0.18/0.38 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.left_idem
% 0.18/0.38 thf(fact_158_sup__idem,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A] :
% 0.18/0.38 ( ( sup_sup @ A @ X @ X )
% 0.18/0.38 = X ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_idem
% 0.18/0.38 thf(fact_159_sup_Oidem,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A] :
% 0.18/0.38 ( ( sup_sup @ A @ A2 @ A2 )
% 0.18/0.38 = A2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.idem
% 0.18/0.38 thf(fact_160_sup__left__commute,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A,Z: A] :
% 0.18/0.38 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.18/0.38 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_left_commute
% 0.18/0.38 thf(fact_161_sup_Oleft__commute,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,A2: A,C3: A] :
% 0.18/0.38 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A2 @ C3 ) )
% 0.18/0.38 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.left_commute
% 0.18/0.38 thf(fact_162_sup__commute,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( sup_sup @ A )
% 0.18/0.38 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_commute
% 0.18/0.38 thf(fact_163_sup_Ocommute,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( sup_sup @ A )
% 0.18/0.38 = ( ^ [A3: A,B6: A] : ( sup_sup @ A @ B6 @ A3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.commute
% 0.18/0.38 thf(fact_164_sup__assoc,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A,Z: A] :
% 0.18/0.38 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.18/0.38 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_assoc
% 0.18/0.38 thf(fact_165_sup_Oassoc,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A,C3: A] :
% 0.18/0.38 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ C3 )
% 0.18/0.38 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.assoc
% 0.18/0.38 thf(fact_166_sup__fun__def,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.18/0.38 => ( ( sup_sup @ ( A > B ) )
% 0.18/0.38 = ( ^ [F5: A > B,G4: A > B,X3: A] : ( sup_sup @ B @ ( F5 @ X3 ) @ ( G4 @ X3 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_fun_def
% 0.18/0.38 thf(fact_167_inf__sup__aci_I5_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( lattice @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( sup_sup @ A )
% 0.18/0.38 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % inf_sup_aci(5)
% 0.18/0.38 thf(fact_168_inf__sup__aci_I6_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( lattice @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A,Z: A] :
% 0.18/0.38 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.18/0.38 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % inf_sup_aci(6)
% 0.18/0.38 thf(fact_169_inf__sup__aci_I7_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( lattice @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A,Z: A] :
% 0.18/0.38 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.18/0.38 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % inf_sup_aci(7)
% 0.18/0.38 thf(fact_170_inf__sup__aci_I8_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( lattice @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A] :
% 0.18/0.38 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.18/0.38 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % inf_sup_aci(8)
% 0.18/0.38 thf(fact_171_Un__left__commute,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 0.18/0.38 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C4 ) )
% 0.18/0.38 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_left_commute
% 0.18/0.38 thf(fact_172_Un__left__absorb,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.18/0.38 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_left_absorb
% 0.18/0.38 thf(fact_173_Un__commute,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( sup_sup @ ( set @ A ) )
% 0.18/0.38 = ( ^ [A6: set @ A,B7: set @ A] : ( sup_sup @ ( set @ A ) @ B7 @ A6 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_commute
% 0.18/0.38 thf(fact_174_Un__absorb,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A] :
% 0.18/0.38 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 0.18/0.38 = A4 ) ).
% 0.18/0.38
% 0.18/0.38 % Un_absorb
% 0.18/0.38 thf(fact_175_Un__assoc,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 0.18/0.38 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C4 )
% 0.18/0.38 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_assoc
% 0.18/0.38 thf(fact_176_ball__Un,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 0.18/0.38 ( ( ! [X3: A] :
% 0.18/0.38 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.18/0.38 => ( P @ X3 ) ) )
% 0.18/0.38 = ( ! [X3: A] :
% 0.18/0.38 ( ( member @ A @ X3 @ A4 )
% 0.18/0.38 => ( P @ X3 ) )
% 0.18/0.38 & ! [X3: A] :
% 0.18/0.38 ( ( member @ A @ X3 @ B5 )
% 0.18/0.38 => ( P @ X3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % ball_Un
% 0.18/0.38 thf(fact_177_bex__Un,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 0.18/0.38 ( ( ? [X3: A] :
% 0.18/0.38 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.18/0.38 & ( P @ X3 ) ) )
% 0.18/0.38 = ( ? [X3: A] :
% 0.18/0.38 ( ( member @ A @ X3 @ A4 )
% 0.18/0.38 & ( P @ X3 ) )
% 0.18/0.38 | ? [X3: A] :
% 0.18/0.38 ( ( member @ A @ X3 @ B5 )
% 0.18/0.38 & ( P @ X3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % bex_Un
% 0.18/0.38 thf(fact_178_UnI2,axiom,
% 0.18/0.38 ! [A: $tType,C3: A,B5: set @ A,A4: set @ A] :
% 0.18/0.38 ( ( member @ A @ C3 @ B5 )
% 0.18/0.38 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % UnI2
% 0.18/0.38 thf(fact_179_UnI1,axiom,
% 0.18/0.38 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( member @ A @ C3 @ A4 )
% 0.18/0.38 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % UnI1
% 0.18/0.38 thf(fact_180_UnE,axiom,
% 0.18/0.38 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 0.18/0.38 => ( ~ ( member @ A @ C3 @ A4 )
% 0.18/0.38 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % UnE
% 0.18/0.38 thf(fact_181_internal__case__prod__conv,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.18/0.38 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.18/0.38 = ( C3 @ A2 @ B2 ) ) ).
% 0.18/0.38
% 0.18/0.38 % internal_case_prod_conv
% 0.18/0.38 thf(fact_182_lset__lappend,axiom,
% 0.18/0.38 ! [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 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % lset_lappend
% 0.18/0.38 thf(fact_183_llist_Orel__sel,axiom,
% 0.18/0.38 ! [B: $tType,A: $tType] :
% 0.18/0.38 ( ( coindu987187967t_all2 @ A @ B )
% 0.18/0.38 = ( ^ [R2: A > B > $o,A3: coindu1593790203_llist @ A,B6: coindu1593790203_llist @ B] :
% 0.18/0.38 ( ( ( coindu335574135_lnull @ A @ A3 )
% 0.18/0.38 = ( coindu335574135_lnull @ B @ B6 ) )
% 0.18/0.38 & ( ~ ( coindu335574135_lnull @ A @ A3 )
% 0.18/0.38 => ( ~ ( coindu335574135_lnull @ B @ B6 )
% 0.18/0.38 => ( ( R2 @ ( coindu1046438764le_lhd @ A @ A3 ) @ ( coindu1046438764le_lhd @ B @ B6 ) )
% 0.18/0.38 & ( coindu987187967t_all2 @ A @ B @ R2 @ ( coindu1047225960le_ltl @ A @ A3 ) @ ( coindu1047225960le_ltl @ B @ B6 ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.rel_sel
% 0.18/0.38 thf(fact_184_subset__antisym,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.18/0.38 => ( A4 = B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % subset_antisym
% 0.18/0.38 thf(fact_185_subsetI,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ! [X2: A] :
% 0.18/0.38 ( ( member @ A @ X2 @ A4 )
% 0.18/0.38 => ( member @ A @ X2 @ B5 ) )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.18/0.38
% 0.18/0.38 % subsetI
% 0.18/0.38 thf(fact_186_le__sup__iff,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A,Z: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.18/0.38 = ( ( ord_less_eq @ A @ X @ Z )
% 0.18/0.38 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % le_sup_iff
% 0.18/0.38 thf(fact_187_sup_Obounded__iff,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,C3: A,A2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C3 ) @ A2 )
% 0.18/0.38 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.18/0.38 & ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.bounded_iff
% 0.18/0.38 thf(fact_188_Un__subset__iff,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C4 )
% 0.18/0.38 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C4 )
% 0.18/0.38 & ( ord_less_eq @ ( set @ A ) @ B5 @ C4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_subset_iff
% 0.18/0.38 thf(fact_189_llist_Orel__inject_I2_J,axiom,
% 0.18/0.38 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.18/0.38 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 0.18/0.38 = ( ( R @ X21 @ Y21 )
% 0.18/0.38 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % llist.rel_inject(2)
% 0.18/0.38 thf(fact_190_inf__sup__ord_I4_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( lattice @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % inf_sup_ord(4)
% 0.18/0.38 thf(fact_191_inf__sup__ord_I3_J,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( lattice @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % inf_sup_ord(3)
% 0.18/0.38 thf(fact_192_Un__mono,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,C4: set @ A,B5: set @ A,D3: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C4 )
% 0.18/0.38 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ D3 )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_mono
% 0.18/0.38 thf(fact_193_Un__least,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,C4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C4 )
% 0.18/0.38 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_least
% 0.18/0.38 thf(fact_194_Un__upper1,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_upper1
% 0.18/0.38 thf(fact_195_Un__upper2,axiom,
% 0.18/0.38 ! [A: $tType,B5: set @ A,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_upper2
% 0.18/0.38 thf(fact_196_Un__absorb1,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 => ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 = B5 ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_absorb1
% 0.18/0.38 thf(fact_197_Un__absorb2,axiom,
% 0.18/0.38 ! [A: $tType,B5: set @ A,A4: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.18/0.38 => ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 = A4 ) ) ).
% 0.18/0.38
% 0.18/0.38 % Un_absorb2
% 0.18/0.38 thf(fact_198_subset__Un__eq,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) )
% 0.18/0.38 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.18/0.38 ( ( sup_sup @ ( set @ A ) @ A6 @ B7 )
% 0.18/0.38 = B7 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % subset_Un_eq
% 0.18/0.38 thf(fact_199_le__supE,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A,X: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X )
% 0.18/0.38 => ~ ( ( ord_less_eq @ A @ A2 @ X )
% 0.18/0.38 => ~ ( ord_less_eq @ A @ B2 @ X ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % le_supE
% 0.18/0.38 thf(fact_200_le__supI,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,X: A,B2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ A2 @ X )
% 0.18/0.38 => ( ( ord_less_eq @ A @ B2 @ X )
% 0.18/0.38 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % le_supI
% 0.18/0.38 thf(fact_201_sup__ge1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_ge1
% 0.18/0.38 thf(fact_202_sup__ge2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_ge2
% 0.18/0.38 thf(fact_203_le__supI1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,A2: A,B2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ X @ A2 )
% 0.18/0.38 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % le_supI1
% 0.18/0.38 thf(fact_204_le__supI2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,B2: A,A2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ X @ B2 )
% 0.18/0.38 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % le_supI2
% 0.18/0.38 thf(fact_205_sup_Omono,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [C3: A,A2: A,D4: A,B2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ C3 @ A2 )
% 0.18/0.38 => ( ( ord_less_eq @ A @ D4 @ B2 )
% 0.18/0.38 => ( ord_less_eq @ A @ ( sup_sup @ A @ C3 @ D4 ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.mono
% 0.18/0.38 thf(fact_206_sup__mono,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,C3: A,B2: A,D4: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ A2 @ C3 )
% 0.18/0.38 => ( ( ord_less_eq @ A @ B2 @ D4 )
% 0.18/0.38 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C3 @ D4 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_mono
% 0.18/0.38 thf(fact_207_sup__least,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [Y: A,X: A,Z: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ Y @ X )
% 0.18/0.38 => ( ( ord_less_eq @ A @ Z @ X )
% 0.18/0.38 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_least
% 0.18/0.38 thf(fact_208_le__iff__sup,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( ord_less_eq @ A )
% 0.18/0.38 = ( ^ [X3: A,Y3: A] :
% 0.18/0.38 ( ( sup_sup @ A @ X3 @ Y3 )
% 0.18/0.38 = Y3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % le_iff_sup
% 0.18/0.38 thf(fact_209_sup_OorderE,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,A2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.18/0.38 => ( A2
% 0.18/0.38 = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.orderE
% 0.18/0.38 thf(fact_210_sup_OorderI,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A] :
% 0.18/0.38 ( ( A2
% 0.18/0.38 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.18/0.38 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.orderI
% 0.18/0.38 thf(fact_211_sup__unique,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [F: A > A > A,X: A,Y: A] :
% 0.18/0.38 ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y2 ) )
% 0.18/0.38 => ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ Y2 @ ( F @ X2 @ Y2 ) )
% 0.18/0.38 => ( ! [X2: A,Y2: A,Z3: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 0.18/0.38 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.18/0.38 => ( ord_less_eq @ A @ ( F @ Y2 @ Z3 ) @ X2 ) ) )
% 0.18/0.38 => ( ( sup_sup @ A @ X @ Y )
% 0.18/0.38 = ( F @ X @ Y ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_unique
% 0.18/0.38 thf(fact_212_sup_Oabsorb1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,A2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.18/0.38 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.18/0.38 = A2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.absorb1
% 0.18/0.38 thf(fact_213_sup_Oabsorb2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.18/0.38 => ( ( sup_sup @ A @ A2 @ B2 )
% 0.18/0.38 = B2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.absorb2
% 0.18/0.38 thf(fact_214_sup__absorb1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [Y: A,X: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ Y @ X )
% 0.18/0.38 => ( ( sup_sup @ A @ X @ Y )
% 0.18/0.38 = X ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_absorb1
% 0.18/0.38 thf(fact_215_sup__absorb2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [X: A,Y: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ X @ Y )
% 0.18/0.38 => ( ( sup_sup @ A @ X @ Y )
% 0.18/0.38 = Y ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup_absorb2
% 0.18/0.38 thf(fact_216_sup_OboundedE,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,C3: A,A2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C3 ) @ A2 )
% 0.18/0.38 => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.18/0.38 => ~ ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.boundedE
% 0.18/0.38 thf(fact_217_sup_OboundedI,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,A2: A,C3: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.18/0.38 => ( ( ord_less_eq @ A @ C3 @ A2 )
% 0.18/0.38 => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C3 ) @ A2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.boundedI
% 0.18/0.38 thf(fact_218_sup_Oorder__iff,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( ord_less_eq @ A )
% 0.18/0.38 = ( ^ [B6: A,A3: A] :
% 0.18/0.38 ( A3
% 0.18/0.38 = ( sup_sup @ A @ A3 @ B6 ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.order_iff
% 0.18/0.38 thf(fact_219_sup_Ocobounded1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.cobounded1
% 0.18/0.38 thf(fact_220_sup_Ocobounded2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.cobounded2
% 0.18/0.38 thf(fact_221_sup_Oabsorb__iff1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( ord_less_eq @ A )
% 0.18/0.38 = ( ^ [B6: A,A3: A] :
% 0.18/0.38 ( ( sup_sup @ A @ A3 @ B6 )
% 0.18/0.38 = A3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.absorb_iff1
% 0.18/0.38 thf(fact_222_sup_Oabsorb__iff2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ( ( ord_less_eq @ A )
% 0.18/0.38 = ( ^ [A3: A,B6: A] :
% 0.18/0.38 ( ( sup_sup @ A @ A3 @ B6 )
% 0.18/0.38 = B6 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.absorb_iff2
% 0.18/0.38 thf(fact_223_sup_OcoboundedI1,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [C3: A,A2: A,B2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ C3 @ A2 )
% 0.18/0.38 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.coboundedI1
% 0.18/0.38 thf(fact_224_sup_OcoboundedI2,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.18/0.38 => ! [C3: A,B2: A,A2: A] :
% 0.18/0.38 ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.18/0.38 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % sup.coboundedI2
% 0.18/0.38 thf(fact_225_Collect__mono__iff,axiom,
% 0.18/0.38 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.18/0.38 = ( ! [X3: A] :
% 0.18/0.38 ( ( P @ X3 )
% 0.18/0.38 => ( Q @ X3 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Collect_mono_iff
% 0.18/0.38 thf(fact_226_contra__subsetD,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 => ( ~ ( member @ A @ C3 @ B5 )
% 0.18/0.38 => ~ ( member @ A @ C3 @ A4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % contra_subsetD
% 0.18/0.38 thf(fact_227_set__eq__subset,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( ^ [Y4: set @ A,Z4: set @ A] : ( Y4 = Z4 ) )
% 0.18/0.38 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B7 )
% 0.18/0.38 & ( ord_less_eq @ ( set @ A ) @ B7 @ A6 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % set_eq_subset
% 0.18/0.38 thf(fact_228_subset__trans,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % subset_trans
% 0.18/0.38 thf(fact_229_Collect__mono,axiom,
% 0.18/0.38 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.18/0.38 ( ! [X2: A] :
% 0.18/0.38 ( ( P @ X2 )
% 0.18/0.38 => ( Q @ X2 ) )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % Collect_mono
% 0.18/0.38 thf(fact_230_subset__refl,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.18/0.38
% 0.18/0.38 % subset_refl
% 0.18/0.38 thf(fact_231_rev__subsetD,axiom,
% 0.18/0.38 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( member @ A @ C3 @ A4 )
% 0.18/0.38 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % rev_subsetD
% 0.18/0.38 thf(fact_232_subset__iff,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) )
% 0.18/0.38 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.18/0.38 ! [T2: A] :
% 0.18/0.38 ( ( member @ A @ T2 @ A6 )
% 0.18/0.38 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % subset_iff
% 0.18/0.38 thf(fact_233_set__rev__mp,axiom,
% 0.18/0.38 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( member @ A @ X @ A4 )
% 0.18/0.38 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.38 => ( member @ A @ X @ B5 ) ) ) ).
% 0.18/0.38
% 0.18/0.38 % set_rev_mp
% 0.18/0.38 thf(fact_234_equalityD2,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( A4 = B5 )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.18/0.38
% 0.18/0.38 % equalityD2
% 0.18/0.38 thf(fact_235_equalityD1,axiom,
% 0.18/0.38 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.38 ( ( A4 = B5 )
% 0.18/0.38 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.18/0.38
% 0.18/0.38 % equalityD1
% 0.18/0.38 thf(fact_236_subset__eq,axiom,
% 0.18/0.38 ! [A: $tType] :
% 0.18/0.38 ( ( ord_less_eq @ ( set @ A ) )
% 0.18/0.38 = ( ^ [A6: set @ A,B7: set @ A] :
% 0.18/0.38 ! [X3: A] :
% 0.18/0.39 ( ( member @ A @ X3 @ A6 )
% 0.18/0.39 => ( member @ A @ X3 @ B7 ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % subset_eq
% 0.18/0.39 thf(fact_237_equalityE,axiom,
% 0.18/0.39 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.18/0.39 ( ( A4 = B5 )
% 0.18/0.39 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.39 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % equalityE
% 0.18/0.39 thf(fact_238_subsetCE,axiom,
% 0.18/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 0.18/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.39 => ( ( member @ A @ C3 @ A4 )
% 0.18/0.39 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % subsetCE
% 0.18/0.39 thf(fact_239_subsetD,axiom,
% 0.18/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 0.18/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.39 => ( ( member @ A @ C3 @ A4 )
% 0.18/0.39 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % subsetD
% 0.18/0.39 thf(fact_240_in__mono,axiom,
% 0.18/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.18/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.39 => ( ( member @ A @ X @ A4 )
% 0.18/0.39 => ( member @ A @ X @ B5 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % in_mono
% 0.18/0.39 thf(fact_241_set__mp,axiom,
% 0.18/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.18/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.18/0.39 => ( ( member @ A @ X @ A4 )
% 0.18/0.39 => ( member @ A @ X @ B5 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % set_mp
% 0.18/0.39 thf(fact_242_wlog__linorder__le,axiom,
% 0.18/0.39 ! [A: $tType] :
% 0.18/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.18/0.39 => ! [P: A > A > $o,B2: A,A2: A] :
% 0.18/0.39 ( ! [A7: A,B4: A] :
% 0.18/0.39 ( ( ord_less_eq @ A @ A7 @ B4 )
% 0.18/0.39 => ( P @ A7 @ B4 ) )
% 0.18/0.39 => ( ( ( P @ B2 @ A2 )
% 0.18/0.39 => ( P @ A2 @ B2 ) )
% 0.18/0.39 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % wlog_linorder_le
% 0.18/0.39 thf(fact_243_llist_Orel__eq,axiom,
% 0.18/0.39 ! [A: $tType] :
% 0.18/0.39 ( ( coindu987187967t_all2 @ A @ A
% 0.18/0.39 @ ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 0.18/0.39 = ( ^ [Y4: coindu1593790203_llist @ A,Z4: coindu1593790203_llist @ A] : ( Y4 = Z4 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_eq
% 0.18/0.39 thf(fact_244_llist_Orel__refl,axiom,
% 0.18/0.39 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 0.18/0.39 ( ! [X2: B] : ( Ra @ X2 @ X2 )
% 0.18/0.39 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_refl
% 0.18/0.39 thf(fact_245_llist_Octr__transfer_I1_J,axiom,
% 0.18/0.39 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.ctr_transfer(1)
% 0.18/0.39 thf(fact_246_llist_Orel__refl__strong,axiom,
% 0.18/0.39 ! [A: $tType,X: coindu1593790203_llist @ A,Ra: A > A > $o] :
% 0.18/0.39 ( ! [Z3: A] :
% 0.18/0.39 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.18/0.39 => ( Ra @ Z3 @ Z3 ) )
% 0.18/0.39 => ( coindu987187967t_all2 @ A @ A @ Ra @ X @ X ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_refl_strong
% 0.18/0.39 thf(fact_247_llist_Orel__mono__strong,axiom,
% 0.18/0.39 ! [A: $tType,B: $tType,R: A > B > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,Ra: A > B > $o] :
% 0.18/0.39 ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 0.18/0.39 => ( ! [Z3: A,Yb: B] :
% 0.18/0.39 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 0.18/0.39 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Y ) )
% 0.18/0.39 => ( ( R @ Z3 @ Yb )
% 0.18/0.39 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.18/0.39 => ( coindu987187967t_all2 @ A @ B @ Ra @ X @ Y ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_mono_strong
% 0.18/0.39 thf(fact_248_llist_Orel__cong,axiom,
% 0.18/0.39 ! [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] :
% 0.18/0.39 ( ( X = Ya )
% 0.18/0.39 => ( ( Y = Xa )
% 0.18/0.39 => ( ! [Z3: A,Yb: B] :
% 0.18/0.39 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ Ya ) )
% 0.18/0.39 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Xa ) )
% 0.18/0.39 => ( ( R @ Z3 @ Yb )
% 0.18/0.39 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.18/0.39 => ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 0.18/0.39 = ( coindu987187967t_all2 @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_cong
% 0.18/0.39 thf(fact_249_llist_Orel__intros_I2_J,axiom,
% 0.18/0.39 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 0.18/0.39 ( ( R @ X21 @ Y21 )
% 0.18/0.39 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 0.18/0.39 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_intros(2)
% 0.18/0.39 thf(fact_250_llist_Orel__distinct_I2_J,axiom,
% 0.18/0.39 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.18/0.39 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_distinct(2)
% 0.18/0.39 thf(fact_251_llist_Orel__distinct_I1_J,axiom,
% 0.18/0.39 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.18/0.39 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_distinct(1)
% 0.18/0.39 thf(fact_252_llist_Orel__cases,axiom,
% 0.18/0.39 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 0.18/0.39 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 0.18/0.39 => ( ( ( A2
% 0.18/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.18/0.39 => ( B2
% 0.18/0.39 != ( coindu1598213697e_LNil @ B ) ) )
% 0.18/0.39 => ~ ! [X12: A,X24: coindu1593790203_llist @ A] :
% 0.18/0.39 ( ( A2
% 0.18/0.39 = ( coindu1121789889_LCons @ A @ X12 @ X24 ) )
% 0.18/0.39 => ! [Y12: B,Y24: coindu1593790203_llist @ B] :
% 0.18/0.39 ( ( B2
% 0.18/0.39 = ( coindu1121789889_LCons @ B @ Y12 @ Y24 ) )
% 0.18/0.39 => ( ( R @ X12 @ Y12 )
% 0.18/0.39 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X24 @ Y24 ) ) ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % llist.rel_cases
% 0.18/0.39 thf(fact_253_lset__ltl,axiom,
% 0.18/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) @ ( coindu1112613586e_lset @ A @ Xs ) ) ).
% 0.18/0.39
% 0.18/0.39 % lset_ltl
% 0.18/0.39 thf(fact_254_lset__lappend1,axiom,
% 0.18/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.18/0.39
% 0.18/0.39 % lset_lappend1
% 0.18/0.39
% 0.18/0.39 %----Type constructors (7)
% 0.18/0.39 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.18/0.39 ! [A8: $tType,A9: $tType] :
% 0.18/0.39 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.18/0.39 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.18/0.39 ! [A8: $tType,A9: $tType] :
% 0.18/0.39 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 0.18/0.39 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 0.18/0.39 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(tcon_Set_Oset___Lattices_Olattice_2,axiom,
% 0.18/0.39 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_3,axiom,
% 0.18/0.39 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.18/0.39
% 0.18/0.39 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.18/0.39 linorder @ $o @ ( type2 @ $o ) ).
% 0.18/0.39
% 0.18/0.39 thf(tcon_HOL_Obool___Lattices_Olattice_4,axiom,
% 0.18/0.39 lattice @ $o @ ( type2 @ $o ) ).
% 0.18/0.39
% 0.18/0.39 %----Helper facts (3)
% 0.18/0.39 thf(help_If_3_1_T,axiom,
% 0.18/0.39 ! [P: $o] :
% 0.18/0.39 ( ( P = $true )
% 0.18/0.39 | ( P = $false ) ) ).
% 0.18/0.39
% 0.18/0.39 thf(help_If_2_1_T,axiom,
% 0.18/0.39 ! [A: $tType,X: A,Y: A] :
% 0.18/0.39 ( ( if @ A @ $false @ X @ Y )
% 0.18/0.39 = Y ) ).
% 0.18/0.39
% 0.18/0.39 thf(help_If_1_1_T,axiom,
% 0.18/0.39 ! [A: $tType,X: A,Y: A] :
% 0.18/0.39 ( ( if @ A @ $true @ X @ Y )
% 0.18/0.39 = X ) ).
% 0.18/0.39
% 0.18/0.39 %----Conjectures (1)
% 0.18/0.39 thf(conj_0,conjecture,
% 0.18/0.39 coindu1696667936prefix @ a @ ( coindu268472904append @ a @ xs @ ys ) @ ( coindu268472904append @ a @ xs @ zs ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 2.57/1.59 ---- Embedded in THF ---
% 2.57/1.59 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.57/1.59 %%% Generated on Tue Feb 24 06:08:07 EST 2026
% 2.57/1.59 %%% using '$$dhol' embedding, version 1.3.0.
% 2.57/1.59 %%% Logic specification used:
% 2.57/1.59 %%% thf(spec, logic, $$dhol).
% 2.57/1.59
% 2.57/1.59 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2DTF29397.p
% 2.57/1.59 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 2.57/1.59 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.57/1.59 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.57/1.59 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.57/1.59 thf(ty_tf_a, type, a: $tType).
% 2.57/1.59 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.57/1.59 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.57/1.59 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.57/1.59 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset, type, coindu1928975208n_lset: (!> [A:$tType]: (((set @ A) > ((coindu1593790203_llist @ A) > (set @ A)))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist, type, coindu882539134_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coindu1593790203_llist @ A) > B)) > ((coindu1593790203_llist @ A) > B)))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist, type, coindu1244876290_llist: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (coindu1593790203_llist @ A)) > ((C > C) > (C > (coindu1593790203_llist @ A)))))))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd, type, coindu1046438764le_lhd: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 2.57/1.59 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) > $o)))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset, type, coindu1112613586e_lset: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (set @ A))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl, type, coindu1047225960le_ltl: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 2.57/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist, type, coindu1599971794_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coindu1593790203_llist @ B)))))))).
% 2.57/1.59 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.57/1.59 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.57/1.59 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.57/1.59 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.57/1.59 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.57/1.59 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.57/1.59 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.57/1.59 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.57/1.59 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.57/1.59 thf(sy_v_xs, type, xs: (coindu1593790203_llist @ a)).
% 2.57/1.59 thf(sy_v_ys, type, ys: (coindu1593790203_llist @ a)).
% 2.57/1.59 thf(sy_v_zs, type, zs: (coindu1593790203_llist @ a)).
% 2.57/1.59 thf(fact_0_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 2.57/1.59 thf(fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062, axiom, (((coindu1213758845finite @ a) @ xs) => (((coindu1696667936prefix @ a) @ ys) @ zs))).
% 2.57/1.59 thf(fact_2_lappend__assoc, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) = (((coindu268472904append @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs)))))).
% 2.57/1.59 thf(fact_3_lprefix__trans, axiom, (! [A:$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)))))).
% 2.57/1.59 thf(fact_4_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 2.57/1.59 thf(fact_5_lprefix__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 2.57/1.59 thf(fact_6_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Zs) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) | (((coindu1696667936prefix @ A) @ Ys) @ Xs))))))).
% 2.57/1.59 thf(fact_7_lprefix__lappend__sameI, axiom, (! [A:$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)))))).
% 2.57/1.59 thf(fact_8_lfinite__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & ((coindu1213758845finite @ A) @ Ys)))))).
% 2.57/1.59 thf(fact_9_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 2.57/1.59 thf(fact_10_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 2.57/1.59 thf(fact_11_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 2.57/1.59 thf(fact_12_lappend__inf, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.57/1.59 thf(fact_13_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 2.57/1.59 thf(fact_14_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1121789889_LCons @ A) @ Xa) @ X)) @ Ys) = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu268472904append @ A) @ X) @ Ys)))))).
% 2.57/1.59 thf(fact_15_LCons__lprefix__LCons, axiom, (! [A:$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)))))).
% 2.57/1.59 thf(fact_16_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.57/1.59 thf(fact_17_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 2.57/1.59 thf(fact_18_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.57/1.59 thf(fact_19_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.57/1.59 thf(fact_20_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.57/1.59 thf(fact_21_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 2.57/1.59 thf(fact_22_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 2.57/1.59 thf(fact_23_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.57/1.59 thf(fact_24_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 2.57/1.59 thf(fact_25_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 2.57/1.59 thf(fact_26_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.57/1.59 thf(fact_27_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist))))))).
% 2.57/1.59 thf(fact_28_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 2.57/1.59 thf(fact_29_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 2.57/1.59 thf(fact_30_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 2.57/1.59 thf(fact_31_lfinite_Ocases, axiom, (! [A:$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))))))))))))).
% 2.57/1.59 thf(fact_32_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A3:(coindu1593790203_llist @ A)]: (((A3 = (coindu1598213697e_LNil @ A)) | (? [Xs3:(coindu1593790203_llist @ A),X3:A]: (((A3 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((coindu1213758845finite @ A) @ Xs3))))))))))).
% 2.57/1.59 thf(fact_33_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 2.57/1.59 thf(fact_34_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X3:A,Xs4:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs4)))))))).
% 2.57/1.59 thf(fact_35_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X3:A,Xs4:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs4)))))))).
% 2.57/1.59 thf(fact_36_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.57/1.59 thf(fact_37_lfinite_Oinducts, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs2:(coindu1593790203_llist @ A),X2:A]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))) => (P @ X))))))).
% 2.57/1.59 thf(fact_38_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist2:(coindu1593790203_llist @ A)]: ((Llist2 = (coindu1598213697e_LNil @ A)))))))).
% 2.57/1.59 thf(fact_39_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 2.57/1.59 thf(fact_40_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.57/1.59 thf(fact_41_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 2.57/1.59 thf(fact_42_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 2.57/1.59 thf(fact_43_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ (coindu1598213697e_LNil @ A)))) @ Ys) = (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 2.57/1.59 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.57/1.59 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) = A4)))).
% 2.57/1.59 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.57/1.59 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.57/1.59 thf(fact_48_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs4:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs4)) & (((coindu1696667936prefix @ A) @ Xs4) @ Ys))))))))).
% 2.57/1.59 thf(fact_49_lprefix_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A)]: ((((X4 @ X) @ Xa) => ((! [X2:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X4 @ X2) @ Xa2) => ((? [Xs5:(coindu1593790203_llist @ A)]: (((X2 = (coindu1598213697e_LNil @ A)) & (Xa2 = Xs5)))) | (? [Xs5:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),Xb:A]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys2)) & (((X4 @ Xs5) @ Ys2) | (((coindu1696667936prefix @ A) @ Xs5) @ Ys2)))))))))) => (((coindu1696667936prefix @ A) @ X) @ Xa)))))).
% 2.57/1.59 thf(fact_50_lprefix_Osimps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((? [Xs3:(coindu1593790203_llist @ A)]: (((A1 = (coindu1598213697e_LNil @ A)) & (A22 = Xs3)))) | (? [Xs3:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X3:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((A22 = (((coindu1121789889_LCons @ A) @ X3) @ Ys3)) & (((coindu1696667936prefix @ A) @ Xs3) @ Ys3)))))))))))).
% 2.57/1.59 thf(fact_51_lprefix_Ocases, axiom, (! [A:$tType,A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ A12) @ A23) => (((A12 = (coindu1598213697e_LNil @ A)) => (! [Xs2:(coindu1593790203_llist @ A)]: ((A23 != Xs2)))) => (~ ((! [Xs2:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),X2:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) => ((A23 = (((coindu1121789889_LCons @ A) @ X2) @ Ys4)) => (~ ((((coindu1696667936prefix @ A) @ Xs2) @ Ys4)))))))))))))).
% 2.57/1.59 thf(fact_52_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((~ ((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 2.57/1.59 thf(fact_53_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.57/1.59 thf(fact_54_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 2.57/1.59 thf(fact_55_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.57/1.59 thf(fact_56_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 2.57/1.59 thf(fact_57_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 2.57/1.59 thf(fact_58_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 2.57/1.59 thf(fact_59_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 2.57/1.59 thf(fact_60_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 2.57/1.59 thf(fact_61_LCons__lprefix__conv, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Ys5:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ X) @ Ys5)) & (((coindu1696667936prefix @ A) @ Xs) @ Ys5)))))))).
% 2.57/1.59 thf(fact_62_Le__LCons, axiom, (! [A:$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)))))).
% 2.57/1.59 thf(fact_63_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 2.57/1.59 thf(fact_64_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.57/1.59 thf(fact_65_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 2.57/1.59 thf(fact_66_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 2.57/1.59 thf(fact_67_lprefixI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X4:(set @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)))]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs) @ Ys)) @ X4) => ((! [Xs2:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs2) @ Ys4)) @ X4) => (((coindu335574135_lnull @ A) @ Xs2) | (? [X5:A,Xs6:(coindu1593790203_llist @ A),Ys6:(coindu1593790203_llist @ A)]: (((Xs2 = (((coindu1121789889_LCons @ A) @ X5) @ Xs6)) & ((Ys4 = (((coindu1121789889_LCons @ A) @ X5) @ Ys6)) & ((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs6) @ Ys6)) @ X4) | (((coindu1696667936prefix @ A) @ Xs6) @ Ys6)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 2.57/1.59 thf(fact_68_split__llist, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (? [Ys4:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: (((Xs = (((coindu268472904append @ A) @ Ys4) @ (((coindu1121789889_LCons @ A) @ X) @ Zs2))) & ((coindu1213758845finite @ A) @ Ys4)))))))).
% 2.57/1.59 thf(fact_69_split__llist__first, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (? [Ys4:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: (((Xs = (((coindu268472904append @ A) @ Ys4) @ (((coindu1121789889_LCons @ A) @ X) @ Zs2))) & (((coindu1213758845finite @ A) @ Ys4) & (~ ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Ys4)))))))))))).
% 2.57/1.59 thf(fact_70_lhd__lappend, axiom, (! [A:$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))))))).
% 2.57/1.59 thf(fact_71_gen__lset__code_I1_J, axiom, (! [A:$tType,A4:(set @ A)]: (((((coindu1928975208n_lset @ A) @ A4) @ (coindu1598213697e_LNil @ A)) = A4)))).
% 2.57/1.59 thf(fact_72_llist_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((coindu1244876290_llist @ C) @ A) = (^ [P2:(C > $o),G21:(C > A),Q22:(C > $o),G221:(C > (coindu1593790203_llist @ A)),G222:(C > C),A3:C]: (((((if @ (coindu1593790203_llist @ A)) @ (P2 @ A3)) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ (G21 @ A3)) @ ((((if @ (coindu1593790203_llist @ A)) @ (Q22 @ A3)) @ (G221 @ A3)) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q22) @ G221) @ G222) @ (G222 @ A3))))))))))).
% 2.57/1.59 thf(fact_73_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1599971794_llist @ A) @ B) = (^ [P2:(A > $o),G21:(A > B),G22:(A > A),A3:A]: (((((if @ (coindu1593790203_llist @ B)) @ (P2 @ A3)) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ (G21 @ A3)) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A3)))))))))).
% 2.57/1.59 thf(fact_74_ltl__lappend, axiom, (! [A:$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))))))).
% 2.57/1.59 thf(fact_75_unfold__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),G212:(A > B),G223:(A > A),A2:A]: ((((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2)) = (P3 @ A2))))).
% 2.57/1.59 thf(fact_76_unfold__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),G212:(A > B),G223:(A > A),A2:A]: (((~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2)))) = (~ ((P3 @ A2))))))).
% 2.57/1.59 thf(fact_77_lfinite__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 2.57/1.59 thf(fact_78_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B2:B,X:A,Xs:(coindu1593790203_llist @ A)]: (((((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B2) = (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((~ ((IS_LNIL @ B2))) & ((X = (LHD @ B2)) & (Xs = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B2))))))))).
% 2.57/1.59 thf(fact_79_llist_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C),A2:C]: ((((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (P3 @ A2))))).
% 2.57/1.59 thf(fact_80_llist_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C),A2:C]: (((~ (((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))) = (~ ((P3 @ A2))))))).
% 2.57/1.59 thf(fact_81_unfold__llist__id, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((((((coindu1599971794_llist @ (coindu1593790203_llist @ A)) @ A) @ (coindu335574135_lnull @ A)) @ (coindu1046438764le_lhd @ A)) @ (coindu1047225960le_ltl @ A)) @ Xs) = Xs)))).
% 2.57/1.59 thf(fact_82_lhd__LCons__ltl, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist)) = Llist))))).
% 2.57/1.59 thf(fact_83_llist__set__induct, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs2)) @ Xs2)))) => ((! [Xs2:(coindu1593790203_llist @ A),Y2:A]: (((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((((member @ A) @ Y2) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2))) => (((P @ Y2) @ ((coindu1047225960le_ltl @ A) @ Xs2)) => ((P @ Y2) @ Xs2)))))) => ((P @ X) @ Xs))))))).
% 2.57/1.59 thf(fact_84_lset__lmember, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) = (((coindu567634248member @ A) @ X) @ Xs))))).
% 2.57/1.59 thf(fact_85_in__lset__ltlD, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs))) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)))))).
% 2.57/1.59 thf(fact_86_unfold__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((~ ((P3 @ A2))) => (((coindu1046438764le_lhd @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2)) = (G212 @ A2)))))).
% 2.57/1.59 thf(fact_87_unfold__llist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((~ ((P3 @ A2))) => (((coindu1047225960le_ltl @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2)) = ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ (G223 @ A2))))))).
% 2.57/1.59 thf(fact_88_llist_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C)]: (((~ ((P3 @ A2))) => (((coindu1046438764le_lhd @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G212 @ A2)))))).
% 2.57/1.59 thf(fact_89_llist_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A2:C,Q222:(C > $o),G212:(C > A),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C)]: (((~ ((P3 @ A2))) => (((Q222 @ A2) => (((coindu1047225960le_ltl @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = (G2212 @ A2))) & ((~ ((Q222 @ A2))) => (((coindu1047225960le_ltl @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)) = ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.57/1.59 thf(fact_90_llist_Oset__sel_I2_J, axiom, (! [A:$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))))))).
% 2.57/1.59 thf(fact_91_llist_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ A2))) => (((member @ A) @ ((coindu1046438764le_lhd @ A) @ A2)) @ ((coindu1112613586e_lset @ A) @ A2)))))).
% 2.57/1.59 thf(fact_92_llist_Ocoinduct__strong, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist3) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ A) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist4) = ((coindu1046438764le_lhd @ A) @ Llist5)) & (((R @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ A) @ Llist5)) | (((coindu1047225960le_ltl @ A) @ Llist4) = ((coindu1047225960le_ltl @ A) @ Llist5)))))))))) => (Llist = Llist3)))))).
% 2.57/1.59 thf(fact_93_llist_Ocoinduct, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist3) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ A) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist4) = ((coindu1046438764le_lhd @ A) @ Llist5)) & ((R @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ A) @ Llist5))))))))) => (Llist = Llist3)))))).
% 2.57/1.59 thf(fact_94_llist_Oexpand, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Llist) = ((coindu335574135_lnull @ A) @ Llist3)) => (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((((coindu1046438764le_lhd @ A) @ Llist) = ((coindu1046438764le_lhd @ A) @ Llist3)) & (((coindu1047225960le_ltl @ A) @ Llist) = ((coindu1047225960le_ltl @ A) @ Llist3))))) => (Llist = Llist3)))))).
% 2.57/1.59 thf(fact_95_ltl__unfold__llist, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),A2:B,LHD:(B > A),LTL:(B > B)]: ((((IS_LNIL @ A2) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = (coindu1598213697e_LNil @ A))) & ((~ ((IS_LNIL @ A2))) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ A2)))))))).
% 2.57/1.59 thf(fact_96_llist_Oexhaust__sel, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist != (coindu1598213697e_LNil @ A)) => (Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))).
% 2.57/1.59 thf(fact_97_eq__LConsD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) => ((Xs != (coindu1598213697e_LNil @ A)) & ((((coindu1046438764le_lhd @ A) @ Xs) = Y) & (((coindu1047225960le_ltl @ A) @ Xs) = Ys))))))).
% 2.57/1.59 thf(fact_98_lprefix__coinduct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((P @ Xs) @ Ys) => ((! [Xs2:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: ((((P @ Xs2) @ Ys4) => ((((coindu335574135_lnull @ A) @ Ys4) => ((coindu335574135_lnull @ A) @ Xs2)) & ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((~ (((coindu335574135_lnull @ A) @ Ys4))) => ((((coindu1046438764le_lhd @ A) @ Xs2) = ((coindu1046438764le_lhd @ A) @ Ys4)) & (((P @ ((coindu1047225960le_ltl @ A) @ Xs2)) @ ((coindu1047225960le_ltl @ A) @ Ys4)) | (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2)) @ ((coindu1047225960le_ltl @ A) @ Ys4)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 2.57/1.59 thf(fact_99_lprefix__expand, axiom, (! [A:$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))))).
% 2.57/1.59 thf(fact_100_llist_Oset__induct, axiom, (! [A:$tType,X:A,A2:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A2)) => ((! [Z1:A,Z2:(coindu1593790203_llist @ A)]: (((P @ Z1) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(coindu1593790203_llist @ A),Xa2:A]: (((((member @ A) @ Xa2) @ ((coindu1112613586e_lset @ A) @ Z2)) => (((P @ Xa2) @ Z2) => ((P @ Xa2) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z2)))))) => ((P @ X) @ A2))))))).
% 2.57/1.59 thf(fact_101_llist_Oset__cases, axiom, (! [A:$tType,E:A,A2:(coindu1593790203_llist @ A)]: (((((member @ A) @ E) @ ((coindu1112613586e_lset @ A) @ A2)) => ((! [Z2:(coindu1593790203_llist @ A)]: ((A2 != (((coindu1121789889_LCons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((coindu1112613586e_lset @ A) @ Z2)))))))))))))).
% 2.57/1.59 thf(fact_102_lset__induct_H, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X) @ Xs2)))) => ((! [X6:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X6) @ Xs2)))))) => (P @ Xs))))))).
% 2.57/1.59 thf(fact_103_lset__induct, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X) @ Xs2)))) => ((! [X6:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((X != X6) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X6) @ Xs2))))))) => (P @ Xs))))))).
% 2.57/1.59 thf(fact_104_lset__cases, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs7:(coindu1593790203_llist @ A)]: ((Xs != (((coindu1121789889_LCons @ A) @ X) @ Xs7)))) => (~ ((! [X6:A,Xs7:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ X6) @ Xs7)) => (~ ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs7)))))))))))))).
% 2.57/1.59 thf(fact_105_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A12:A,A23:(coindu1593790203_llist @ A)]: ((((member @ A) @ A12) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A12) @ A23)))))).
% 2.57/1.59 thf(fact_106_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A23:(coindu1593790203_llist @ A),A12:A]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A23)) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A12) @ A23))))))).
% 2.57/1.59 thf(fact_107_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 2.57/1.59 thf(fact_108_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),X7:A]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X7) @ Xs))))))).
% 2.57/1.59 thf(fact_109_lnull__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu335574135_lnull @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))))).
% 2.57/1.59 thf(fact_110_ltl__simps_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1047225960le_ltl @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X22)))).
% 2.57/1.59 thf(fact_111_ltl__simps_I1_J, axiom, (! [A:$tType]: ((((coindu1047225960le_ltl @ A) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.57/1.59 thf(fact_112_lprefix__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys)))))).
% 2.57/1.59 thf(fact_113_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1046438764le_lhd @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X21)))).
% 2.57/1.59 thf(fact_114_unfold__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((P3 @ A2) => ((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2)))))).
% 2.57/1.59 thf(fact_115_unfold__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((~ ((P3 @ A2))) => (~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2)))))))).
% 2.57/1.59 thf(fact_116_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((~ ((P3 @ A2))) => (((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2) = (((coindu1121789889_LCons @ B) @ (G212 @ A2)) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ (G223 @ A2)))))))).
% 2.57/1.59 thf(fact_117_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((P3 @ A2) => (((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2) = (coindu1598213697e_LNil @ B)))))).
% 2.57/1.59 thf(fact_118_llist_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C)]: (((P3 @ A2) => ((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))))).
% 2.57/1.59 thf(fact_119_llist_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C)]: (((~ ((P3 @ A2))) => (~ (((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2)))))))).
% 2.57/1.59 thf(fact_120_llist_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C)]: (((~ ((P3 @ A2))) => (((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = (((coindu1121789889_LCons @ A) @ (G212 @ A2)) @ ((((if @ (coindu1593790203_llist @ A)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.57/1.59 thf(fact_121_llist_Ocorec_I1_J, axiom, (! [C:$tType,A:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2222:(C > C)]: (((P3 @ A2) => (((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = (coindu1598213697e_LNil @ A)))))).
% 2.57/1.59 thf(fact_122_in__lset__lappend__iff, axiom, (! [A:$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)))))))).
% 2.57/1.59 thf(fact_123_lappend__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((((coindu268472904append @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ Ys) = ((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 2.57/1.59 thf(fact_124_lfinite__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs2) => (P @ Xs2)))) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((P @ ((coindu1047225960le_ltl @ A) @ Xs2)) => (P @ Xs2)))))) => (P @ Xs))))))).
% 2.57/1.59 thf(fact_125_lprefix__lhdD, axiom, (! [A:$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))))))).
% 2.57/1.59 thf(fact_126_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B3)) = ((A2 = A5) & (B2 = B3)))))).
% 2.57/1.59 thf(fact_127_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X23:B,Y1:A,Y23:B]: (((((((product_Pair @ A) @ B) @ X1) @ X23) = ((((product_Pair @ A) @ B) @ Y1) @ Y23)) = ((X1 = Y1) & (X23 = Y23)))))).
% 2.57/1.59 thf(fact_128_llist_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (~ ((((Llist = (coindu1598213697e_LNil @ A)) & (~ ((P @ F1)))) | ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) & (~ ((P @ ((F2 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))))))).
% 2.57/1.59 thf(fact_129_llist_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (((Llist = (coindu1598213697e_LNil @ A)) => (P @ F1)) & ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) => (P @ ((F2 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))).
% 2.57/1.59 thf(fact_130_llist_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((coindu882539134_llist @ B) @ A) = (^ [F12:B,F22:(A > ((coindu1593790203_llist @ A) > B)),Llist2:(coindu1593790203_llist @ A)]: (((((if @ B) @ ((coindu335574135_lnull @ A) @ Llist2)) @ F12) @ ((F22 @ ((coindu1046438764le_lhd @ A) @ Llist2)) @ ((coindu1047225960le_ltl @ A) @ Llist2))))))))).
% 2.57/1.59 thf(fact_131_lset__lappend__lfinite, axiom, (! [A:$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))))))).
% 2.57/1.59 thf(fact_132_llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),X21:A,X22:(coindu1593790203_llist @ A)]: (((((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 2.57/1.59 thf(fact_133_llist_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:(A > ((coindu1593790203_llist @ A) > B))]: (((((((coindu882539134_llist @ B) @ A) @ F1) @ F2) @ (coindu1598213697e_LNil @ A)) = F1)))).
% 2.57/1.59 thf(fact_134_gen__lset__def, axiom, (! [A:$tType]: (((coindu1928975208n_lset @ A) = (^ [A6:(set @ A),Xs3:(coindu1593790203_llist @ A)]: ((((sup_sup @ (set @ A)) @ A6) @ ((coindu1112613586e_lset @ A) @ Xs3)))))))).
% 2.57/1.59 thf(fact_135_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X2:A,Y2:B]: ((P3 = ((((product_Pair @ A) @ B) @ X2) @ Y2))))))).
% 2.57/1.59 thf(fact_136_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A7:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A7) @ B4)))) => (P @ P3))))).
% 2.57/1.59 thf(fact_137_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A5:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A5) @ B3)) => (~ (((A2 = A5) => (B2 != B3)))))))).
% 2.57/1.59 thf(fact_138_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A7:A,B4:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A7) @ ((((product_Pair @ B) @ C) @ B4) @ C2)))))))))).
% 2.57/1.59 thf(fact_139_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A7:A,B4:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.57/1.59 thf(fact_140_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))))]: ((~ ((! [A7:A,B4:B,C2:C,D2:D,E3:E2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E2)) @ C2) @ ((((product_Pair @ D) @ E2) @ D2) @ E3)))))))))))).
% 2.57/1.59 thf(fact_141_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3)))))]: ((~ ((! [A7:A,B4:B,C2:C,D2:D,E3:E2,F4:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ F3)) @ D2) @ ((((product_Pair @ E2) @ F3) @ E3) @ F4))))))))))))).
% 2.57/1.59 thf(fact_142_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E2:$tType,F3:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2))))))]: ((~ ((! [A7:A,B4:B,C2:C,D2:D,E3:E2,F4:F3,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2)))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2))) @ D2) @ ((((product_Pair @ E2) @ ((product_prod @ F3) @ G2)) @ E3) @ ((((product_Pair @ F3) @ G2) @ F4) @ G3)))))))))))))).
% 2.57/1.59 thf(fact_143_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A7:A,B4:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A7) @ ((((product_Pair @ B) @ C) @ B4) @ C2))))) => (P @ X))))).
% 2.57/1.59 thf(fact_144_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A7:A,B4:B,C2:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P @ X))))).
% 2.57/1.59 thf(fact_145_prod__induct5, axiom, (! [E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))))]: (((! [A7:A,B4:B,C2:C,D2:D,E3:E2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2)))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E2))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E2)) @ C2) @ ((((product_Pair @ D) @ E2) @ D2) @ E3))))))) => (P @ X))))).
% 2.57/1.59 thf(fact_146_prod__induct6, axiom, (! [F3:$tType,E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3)))))]: (((! [A7:A,B4:B,C2:C,D2:D,E3:E2,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ F3))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ F3)) @ D2) @ ((((product_Pair @ E2) @ F3) @ E3) @ F4)))))))) => (P @ X))))).
% 2.57/1.59 thf(fact_147_prod__induct7, axiom, (! [G2:$tType,F3:$tType,E2:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2))))))]: (((! [A7:A,B4:B,C2:C,D2:D,E3:E2,F4:F3,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2)))))) @ A7) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E2) @ ((product_prod @ F3) @ G2))) @ D2) @ ((((product_Pair @ E2) @ ((product_prod @ F3) @ G2)) @ E3) @ ((((product_Pair @ F3) @ G2) @ F4) @ G3))))))))) => (P @ X))))).
% 2.57/1.59 thf(fact_148_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A7:A,B4:B]: ((Y != ((((product_Pair @ A) @ B) @ A7) @ B4))))))))).
% 2.57/1.59 thf(fact_149_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A7:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A7) @ B4)))) => (P @ Prod))))).
% 2.57/1.59 thf(fact_150_lset__lappend__conv, axiom, (! [A:$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))))))).
% 2.57/1.59 thf(fact_151_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 2.57/1.59 thf(fact_152_UnCI, axiom, (! [A:$tType,C3:A,B5:(set @ A),A4:(set @ A)]: ((((~ ((((member @ A) @ C3) @ B5))) => (((member @ A) @ C3) @ A4)) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.57/1.59 thf(fact_153_Un__iff, axiom, (! [A:$tType,C3:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) = ((((member @ A) @ C3) @ A4) | (((member @ A) @ C3) @ B5)))))).
% 2.57/1.59 thf(fact_154_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F5:(A > B),G4:(A > B),X3:A]: ((((sup_sup @ B) @ (F5 @ X3)) @ (G4 @ X3))))))))).
% 2.57/1.59 thf(fact_155_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ B2) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.57/1.59 thf(fact_156_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.57/1.59 thf(fact_157_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)) = (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.57/1.59 thf(fact_158_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 2.57/1.59 thf(fact_159_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ A2) = A2))))))).
% 2.57/1.59 thf(fact_160_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 2.57/1.59 thf(fact_161_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C3:A]: (((((sup_sup @ A) @ B2) @ (((sup_sup @ A) @ A2) @ C3)) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B2) @ C3))))))))).
% 2.57/1.59 thf(fact_162_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X3:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X3)))))))).
% 2.57/1.59 thf(fact_163_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A3:A,B6:A]: ((((sup_sup @ A) @ B6) @ A3)))))))).
% 2.57/1.59 thf(fact_164_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 2.57/1.59 thf(fact_165_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ C3) = (((sup_sup @ A) @ A2) @ (((sup_sup @ A) @ B2) @ C3))))))))).
% 2.57/1.59 thf(fact_166_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F5:(A > B),G4:(A > B),X3:A]: ((((sup_sup @ B) @ (F5 @ X3)) @ (G4 @ X3))))))))).
% 2.57/1.59 thf(fact_167_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X3:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X3)))))))).
% 2.57/1.59 thf(fact_168_inf__sup__aci_I6_J, axiom, (! [A:$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))))))))).
% 2.57/1.59 thf(fact_169_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 2.57/1.59 thf(fact_170_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.57/1.59 thf(fact_171_Un__left__commute, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B5) @ C4)) = (((sup_sup @ (set @ A)) @ B5) @ (((sup_sup @ (set @ A)) @ A4) @ C4)))))).
% 2.57/1.59 thf(fact_172_Un__left__absorb, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) = (((sup_sup @ (set @ A)) @ A4) @ B5))))).
% 2.57/1.59 thf(fact_173_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: ((((sup_sup @ (set @ A)) @ B7) @ A6))))))).
% 2.57/1.59 thf(fact_174_Un__absorb, axiom, (! [A:$tType,A4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ A4) = A4)))).
% 2.57/1.59 thf(fact_175_Un__assoc, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C4) = (((sup_sup @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ B5) @ C4)))))).
% 2.57/1.59 thf(fact_176_ball__Un, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) => (P @ X3)))) = ((! [X3:A]: (((((member @ A) @ X3) @ A4) => (P @ X3)))) & (! [X3:A]: (((((member @ A) @ X3) @ B5) => (P @ X3))))))))).
% 2.57/1.59 thf(fact_177_bex__Un, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) & (P @ X3)))) = ((? [X3:A]: (((((member @ A) @ X3) @ A4) & (P @ X3)))) | (? [X3:A]: (((((member @ A) @ X3) @ B5) & (P @ X3))))))))).
% 2.57/1.59 thf(fact_178_UnI2, axiom, (! [A:$tType,C3:A,B5:(set @ A),A4:(set @ A)]: (((((member @ A) @ C3) @ B5) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.57/1.59 thf(fact_179_UnI1, axiom, (! [A:$tType,C3:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)))))).
% 2.57/1.59 thf(fact_180_UnE, axiom, (! [A:$tType,C3:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C3) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) => ((~ ((((member @ A) @ C3) @ A4))) => (((member @ A) @ C3) @ B5)))))).
% 2.57/1.59 thf(fact_181_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 2.57/1.59 thf(fact_182_lset__lappend, axiom, (! [A:$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)))))).
% 2.57/1.59 thf(fact_183_llist_Orel__sel, axiom, (! [B:$tType,A:$tType]: ((((coindu987187967t_all2 @ A) @ B) = (^ [R2:(A > (B > $o)),A3:(coindu1593790203_llist @ A),B6:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ A3) = ((coindu335574135_lnull @ B) @ B6)) & ((~ (((coindu335574135_lnull @ A) @ A3))) => ((~ (((coindu335574135_lnull @ B) @ B6))) => (((R2 @ ((coindu1046438764le_lhd @ A) @ A3)) @ ((coindu1046438764le_lhd @ B) @ B6)) & (((((coindu987187967t_all2 @ A) @ B) @ R2) @ ((coindu1047225960le_ltl @ A) @ A3)) @ ((coindu1047225960le_ltl @ B) @ B6)))))))))))).
% 2.57/1.59 thf(fact_184_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A4) => (A4 = B5)))))).
% 2.57/1.59 thf(fact_185_subsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.57/1.59 thf(fact_186_le__sup__iff, axiom, (! [A:$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))))))))).
% 2.57/1.59 thf(fact_187_sup_Obounded__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,C3:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C3)) @ A2) = ((((ord_less_eq @ A) @ B2) @ A2) & (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 2.57/1.59 thf(fact_188_Un__subset__iff, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A4) @ C4) & (((ord_less_eq @ (set @ A)) @ B5) @ C4)))))).
% 2.57/1.59 thf(fact_189_llist_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,X22:(coindu1593790203_llist @ A),Y21:B,Y22:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22)) = (((R @ X21) @ Y21) & (((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22)))))).
% 2.57/1.59 thf(fact_190_inf__sup__ord_I4_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.57/1.59 thf(fact_191_inf__sup__ord_I3_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.57/1.59 thf(fact_192_Un__mono, axiom, (! [A:$tType,A4:(set @ A),C4:(set @ A),B5:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C4) => ((((ord_less_eq @ (set @ A)) @ B5) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ (((sup_sup @ (set @ A)) @ C4) @ D3))))))).
% 2.57/1.59 thf(fact_193_Un__least, axiom, (! [A:$tType,A4:(set @ A),C4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ C4) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A4) @ B5)) @ C4)))))).
% 2.57/1.59 thf(fact_194_Un__upper1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ (((sup_sup @ (set @ A)) @ A4) @ B5))))).
% 2.57/1.59 thf(fact_195_Un__upper2, axiom, (! [A:$tType,B5:(set @ A),A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B5) @ (((sup_sup @ (set @ A)) @ A4) @ B5))))).
% 2.57/1.59 thf(fact_196_Un__absorb1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((sup_sup @ (set @ A)) @ A4) @ B5) = B5))))).
% 2.57/1.59 thf(fact_197_Un__absorb2, axiom, (! [A:$tType,B5:(set @ A),A4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A4) => ((((sup_sup @ (set @ A)) @ A4) @ B5) = A4))))).
% 2.57/1.59 thf(fact_198_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: (((((sup_sup @ (set @ A)) @ A6) @ B7) = B7))))))).
% 2.57/1.59 thf(fact_199_le__supE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A,X:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ X) => (~ (((((ord_less_eq @ A) @ A2) @ X) => (~ ((((ord_less_eq @ A) @ B2) @ X))))))))))))).
% 2.57/1.59 thf(fact_200_le__supI, axiom, (! [A:$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))))))))).
% 2.57/1.59 thf(fact_201_sup__ge1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.57/1.59 thf(fact_202_sup__ge2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.57/1.59 thf(fact_203_le__supI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X) @ A2) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.57/1.59 thf(fact_204_le__supI2, axiom, (! [A:$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))))))))).
% 2.57/1.59 thf(fact_205_sup_Omono, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C3:A,A2:A,D4:A,B2:A]: (((((ord_less_eq @ A) @ C3) @ A2) => ((((ord_less_eq @ A) @ D4) @ B2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C3) @ D4)) @ (((sup_sup @ A) @ A2) @ B2)))))))))).
% 2.57/1.59 thf(fact_206_sup__mono, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,C3:A,B2:A,D4:A]: (((((ord_less_eq @ A) @ A2) @ C3) => ((((ord_less_eq @ A) @ B2) @ D4) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B2)) @ (((sup_sup @ A) @ C3) @ D4)))))))))).
% 2.57/1.59 thf(fact_207_sup__least, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A,Z:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ Z) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y) @ Z)) @ X))))))))).
% 2.57/1.59 thf(fact_208_le__iff__sup, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X3:A,Y3:A]: (((((sup_sup @ A) @ X3) @ Y3) = Y3)))))))).
% 2.57/1.59 thf(fact_209_sup_OorderE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => (A2 = (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.57/1.59 thf(fact_210_sup_OorderI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = (((sup_sup @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 2.57/1.59 thf(fact_211_sup__unique, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [F:(A > (A > A)),X:A,Y:A]: (((! [X2:A,Y2:A]: ((((ord_less_eq @ A) @ X2) @ ((F @ X2) @ Y2)))) => ((! [X2:A,Y2:A]: ((((ord_less_eq @ A) @ Y2) @ ((F @ X2) @ Y2)))) => ((! [X2:A,Y2:A,Z3:A]: (((((ord_less_eq @ A) @ Y2) @ X2) => ((((ord_less_eq @ A) @ Z3) @ X2) => (((ord_less_eq @ A) @ ((F @ Y2) @ Z3)) @ X2))))) => ((((sup_sup @ A) @ X) @ Y) = ((F @ X) @ Y))))))))))).
% 2.57/1.59 thf(fact_212_sup_Oabsorb1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((sup_sup @ A) @ A2) @ B2) = A2)))))))).
% 2.57/1.59 thf(fact_213_sup_Oabsorb2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((sup_sup @ A) @ A2) @ B2) = B2)))))))).
% 2.57/1.59 thf(fact_214_sup__absorb1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((sup_sup @ A) @ X) @ Y) = X)))))))).
% 2.57/1.59 thf(fact_215_sup__absorb2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((sup_sup @ A) @ X) @ Y) = Y)))))))).
% 2.57/1.59 thf(fact_216_sup_OboundedE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,C3:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C3)) @ A2) => (~ (((((ord_less_eq @ A) @ B2) @ A2) => (~ ((((ord_less_eq @ A) @ C3) @ A2))))))))))))).
% 2.57/1.59 thf(fact_217_sup_OboundedI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C3) @ A2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B2) @ C3)) @ A2))))))))).
% 2.57/1.59 thf(fact_218_sup_Oorder__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B6:A,A3:A]: ((A3 = (((sup_sup @ A) @ A3) @ B6))))))))).
% 2.57/1.59 thf(fact_219_sup_Ocobounded1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.57/1.59 thf(fact_220_sup_Ocobounded2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: ((((ord_less_eq @ A) @ B2) @ (((sup_sup @ A) @ A2) @ B2)))))))).
% 2.57/1.59 thf(fact_221_sup_Oabsorb__iff1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B6:A,A3:A]: (((((sup_sup @ A) @ A3) @ B6) = A3)))))))).
% 2.57/1.59 thf(fact_222_sup_Oabsorb__iff2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A3:A,B6:A]: (((((sup_sup @ A) @ A3) @ B6) = B6)))))))).
% 2.57/1.59 thf(fact_223_sup_OcoboundedI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C3) @ A2) => (((ord_less_eq @ A) @ C3) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.57/1.59 thf(fact_224_sup_OcoboundedI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C3:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ C3) @ B2) => (((ord_less_eq @ A) @ C3) @ (((sup_sup @ A) @ A2) @ B2))))))))).
% 2.57/1.59 thf(fact_225_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X3:A]: (((P @ X3) => (Q @ X3)))))))).
% 2.57/1.59 thf(fact_226_contra__subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((~ ((((member @ A) @ C3) @ B5))) => (~ ((((member @ A) @ C3) @ A4)))))))).
% 2.57/1.59 thf(fact_227_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y4:(set @ A),Z4:(set @ A)]: ((Y4 = Z4))) = (^ [A6:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A6)))))))).
% 2.57/1.59 thf(fact_228_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ A4) @ C4)))))).
% 2.57/1.59 thf(fact_229_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.57/1.59 thf(fact_230_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.57/1.59 thf(fact_231_rev__subsetD, axiom, (! [A:$tType,C3:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C3) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((member @ A) @ C3) @ B5)))))).
% 2.57/1.59 thf(fact_232_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A6) => (((member @ A) @ T2) @ B7)))))))))).
% 2.57/1.59 thf(fact_233_set__rev__mp, axiom, (! [A:$tType,X:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ X) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((member @ A) @ X) @ B5)))))).
% 2.57/1.59 thf(fact_234_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A4))))).
% 2.57/1.59 thf(fact_235_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.57/1.59 thf(fact_236_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A6:(set @ A),B7:(set @ A)]: ((! [X3:A]: (((((member @ A) @ X3) @ A6) => (((member @ A) @ X3) @ B7)))))))))).
% 2.57/1.59 thf(fact_237_equalityE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))))).
% 2.57/1.59 thf(fact_238_subsetCE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B5)))))).
% 2.57/1.59 thf(fact_239_subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B5)))))).
% 2.57/1.59 thf(fact_240_in__mono, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 2.57/1.59 thf(fact_241_set__mp, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 2.57/1.59 thf(fact_242_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B2:A,A2:A]: (((! [A7:A,B4:A]: (((((ord_less_eq @ A) @ A7) @ B4) => ((P @ A7) @ B4)))) => ((((P @ B2) @ A2) => ((P @ A2) @ B2)) => ((P @ A2) @ B2))))))))).
% 2.57/1.59 thf(fact_243_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu987187967t_all2 @ A) @ A) @ (^ [Y4:A,Z4:A]: ((Y4 = Z4)))) = (^ [Y4:(coindu1593790203_llist @ A),Z4:(coindu1593790203_llist @ A)]: ((Y4 = Z4))))))).
% 2.57/1.59 thf(fact_244_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(coindu1593790203_llist @ B)]: (((! [X2:B]: (((Ra @ X2) @ X2))) => (((((coindu987187967t_all2 @ B) @ B) @ Ra) @ X) @ X))))).
% 2.57/1.59 thf(fact_245_llist_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ B))))).
% 2.57/1.59 thf(fact_246_llist_Orel__refl__strong, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Ra:(A > (A > $o))]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ X)) => ((Ra @ Z3) @ Z3)))) => (((((coindu987187967t_all2 @ A) @ A) @ Ra) @ X) @ X))))).
% 2.57/1.59 thf(fact_247_llist_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ B),Ra:(A > (B > $o))]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ X) @ Y) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ X)) => ((((member @ B) @ Yb) @ ((coindu1112613586e_lset @ B) @ Y)) => (((R @ Z3) @ Yb) => ((Ra @ Z3) @ Yb)))))) => (((((coindu987187967t_all2 @ A) @ B) @ Ra) @ X) @ Y)))))).
% 2.57/1.59 thf(fact_248_llist_Orel__cong, axiom, (! [A:$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 > $o))]: (((X = Ya) => ((Y = Xa) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((coindu1112613586e_lset @ A) @ Ya)) => ((((member @ B) @ Yb) @ ((coindu1112613586e_lset @ B) @ Xa)) => (((R @ Z3) @ Yb) = ((Ra @ Z3) @ Yb)))))) => ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X) @ Y) = (((((coindu987187967t_all2 @ A) @ B) @ Ra) @ Ya) @ Xa)))))))).
% 2.57/1.59 thf(fact_249_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,Y21:B,X22:(coindu1593790203_llist @ A),Y22:(coindu1593790203_llist @ B)]: ((((R @ X21) @ Y21) => ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22) => (((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 2.57/1.59 thf(fact_250_llist_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) @ (coindu1598213697e_LNil @ B))))))).
% 2.57/1.59 thf(fact_251_llist_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:B,Y22:(coindu1593790203_llist @ B)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 2.57/1.59 thf(fact_252_llist_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(coindu1593790203_llist @ A),B2:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ A2) @ B2) => (((A2 = (coindu1598213697e_LNil @ A)) => (B2 != (coindu1598213697e_LNil @ B))) => (~ ((! [X12:A,X24:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X12) @ X24)) => (! [Y12:B,Y24:(coindu1593790203_llist @ B)]: (((B2 = (((coindu1121789889_LCons @ B) @ Y12) @ Y24)) => (((R @ X12) @ Y12) => (~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X24) @ Y24))))))))))))))))).
% 2.57/1.59 thf(fact_253_lset__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((ord_less_eq @ (set @ A)) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs))) @ ((coindu1112613586e_lset @ A) @ Xs))))).
% 2.57/1.59 thf(fact_254_lset__lappend1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((ord_less_eq @ (set @ A)) @ ((coindu1112613586e_lset @ A) @ Xs)) @ ((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))).
% 2.57/1.59 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_sup @ A9) @ (type2 @ A9)) => ((semilattice_sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.57/1.59 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: ((((lattice @ A9) @ (type2 @ A9)) => ((lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.57/1.59 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1, axiom, (! [A8:$tType]: (((semilattice_sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.57/1.59 thf(tcon_Set_Oset___Lattices_Olattice_2, axiom, (! [A8:$tType]: (((lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.57/1.59 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_3, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.57/1.59 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.57/1.59 thf(tcon_HOL_Obool___Lattices_Olattice_4, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.57/1.59 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.57/1.59 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.57/1.59 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.57/1.59 thf(conj_0, conjecture, (((coindu1696667936prefix @ a) @ (((coindu268472904append @ a) @ xs) @ ys)) @ (((coindu268472904append @ a) @ xs) @ zs))).
% 2.57/1.59 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2DTF29397.p
% 2.57/1.59 ------------------------
% 2.83/1.64 ---- Cleaned THF ---
% 2.83/1.64 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 2.83/1.64 coindu1593790203_llist: $tType > $tType ).
% 2.83/1.64
% 2.83/1.64 thf(ty_t_Product__Type_Oprod,type,
% 2.83/1.64 product_prod: $tType > $tType > $tType ).
% 2.83/1.64
% 2.83/1.64 thf(ty_t_Set_Oset,type,
% 2.83/1.64 set: $tType > $tType ).
% 2.83/1.64
% 2.83/1.64 thf(ty_t_itself,type,
% 2.83/1.64 itself: $tType > $tType ).
% 2.83/1.64
% 2.83/1.64 thf(ty_tf_a,type,
% 2.83/1.64 a: $tType ).
% 2.83/1.64
% 2.83/1.64 thf(sy_cl_HOL_Otype,type,
% 2.83/1.64 type:
% 2.83/1.64 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_cl_Lattices_Olattice,type,
% 2.83/1.64 lattice:
% 2.83/1.64 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_cl_Orderings_Olinorder,type,
% 2.83/1.64 linorder:
% 2.83/1.64 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.83/1.64 semilattice_sup:
% 2.83/1.64 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset,type,
% 2.83/1.64 coindu1928975208n_lset:
% 2.83/1.64 !>[A: $tType] : ( ( set @ A ) > ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 2.83/1.64 coindu268472904append:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 2.83/1.64 coindu1213758845finite:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 2.83/1.64 coindu1121789889_LCons:
% 2.83/1.64 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 2.83/1.64 coindu1598213697e_LNil:
% 2.83/1.64 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 2.83/1.64 coindu882539134_llist:
% 2.83/1.64 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist,type,
% 2.83/1.64 coindu1244876290_llist:
% 2.83/1.64 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coindu1593790203_llist @ A ) ) > ( C > C ) > C > ( coindu1593790203_llist @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 2.83/1.64 coindu1046438764le_lhd:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 2.83/1.64 coindu987187967t_all2:
% 2.83/1.64 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 2.83/1.64 coindu335574135_lnull:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 2.83/1.64 coindu1112613586e_lset:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 2.83/1.64 coindu1047225960le_ltl:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 2.83/1.64 coindu567634248member:
% 2.83/1.64 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 2.83/1.64 coindu1696667936prefix:
% 2.83/1.64 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 2.83/1.64 coindu1599971794_llist:
% 2.83/1.64 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_If,type,
% 2.83/1.64 if:
% 2.83/1.64 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.83/1.64 sup_sup:
% 2.83/1.64 !>[A: $tType] : ( A > A > A ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.83/1.64 ord_less_eq:
% 2.83/1.64 !>[A: $tType] : ( A > A > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Product__Type_OPair,type,
% 2.83/1.64 product_Pair:
% 2.83/1.64 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.83/1.64 produc2004651681e_prod:
% 2.83/1.64 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.83/1.64 product_rec_prod:
% 2.83/1.64 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Pure_Otype,type,
% 2.83/1.64 type2:
% 2.83/1.64 !>[A: $tType] : ( itself @ A ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_Set_OCollect,type,
% 2.83/1.64 collect:
% 2.83/1.64 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_c_member,type,
% 2.83/1.64 member:
% 2.83/1.64 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(sy_v_xs,type,
% 2.83/1.64 xs: coindu1593790203_llist @ a ).
% 2.83/1.64
% 2.83/1.64 thf(sy_v_ys,type,
% 2.83/1.64 ys: coindu1593790203_llist @ a ).
% 2.83/1.64
% 2.83/1.64 thf(sy_v_zs,type,
% 2.83/1.64 zs: coindu1593790203_llist @ a ).
% 2.83/1.64
% 2.83/1.64 thf(fact_0_lprefix__refl,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062,axiom,
% 2.83/1.64 ( ( coindu1213758845finite @ a @ xs )
% 2.83/1.64 => ( coindu1696667936prefix @ a @ ys @ zs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_2_lappend__assoc,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 2.83/1.64 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_3_lprefix__trans,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_4_lprefix__antisym,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 2.83/1.64 => ( Xs = Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_5_lprefix__lappend,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_6_lprefix__down__linear,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 2.83/1.64 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 2.83/1.64 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_7_lprefix__lappend__sameI,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_8_lfinite__lappend,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_9_lappend__code_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 2.83/1.64 = Ys ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_10_lprefix__code_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_11_lappend__LNil2,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = Xs ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_12_lappend__inf,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.83/1.64 = Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_13_not__lfinite__lprefix__conv__eq,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 = ( Xs = Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_14_lappend__code_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_15_LCons__lprefix__LCons,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.83/1.64 = ( ( X = Y )
% 2.83/1.64 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_16_lappend_Odisc__iff_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 2.83/1.64 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_17_lnull__lappend,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_18_lappend__LNil__LNil,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_19_LNil__eq__lappend__iff,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu1598213697e_LNil @ A )
% 2.83/1.64 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( ( Xs
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 & ( Ys
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_20_llist_Oinject,axiom,
% 2.83/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 2.83/1.64 = ( ( X21 = Y21 )
% 2.83/1.64 & ( X22 = Y22 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_21_lfinite__code_I2_J,axiom,
% 2.83/1.64 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 2.83/1.64 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_22_lfinite__LCons,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.83/1.64 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_23_lfinite__code_I1_J,axiom,
% 2.83/1.64 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_24_lprefix__LNil,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_25_llist_Odisc_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.83/1.64 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_26_llist_Odisc_I1_J,axiom,
% 2.83/1.64 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_27_llist_OdiscI_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Llist
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.83/1.64 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_28_llist_OdiscI_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Llist
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_29_llist_Ocollapse_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Llist )
% 2.83/1.64 => ( Llist
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_30_llist_Odistinct_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1598213697e_LNil @ A )
% 2.83/1.64 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_31_lfinite_Ocases,axiom,
% 2.83/1.64 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ A2 )
% 2.83/1.64 => ( ( A2
% 2.83/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ? [X2: A] :
% 2.83/1.64 ( A2
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.83/1.64 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_32_lfinite_Osimps,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu1213758845finite @ A )
% 2.83/1.64 = ( ^ [A3: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( A3
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 | ? [Xs3: coindu1593790203_llist @ A,X3: A] :
% 2.83/1.64 ( ( A3
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.83/1.64 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_33_llist_Oexhaust,axiom,
% 2.83/1.64 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Y
% 2.83/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_34_neq__LNil__conv,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs
% 2.83/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = ( ? [X3: A,Xs4: coindu1593790203_llist @ A] :
% 2.83/1.64 ( Xs
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_35_not__lnull__conv,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 2.83/1.64 = ( ? [X3: A,Xs4: coindu1593790203_llist @ A] :
% 2.83/1.64 ( Xs
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_36_lappend_Oexhaust,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_37_lfinite_Oinducts,axiom,
% 2.83/1.64 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ X )
% 2.83/1.64 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.83/1.64 => ( ( P @ Xs2 )
% 2.83/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.83/1.64 => ( P @ X ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_38_lnull__def,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A )
% 2.83/1.64 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( Llist2
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_39_lnull__imp__lfinite,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_40_lfinite__LNil,axiom,
% 2.83/1.64 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_41_lfinite__LConsI,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_42_lappend_Octr_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.83/1.64 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_43_lappend__snocL1__conv__LCons2,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 2.83/1.64 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_44_mem__Collect__eq,axiom,
% 2.83/1.64 ! [A: $tType,A2: A,P: A > $o] :
% 2.83/1.64 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.83/1.64 = ( P @ A2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_45_Collect__mem__eq,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A] :
% 2.83/1.64 ( ( collect @ A
% 2.83/1.64 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 2.83/1.64 = A4 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_46_Collect__cong,axiom,
% 2.83/1.64 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.64 ( ! [X2: A] :
% 2.83/1.64 ( ( P @ X2 )
% 2.83/1.64 = ( Q @ X2 ) )
% 2.83/1.64 => ( ( collect @ A @ P )
% 2.83/1.64 = ( collect @ A @ Q ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_47_ext,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.83/1.64 ( ! [X2: A] :
% 2.83/1.64 ( ( F @ X2 )
% 2.83/1.64 = ( G @ X2 ) )
% 2.83/1.64 => ( F = G ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_48_lprefix__LCons__conv,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.83/1.64 = ( ( Xs
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 | ? [Xs4: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Y @ Xs4 ) )
% 2.83/1.64 & ( coindu1696667936prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_49_lprefix_Ocoinduct,axiom,
% 2.83/1.64 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( X4 @ X @ Xa )
% 2.83/1.64 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( X4 @ X2 @ Xa2 )
% 2.83/1.64 => ( ? [Xs5: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( X2
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 & ( Xa2 = Xs5 ) )
% 2.83/1.64 | ? [Xs5: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,Xb: A] :
% 2.83/1.64 ( ( X2
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Xb @ Xs5 ) )
% 2.83/1.64 & ( Xa2
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Xb @ Ys2 ) )
% 2.83/1.64 & ( ( X4 @ Xs5 @ Ys2 )
% 2.83/1.64 | ( coindu1696667936prefix @ A @ Xs5 @ Ys2 ) ) ) ) )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_50_lprefix_Osimps,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A )
% 2.83/1.64 = ( ^ [A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ? [Xs3: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( A1
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 & ( A22 = Xs3 ) )
% 2.83/1.64 | ? [Xs3: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X3: A] :
% 2.83/1.64 ( ( A1
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.83/1.64 & ( A22
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Ys3 ) )
% 2.83/1.64 & ( coindu1696667936prefix @ A @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_51_lprefix_Ocases,axiom,
% 2.83/1.64 ! [A: $tType,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ A12 @ A23 )
% 2.83/1.64 => ( ( ( A12
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ! [Xs2: coindu1593790203_llist @ A] : ( A23 != Xs2 ) )
% 2.83/1.64 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X2: A] :
% 2.83/1.64 ( ( A12
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.83/1.64 => ( ( A23
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Ys4 ) )
% 2.83/1.64 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys4 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_52_lprefix__code_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_53_lprefix__not__lnullD,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_54_lprefix__lnullD,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.83/1.64 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_55_lappend__lnull2,axiom,
% 2.83/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Ys )
% 2.83/1.64 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.83/1.64 = Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_56_lappend__lnull1,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.83/1.64 = Ys ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_57_lprefix__lnull,axiom,
% 2.83/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Ys )
% 2.83/1.64 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_58_lnull__lprefix,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_59_lappend_Odisc_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.83/1.64 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_60_lappend_Odisc_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.83/1.64 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_61_LCons__lprefix__conv,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 2.83/1.64 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Ys
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X @ Ys5 ) )
% 2.83/1.64 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_62_Le__LCons,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_63_LNil__lprefix,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_64_lappend__eq__LNil__iff,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = ( ( Xs
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 & ( Ys
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_65_lmember__code_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,X: A] :
% 2.83/1.64 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_66_lmember__code_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.83/1.64 = ( ( X = Y )
% 2.83/1.64 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_67_lprefixI,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 2.83/1.64 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs2 @ Ys4 ) @ X4 )
% 2.83/1.64 => ( ( coindu335574135_lnull @ A @ Xs2 )
% 2.83/1.64 | ? [X5: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs2
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X5 @ Xs6 ) )
% 2.83/1.64 & ( Ys4
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X5 @ Ys6 ) )
% 2.83/1.64 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 2.83/1.64 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_68_split__llist,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ? [Ys4: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs
% 2.83/1.64 = ( coindu268472904append @ A @ Ys4 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 2.83/1.64 & ( coindu1213758845finite @ A @ Ys4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_69_split__llist__first,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ? [Ys4: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs
% 2.83/1.64 = ( coindu268472904append @ A @ Ys4 @ ( coindu1121789889_LCons @ A @ X @ Zs2 ) ) )
% 2.83/1.64 & ( coindu1213758845finite @ A @ Ys4 )
% 2.83/1.64 & ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys4 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_70_lhd__lappend,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 2.83/1.64 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_71_gen__lset__code_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A] :
% 2.83/1.64 ( ( coindu1928975208n_lset @ A @ A4 @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = A4 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_72_llist_Ocorec__code,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType] :
% 2.83/1.64 ( ( coindu1244876290_llist @ C @ A )
% 2.83/1.64 = ( ^ [P2: C > $o,G21: C > A,Q22: C > $o,G221: C > ( coindu1593790203_llist @ A ),G222: C > C,A3: C] : ( if @ ( coindu1593790203_llist @ A ) @ ( P2 @ A3 ) @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ A @ ( G21 @ A3 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_73_unfold__llist_Ocode,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType] :
% 2.83/1.64 ( ( coindu1599971794_llist @ A @ B )
% 2.83/1.64 = ( ^ [P2: A > $o,G21: A > B,G22: A > A,A3: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P2 @ A3 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G21 @ A3 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_74_ltl__lappend,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 2.83/1.64 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_75_unfold__llist_Odisc__iff_I1_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,G212: A > B,G223: A > A,A2: A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) )
% 2.83/1.64 = ( P3 @ A2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_76_unfold__llist_Odisc__iff_I2_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,G212: A > B,G223: A > A,A2: A] :
% 2.83/1.64 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) ) )
% 2.83/1.64 = ( ~ ( P3 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_77_lfinite__ltl,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 2.83/1.64 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_78_unfold__llist__eq__LCons,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.83/1.64 = ( ~ ( IS_LNIL @ B2 )
% 2.83/1.64 & ( X
% 2.83/1.64 = ( LHD @ B2 ) )
% 2.83/1.64 & ( Xs
% 2.83/1.64 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_79_llist_Ocorec__disc__iff_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C,A2: C] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.83/1.64 = ( P3 @ A2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_80_llist_Ocorec__disc__iff_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C,A2: C] :
% 2.83/1.64 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) )
% 2.83/1.64 = ( ~ ( P3 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_81_unfold__llist__id,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 2.83/1.64 = Xs ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_82_lhd__LCons__ltl,axiom,
% 2.83/1.64 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 2.83/1.64 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 2.83/1.64 = Llist ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_83_llist__set__induct,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 2.83/1.64 => ( P @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ Xs2 ) )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A,Y2: A] :
% 2.83/1.64 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 2.83/1.64 => ( ( member @ A @ Y2 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 2.83/1.64 => ( ( P @ Y2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 2.83/1.64 => ( P @ Y2 @ Xs2 ) ) ) )
% 2.83/1.64 => ( P @ X @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_84_lset__lmember,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 = ( coindu567634248member @ A @ X @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_85_in__lset__ltlD,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) )
% 2.83/1.64 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_86_unfold__llist_Osimps_I3_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) )
% 2.83/1.64 = ( G212 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_87_unfold__llist_Osimps_I4_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) )
% 2.83/1.64 = ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_88_llist_Ocorec__sel_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1046438764le_lhd @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.83/1.64 = ( G212 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_89_llist_Ocorec__sel_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,A2: C,Q222: C > $o,G212: C > A,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ( ( ( Q222 @ A2 )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.83/1.64 = ( G2212 @ A2 ) ) )
% 2.83/1.64 & ( ~ ( Q222 @ A2 )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) )
% 2.83/1.64 = ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_90_llist_Oset__sel_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,A2: coindu1593790203_llist @ A,X: A] :
% 2.83/1.64 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 2.83/1.64 => ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ A2 ) ) )
% 2.83/1.64 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_91_llist_Oset__sel_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 2.83/1.64 => ( member @ A @ ( coindu1046438764le_lhd @ A @ A2 ) @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_92_llist_Ocoinduct__strong,axiom,
% 2.83/1.64 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( R @ Llist @ Llist3 )
% 2.83/1.64 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( R @ Llist4 @ Llist5 )
% 2.83/1.64 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 2.83/1.64 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 2.83/1.64 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 2.83/1.64 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 2.83/1.64 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) )
% 2.83/1.64 | ( ( coindu1047225960le_ltl @ A @ Llist4 )
% 2.83/1.64 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 2.83/1.64 => ( Llist = Llist3 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_93_llist_Ocoinduct,axiom,
% 2.83/1.64 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( R @ Llist @ Llist3 )
% 2.83/1.64 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( R @ Llist4 @ Llist5 )
% 2.83/1.64 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 2.83/1.64 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 2.83/1.64 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 2.83/1.64 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 2.83/1.64 & ( R @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 2.83/1.64 => ( Llist = Llist3 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_94_llist_Oexpand,axiom,
% 2.83/1.64 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu335574135_lnull @ A @ Llist )
% 2.83/1.64 = ( coindu335574135_lnull @ A @ Llist3 ) )
% 2.83/1.64 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 2.83/1.64 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Llist3 ) )
% 2.83/1.64 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 2.83/1.64 = ( coindu1047225960le_ltl @ A @ Llist3 ) ) ) ) )
% 2.83/1.64 => ( Llist = Llist3 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_95_ltl__unfold__llist,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 2.83/1.64 ( ( ( IS_LNIL @ A2 )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) )
% 2.83/1.64 & ( ~ ( IS_LNIL @ A2 )
% 2.83/1.64 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 2.83/1.64 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_96_llist_Oexhaust__sel,axiom,
% 2.83/1.64 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Llist
% 2.83/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ( Llist
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_97_eq__LConsD,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.83/1.64 => ( ( Xs
% 2.83/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 2.83/1.64 = Y )
% 2.83/1.64 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 2.83/1.64 = Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_98_lprefix__coinduct,axiom,
% 2.83/1.64 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( P @ Xs @ Ys )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( P @ Xs2 @ Ys4 )
% 2.83/1.64 => ( ( ( coindu335574135_lnull @ A @ Ys4 )
% 2.83/1.64 => ( coindu335574135_lnull @ A @ Xs2 ) )
% 2.83/1.64 & ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Ys4 )
% 2.83/1.64 => ( ( ( coindu1046438764le_lhd @ A @ Xs2 )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Ys4 ) )
% 2.83/1.64 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys4 ) )
% 2.83/1.64 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys4 ) ) ) ) ) ) ) )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_99_lprefix__expand,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 2.83/1.64 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 2.83/1.64 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_100_llist_Oset__induct,axiom,
% 2.83/1.64 ! [A: $tType,X: A,A2: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A2 ) )
% 2.83/1.64 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 2.83/1.64 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A,Xa2: A] :
% 2.83/1.64 ( ( member @ A @ Xa2 @ ( coindu1112613586e_lset @ A @ Z2 ) )
% 2.83/1.64 => ( ( P @ Xa2 @ Z2 )
% 2.83/1.64 => ( P @ Xa2 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) ) ) )
% 2.83/1.64 => ( P @ X @ A2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_101_llist_Oset__cases,axiom,
% 2.83/1.64 ! [A: $tType,E: A,A2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A2 ) )
% 2.83/1.64 => ( ! [Z2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( A2
% 2.83/1.64 != ( coindu1121789889_LCons @ A @ E @ Z2 ) )
% 2.83/1.64 => ~ ! [Z1: A,Z2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( A2
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 2.83/1.64 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z2 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_102_lset__induct_H,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 2.83/1.64 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 2.83/1.64 => ( ( P @ Xs2 )
% 2.83/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) )
% 2.83/1.64 => ( P @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_103_lset__induct,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 2.83/1.64 => ( ! [X6: A,Xs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 2.83/1.64 => ( ( X != X6 )
% 2.83/1.64 => ( ( P @ Xs2 )
% 2.83/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) ) ) ) )
% 2.83/1.64 => ( P @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_104_lset__cases,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ( ! [Xs7: coindu1593790203_llist @ A] :
% 2.83/1.64 ( Xs
% 2.83/1.64 != ( coindu1121789889_LCons @ A @ X @ Xs7 ) )
% 2.83/1.64 => ~ ! [X6: A,Xs7: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( Xs
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X6 @ Xs7 ) )
% 2.83/1.64 => ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs7 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_105_llist_Oset__intros_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,A12: A,A23: coindu1593790203_llist @ A] : ( member @ A @ A12 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A12 @ A23 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_106_llist_Oset__intros_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,X: A,A23: coindu1593790203_llist @ A,A12: A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A23 ) )
% 2.83/1.64 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A12 @ A23 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_107_lset__intros_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_108_lset__intros_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,X7: A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X7 @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_109_lnull__ltlI,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_110_ltl__simps_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.83/1.64 = X22 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_111_ltl__simps_I1_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_112_lprefix__ltlI,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_113_lhd__LCons,axiom,
% 2.83/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.83/1.64 = X21 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_114_unfold__llist_Odisc_I1_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.83/1.64 ( ( P3 @ A2 )
% 2.83/1.64 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_115_unfold__llist_Odisc_I2_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_116_unfold__llist_Octr_I2_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 2.83/1.64 = ( coindu1121789889_LCons @ B @ ( G212 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_117_unfold__llist_Octr_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.83/1.64 ( ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 2.83/1.64 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_118_llist_Ocorec__disc_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 2.83/1.64 ( ( P3 @ A2 )
% 2.83/1.64 => ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_119_llist_Ocorec__disc_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_120_llist_Ocorec_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 2.83/1.64 ( ~ ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ ( G212 @ A2 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_121_llist_Ocorec_I1_J,axiom,
% 2.83/1.64 ! [C: $tType,A: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2222: C > C] :
% 2.83/1.64 ( ( P3 @ A2 )
% 2.83/1.64 => ( ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_122_in__lset__lappend__iff,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 2.83/1.64 = ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.83/1.64 | ( ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 & ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_123_lappend__ltl,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys )
% 2.83/1.64 = ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_124_lfinite__induct,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu335574135_lnull @ A @ Xs2 )
% 2.83/1.64 => ( P @ Xs2 ) )
% 2.83/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 2.83/1.64 => ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 2.83/1.64 => ( P @ Xs2 ) ) ) )
% 2.83/1.64 => ( P @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_125_lprefix__lhdD,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.83/1.64 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 2.83/1.64 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_126_old_Oprod_Oinject,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 2.83/1.64 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.83/1.64 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 2.83/1.64 = ( ( A2 = A5 )
% 2.83/1.64 & ( B2 = B3 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_127_prod_Oinject,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y23: B] :
% 2.83/1.64 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 2.83/1.64 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 2.83/1.64 = ( ( X1 = Y1 )
% 2.83/1.64 & ( X23 = Y23 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_128_llist_Osplit__sel__asm,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 2.83/1.64 = ( ~ ( ( ( Llist
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 & ~ ( P @ F1 ) )
% 2.83/1.64 | ( ( Llist
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 2.83/1.64 & ~ ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_129_llist_Osplit__sel,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( P @ ( coindu882539134_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 2.83/1.64 = ( ( ( Llist
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ( P @ F1 ) )
% 2.83/1.64 & ( ( Llist
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 2.83/1.64 => ( P @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_130_llist_Ocase__eq__if,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType] :
% 2.83/1.64 ( ( coindu882539134_llist @ B @ A )
% 2.83/1.64 = ( ^ [F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist2: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist2 ) @ F12 @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_131_lset__lappend__lfinite,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_132_llist_Osimps_I5_J,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.83/1.64 = ( F2 @ X21 @ X22 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_133_llist_Osimps_I4_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,F1: B,F2: A > ( coindu1593790203_llist @ A ) > B] :
% 2.83/1.64 ( ( coindu882539134_llist @ B @ A @ F1 @ F2 @ ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 = F1 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_134_gen__lset__def,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu1928975208n_lset @ A )
% 2.83/1.64 = ( ^ [A6: set @ A,Xs3: coindu1593790203_llist @ A] : ( sup_sup @ ( set @ A ) @ A6 @ ( coindu1112613586e_lset @ A @ Xs3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_135_surj__pair,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 2.83/1.64 ? [X2: A,Y2: B] :
% 2.83/1.64 ( P3
% 2.83/1.64 = ( product_Pair @ A @ B @ X2 @ Y2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_136_prod__cases,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 2.83/1.64 ( ! [A7: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B4 ) )
% 2.83/1.64 => ( P @ P3 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_137_Pair__inject,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,A2: A,B2: B,A5: A,B3: B] :
% 2.83/1.64 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 2.83/1.64 = ( product_Pair @ A @ B @ A5 @ B3 ) )
% 2.83/1.64 => ~ ( ( A2 = A5 )
% 2.83/1.64 => ( B2 != B3 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_138_prod__cases3,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.83/1.64 ~ ! [A7: A,B4: B,C2: C] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_139_prod__cases4,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.83/1.64 ~ ! [A7: A,B4: B,C2: C,D2: D] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_140_prod__cases5,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 2.83/1.64 ~ ! [A7: A,B4: B,C2: C,D2: D,E3: E2] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_141_prod__cases6,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) )] :
% 2.83/1.64 ~ ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F3 ) @ D2 @ ( product_Pair @ E2 @ F3 @ E3 @ F4 ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_142_prod__cases7,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,C: $tType,D: $tType,E2: $tType,F3: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 2.83/1.64 ~ ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3,G3: G2] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F3 @ G2 ) @ E3 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_143_prod__induct3,axiom,
% 2.83/1.64 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.83/1.64 ( ! [A7: A,B4: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A7 @ ( product_Pair @ B @ C @ B4 @ C2 ) ) )
% 2.83/1.64 => ( P @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_144_prod__induct4,axiom,
% 2.83/1.64 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.83/1.64 ( ! [A7: A,B4: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.83/1.64 => ( P @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_145_prod__induct5,axiom,
% 2.83/1.64 ! [E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) )] :
% 2.83/1.64 ( ! [A7: A,B4: B,C2: C,D2: D,E3: E2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E2 ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E2 ) @ C2 @ ( product_Pair @ D @ E2 @ D2 @ E3 ) ) ) ) )
% 2.83/1.64 => ( P @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_146_prod__induct6,axiom,
% 2.83/1.64 ! [F3: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) )] :
% 2.83/1.64 ( ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ F3 ) @ D2 @ ( product_Pair @ E2 @ F3 @ E3 @ F4 ) ) ) ) ) )
% 2.83/1.64 => ( P @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_147_prod__induct7,axiom,
% 2.83/1.64 ! [G2: $tType,F3: $tType,E2: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 2.83/1.64 ( ! [A7: A,B4: B,C2: C,D2: D,E3: E2,F4: F3,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A7 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E2 @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E2 @ ( product_prod @ F3 @ G2 ) @ E3 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) )
% 2.83/1.64 => ( P @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_148_old_Oprod_Oexhaust,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.83/1.64 ~ ! [A7: A,B4: B] :
% 2.83/1.64 ( Y
% 2.83/1.64 != ( product_Pair @ A @ B @ A7 @ B4 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_149_old_Oprod_Oinducts,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.83/1.64 ( ! [A7: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A7 @ B4 ) )
% 2.83/1.64 => ( P @ Prod ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_150_lset__lappend__conv,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( sup_sup @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ Ys ) ) ) )
% 2.83/1.64 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.83/1.64 => ( ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.83/1.64 = ( coindu1112613586e_lset @ A @ Xs ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_151_old_Oprod_Orec,axiom,
% 2.83/1.64 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 2.83/1.64 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.83/1.64 = ( F1 @ A2 @ B2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_152_UnCI,axiom,
% 2.83/1.64 ! [A: $tType,C3: A,B5: set @ A,A4: set @ A] :
% 2.83/1.64 ( ( ~ ( member @ A @ C3 @ B5 )
% 2.83/1.64 => ( member @ A @ C3 @ A4 ) )
% 2.83/1.64 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_153_Un__iff,axiom,
% 2.83/1.64 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.83/1.64 = ( ( member @ A @ C3 @ A4 )
% 2.83/1.64 | ( member @ A @ C3 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_154_sup__apply,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.83/1.64 => ( ( sup_sup @ ( A > B ) )
% 2.83/1.64 = ( ^ [F5: A > B,G4: A > B,X3: A] : ( sup_sup @ B @ ( F5 @ X3 ) @ ( G4 @ X3 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_155_sup_Oright__idem,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A] :
% 2.83/1.64 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ B2 )
% 2.83/1.64 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_156_sup__left__idem,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A] :
% 2.83/1.64 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.83/1.64 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_157_sup_Oleft__idem,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A] :
% 2.83/1.64 ( ( sup_sup @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) )
% 2.83/1.64 = ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_158_sup__idem,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A] :
% 2.83/1.64 ( ( sup_sup @ A @ X @ X )
% 2.83/1.64 = X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_159_sup_Oidem,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A] :
% 2.83/1.64 ( ( sup_sup @ A @ A2 @ A2 )
% 2.83/1.64 = A2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_160_sup__left__commute,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A,Z: A] :
% 2.83/1.64 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 2.83/1.64 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_161_sup_Oleft__commute,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,A2: A,C3: A] :
% 2.83/1.64 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A2 @ C3 ) )
% 2.83/1.64 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_162_sup__commute,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( sup_sup @ A )
% 2.83/1.64 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_163_sup_Ocommute,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( sup_sup @ A )
% 2.83/1.64 = ( ^ [A3: A,B6: A] : ( sup_sup @ A @ B6 @ A3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_164_sup__assoc,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A,Z: A] :
% 2.83/1.64 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.83/1.64 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_165_sup_Oassoc,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A,C3: A] :
% 2.83/1.64 ( ( sup_sup @ A @ ( sup_sup @ A @ A2 @ B2 ) @ C3 )
% 2.83/1.64 = ( sup_sup @ A @ A2 @ ( sup_sup @ A @ B2 @ C3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_166_sup__fun__def,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.83/1.64 => ( ( sup_sup @ ( A > B ) )
% 2.83/1.64 = ( ^ [F5: A > B,G4: A > B,X3: A] : ( sup_sup @ B @ ( F5 @ X3 ) @ ( G4 @ X3 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_167_inf__sup__aci_I5_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( sup_sup @ A )
% 2.83/1.64 = ( ^ [X3: A,Y3: A] : ( sup_sup @ A @ Y3 @ X3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_168_inf__sup__aci_I6_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A,Z: A] :
% 2.83/1.64 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.83/1.64 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_169_inf__sup__aci_I7_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A,Z: A] :
% 2.83/1.64 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 2.83/1.64 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_170_inf__sup__aci_I8_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A] :
% 2.83/1.64 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.83/1.64 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_171_Un__left__commute,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 2.83/1.64 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C4 ) )
% 2.83/1.64 = ( sup_sup @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_172_Un__left__absorb,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.83/1.64 = ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_173_Un__commute,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( sup_sup @ ( set @ A ) )
% 2.83/1.64 = ( ^ [A6: set @ A,B7: set @ A] : ( sup_sup @ ( set @ A ) @ B7 @ A6 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_174_Un__absorb,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A] :
% 2.83/1.64 ( ( sup_sup @ ( set @ A ) @ A4 @ A4 )
% 2.83/1.64 = A4 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_175_Un__assoc,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 2.83/1.64 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C4 )
% 2.83/1.64 = ( sup_sup @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ B5 @ C4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_176_ball__Un,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 2.83/1.64 ( ( ! [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.83/1.64 => ( P @ X3 ) ) )
% 2.83/1.64 = ( ! [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ A4 )
% 2.83/1.64 => ( P @ X3 ) )
% 2.83/1.64 & ! [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ B5 )
% 2.83/1.64 => ( P @ X3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_177_bex__Un,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,P: A > $o] :
% 2.83/1.64 ( ( ? [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.83/1.64 & ( P @ X3 ) ) )
% 2.83/1.64 = ( ? [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ A4 )
% 2.83/1.64 & ( P @ X3 ) )
% 2.83/1.64 | ? [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ B5 )
% 2.83/1.64 & ( P @ X3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_178_UnI2,axiom,
% 2.83/1.64 ! [A: $tType,C3: A,B5: set @ A,A4: set @ A] :
% 2.83/1.64 ( ( member @ A @ C3 @ B5 )
% 2.83/1.64 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_179_UnI1,axiom,
% 2.83/1.64 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( member @ A @ C3 @ A4 )
% 2.83/1.64 => ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_180_UnE,axiom,
% 2.83/1.64 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( member @ A @ C3 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) )
% 2.83/1.64 => ( ~ ( member @ A @ C3 @ A4 )
% 2.83/1.64 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_181_internal__case__prod__conv,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 2.83/1.64 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 2.83/1.64 = ( C3 @ A2 @ B2 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_182_lset__lappend,axiom,
% 2.83/1.64 ! [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 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_183_llist_Orel__sel,axiom,
% 2.83/1.64 ! [B: $tType,A: $tType] :
% 2.83/1.64 ( ( coindu987187967t_all2 @ A @ B )
% 2.83/1.64 = ( ^ [R2: A > B > $o,A3: coindu1593790203_llist @ A,B6: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ( ( coindu335574135_lnull @ A @ A3 )
% 2.83/1.64 = ( coindu335574135_lnull @ B @ B6 ) )
% 2.83/1.64 & ( ~ ( coindu335574135_lnull @ A @ A3 )
% 2.83/1.64 => ( ~ ( coindu335574135_lnull @ B @ B6 )
% 2.83/1.64 => ( ( R2 @ ( coindu1046438764le_lhd @ A @ A3 ) @ ( coindu1046438764le_lhd @ B @ B6 ) )
% 2.83/1.64 & ( coindu987187967t_all2 @ A @ B @ R2 @ ( coindu1047225960le_ltl @ A @ A3 ) @ ( coindu1047225960le_ltl @ B @ B6 ) ) ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_184_subset__antisym,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.83/1.64 => ( A4 = B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_185_subsetI,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ! [X2: A] :
% 2.83/1.64 ( ( member @ A @ X2 @ A4 )
% 2.83/1.64 => ( member @ A @ X2 @ B5 ) )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_186_le__sup__iff,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A,Z: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.83/1.64 = ( ( ord_less_eq @ A @ X @ Z )
% 2.83/1.64 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_187_sup_Obounded__iff,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,C3: A,A2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C3 ) @ A2 )
% 2.83/1.64 = ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.64 & ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_188_Un__subset__iff,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C4 )
% 2.83/1.64 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ C4 )
% 2.83/1.64 & ( ord_less_eq @ ( set @ A ) @ B5 @ C4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_189_llist_Orel__inject_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 2.83/1.64 = ( ( R @ X21 @ Y21 )
% 2.83/1.64 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_190_inf__sup__ord_I4_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_191_inf__sup__ord_I3_J,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( lattice @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_192_Un__mono,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,C4: set @ A,B5: set @ A,D3: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C4 )
% 2.83/1.64 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ D3 )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_193_Un__least,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,C4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ C4 )
% 2.83/1.64 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) @ C4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_194_Un__upper1,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_195_Un__upper2,axiom,
% 2.83/1.64 ! [A: $tType,B5: set @ A,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ B5 @ ( sup_sup @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_196_Un__absorb1,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 = B5 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_197_Un__absorb2,axiom,
% 2.83/1.64 ! [A: $tType,B5: set @ A,A4: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.83/1.64 => ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 = A4 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_198_subset__Un__eq,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.64 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.83/1.64 ( ( sup_sup @ ( set @ A ) @ A6 @ B7 )
% 2.83/1.64 = B7 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_199_le__supE,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A,X: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X )
% 2.83/1.64 => ~ ( ( ord_less_eq @ A @ A2 @ X )
% 2.83/1.64 => ~ ( ord_less_eq @ A @ B2 @ X ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_200_le__supI,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,X: A,B2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ A2 @ X )
% 2.83/1.64 => ( ( ord_less_eq @ A @ B2 @ X )
% 2.83/1.64 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ X ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_201_sup__ge1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_202_sup__ge2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_203_le__supI1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,A2: A,B2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ X @ A2 )
% 2.83/1.64 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_204_le__supI2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,B2: A,A2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ X @ B2 )
% 2.83/1.64 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_205_sup_Omono,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [C3: A,A2: A,D4: A,B2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ C3 @ A2 )
% 2.83/1.64 => ( ( ord_less_eq @ A @ D4 @ B2 )
% 2.83/1.64 => ( ord_less_eq @ A @ ( sup_sup @ A @ C3 @ D4 ) @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_206_sup__mono,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,C3: A,B2: A,D4: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ A2 @ C3 )
% 2.83/1.64 => ( ( ord_less_eq @ A @ B2 @ D4 )
% 2.83/1.64 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B2 ) @ ( sup_sup @ A @ C3 @ D4 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_207_sup__least,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [Y: A,X: A,Z: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ Y @ X )
% 2.83/1.64 => ( ( ord_less_eq @ A @ Z @ X )
% 2.83/1.64 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_208_le__iff__sup,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( ord_less_eq @ A )
% 2.83/1.64 = ( ^ [X3: A,Y3: A] :
% 2.83/1.64 ( ( sup_sup @ A @ X3 @ Y3 )
% 2.83/1.64 = Y3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_209_sup_OorderE,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,A2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.64 => ( A2
% 2.83/1.64 = ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_210_sup_OorderI,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A] :
% 2.83/1.64 ( ( A2
% 2.83/1.64 = ( sup_sup @ A @ A2 @ B2 ) )
% 2.83/1.64 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_211_sup__unique,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [F: A > A > A,X: A,Y: A] :
% 2.83/1.64 ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y2 ) )
% 2.83/1.64 => ( ! [X2: A,Y2: A] : ( ord_less_eq @ A @ Y2 @ ( F @ X2 @ Y2 ) )
% 2.83/1.64 => ( ! [X2: A,Y2: A,Z3: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ Y2 @ X2 )
% 2.83/1.64 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 2.83/1.64 => ( ord_less_eq @ A @ ( F @ Y2 @ Z3 ) @ X2 ) ) )
% 2.83/1.64 => ( ( sup_sup @ A @ X @ Y )
% 2.83/1.64 = ( F @ X @ Y ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_212_sup_Oabsorb1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,A2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.64 => ( ( sup_sup @ A @ A2 @ B2 )
% 2.83/1.64 = A2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_213_sup_Oabsorb2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.83/1.64 => ( ( sup_sup @ A @ A2 @ B2 )
% 2.83/1.64 = B2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_214_sup__absorb1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [Y: A,X: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ Y @ X )
% 2.83/1.64 => ( ( sup_sup @ A @ X @ Y )
% 2.83/1.64 = X ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_215_sup__absorb2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [X: A,Y: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ X @ Y )
% 2.83/1.64 => ( ( sup_sup @ A @ X @ Y )
% 2.83/1.64 = Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_216_sup_OboundedE,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,C3: A,A2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C3 ) @ A2 )
% 2.83/1.64 => ~ ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.64 => ~ ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_217_sup_OboundedI,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,A2: A,C3: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.83/1.64 => ( ( ord_less_eq @ A @ C3 @ A2 )
% 2.83/1.64 => ( ord_less_eq @ A @ ( sup_sup @ A @ B2 @ C3 ) @ A2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_218_sup_Oorder__iff,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( ord_less_eq @ A )
% 2.83/1.64 = ( ^ [B6: A,A3: A] :
% 2.83/1.64 ( A3
% 2.83/1.64 = ( sup_sup @ A @ A3 @ B6 ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_219_sup_Ocobounded1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_220_sup_Ocobounded2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [B2: A,A2: A] : ( ord_less_eq @ A @ B2 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_221_sup_Oabsorb__iff1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( ord_less_eq @ A )
% 2.83/1.64 = ( ^ [B6: A,A3: A] :
% 2.83/1.64 ( ( sup_sup @ A @ A3 @ B6 )
% 2.83/1.64 = A3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_222_sup_Oabsorb__iff2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ( ( ord_less_eq @ A )
% 2.83/1.64 = ( ^ [A3: A,B6: A] :
% 2.83/1.64 ( ( sup_sup @ A @ A3 @ B6 )
% 2.83/1.64 = B6 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_223_sup_OcoboundedI1,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [C3: A,A2: A,B2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ C3 @ A2 )
% 2.83/1.64 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_224_sup_OcoboundedI2,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [C3: A,B2: A,A2: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ C3 @ B2 )
% 2.83/1.64 => ( ord_less_eq @ A @ C3 @ ( sup_sup @ A @ A2 @ B2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_225_Collect__mono__iff,axiom,
% 2.83/1.64 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.83/1.64 = ( ! [X3: A] :
% 2.83/1.64 ( ( P @ X3 )
% 2.83/1.64 => ( Q @ X3 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_226_contra__subsetD,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ~ ( member @ A @ C3 @ B5 )
% 2.83/1.64 => ~ ( member @ A @ C3 @ A4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_227_set__eq__subset,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( ^ [Y4: set @ A,Z4: set @ A] : ( Y4 = Z4 ) )
% 2.83/1.64 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A6 @ B7 )
% 2.83/1.64 & ( ord_less_eq @ ( set @ A ) @ B7 @ A6 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_228_subset__trans,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_229_Collect__mono,axiom,
% 2.83/1.64 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.83/1.64 ( ! [X2: A] :
% 2.83/1.64 ( ( P @ X2 )
% 2.83/1.64 => ( Q @ X2 ) )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_230_subset__refl,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_231_rev__subsetD,axiom,
% 2.83/1.64 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( member @ A @ C3 @ A4 )
% 2.83/1.64 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_232_subset__iff,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.64 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.83/1.64 ! [T2: A] :
% 2.83/1.64 ( ( member @ A @ T2 @ A6 )
% 2.83/1.64 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_233_set__rev__mp,axiom,
% 2.83/1.64 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( member @ A @ X @ A4 )
% 2.83/1.64 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( member @ A @ X @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_234_equalityD2,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( A4 = B5 )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_235_equalityD1,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( A4 = B5 )
% 2.83/1.64 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_236_subset__eq,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) )
% 2.83/1.64 = ( ^ [A6: set @ A,B7: set @ A] :
% 2.83/1.64 ! [X3: A] :
% 2.83/1.64 ( ( member @ A @ X3 @ A6 )
% 2.83/1.64 => ( member @ A @ X3 @ B7 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_237_equalityE,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.83/1.64 ( ( A4 = B5 )
% 2.83/1.64 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_238_subsetCE,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( member @ A @ C3 @ A4 )
% 2.83/1.64 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_239_subsetD,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( member @ A @ C3 @ A4 )
% 2.83/1.64 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_240_in__mono,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( member @ A @ X @ A4 )
% 2.83/1.64 => ( member @ A @ X @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_241_set__mp,axiom,
% 2.83/1.64 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.83/1.64 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.83/1.64 => ( ( member @ A @ X @ A4 )
% 2.83/1.64 => ( member @ A @ X @ B5 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_242_wlog__linorder__le,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( linorder @ A @ ( type2 @ A ) )
% 2.83/1.64 => ! [P: A > A > $o,B2: A,A2: A] :
% 2.83/1.64 ( ! [A7: A,B4: A] :
% 2.83/1.64 ( ( ord_less_eq @ A @ A7 @ B4 )
% 2.83/1.64 => ( P @ A7 @ B4 ) )
% 2.83/1.64 => ( ( ( P @ B2 @ A2 )
% 2.83/1.64 => ( P @ A2 @ B2 ) )
% 2.83/1.64 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_243_llist_Orel__eq,axiom,
% 2.83/1.64 ! [A: $tType] :
% 2.83/1.64 ( ( coindu987187967t_all2 @ A @ A
% 2.83/1.64 @ ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 2.83/1.64 = ( ^ [Y4: coindu1593790203_llist @ A,Z4: coindu1593790203_llist @ A] : ( Y4 = Z4 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_244_llist_Orel__refl,axiom,
% 2.83/1.64 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ! [X2: B] : ( Ra @ X2 @ X2 )
% 2.83/1.64 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_245_llist_Octr__transfer_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_246_llist_Orel__refl__strong,axiom,
% 2.83/1.64 ! [A: $tType,X: coindu1593790203_llist @ A,Ra: A > A > $o] :
% 2.83/1.64 ( ! [Z3: A] :
% 2.83/1.64 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 2.83/1.64 => ( Ra @ Z3 @ Z3 ) )
% 2.83/1.64 => ( coindu987187967t_all2 @ A @ A @ Ra @ X @ X ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_247_llist_Orel__mono__strong,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ B,Ra: A > B > $o] :
% 2.83/1.64 ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 2.83/1.64 => ( ! [Z3: A,Yb: B] :
% 2.83/1.64 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ X ) )
% 2.83/1.64 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Y ) )
% 2.83/1.64 => ( ( R @ Z3 @ Yb )
% 2.83/1.64 => ( Ra @ Z3 @ Yb ) ) ) )
% 2.83/1.64 => ( coindu987187967t_all2 @ A @ B @ Ra @ X @ Y ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_248_llist_Orel__cong,axiom,
% 2.83/1.64 ! [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] :
% 2.83/1.64 ( ( X = Ya )
% 2.83/1.64 => ( ( Y = Xa )
% 2.83/1.64 => ( ! [Z3: A,Yb: B] :
% 2.83/1.64 ( ( member @ A @ Z3 @ ( coindu1112613586e_lset @ A @ Ya ) )
% 2.83/1.64 => ( ( member @ B @ Yb @ ( coindu1112613586e_lset @ B @ Xa ) )
% 2.83/1.64 => ( ( R @ Z3 @ Yb )
% 2.83/1.64 = ( Ra @ Z3 @ Yb ) ) ) )
% 2.83/1.64 => ( ( coindu987187967t_all2 @ A @ B @ R @ X @ Y )
% 2.83/1.64 = ( coindu987187967t_all2 @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_249_llist_Orel__intros_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ( R @ X21 @ Y21 )
% 2.83/1.64 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 2.83/1.64 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_250_llist_Orel__distinct_I2_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.83/1.64 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_251_llist_Orel__distinct_I1_J,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 2.83/1.64 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_252_llist_Orel__cases,axiom,
% 2.83/1.64 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 2.83/1.64 => ( ( ( A2
% 2.83/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.83/1.64 => ( B2
% 2.83/1.64 != ( coindu1598213697e_LNil @ B ) ) )
% 2.83/1.64 => ~ ! [X12: A,X24: coindu1593790203_llist @ A] :
% 2.83/1.64 ( ( A2
% 2.83/1.64 = ( coindu1121789889_LCons @ A @ X12 @ X24 ) )
% 2.83/1.64 => ! [Y12: B,Y24: coindu1593790203_llist @ B] :
% 2.83/1.64 ( ( B2
% 2.83/1.64 = ( coindu1121789889_LCons @ B @ Y12 @ Y24 ) )
% 2.83/1.64 => ( ( R @ X12 @ Y12 )
% 2.83/1.64 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X24 @ Y24 ) ) ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_253_lset__ltl,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) @ ( coindu1112613586e_lset @ A @ Xs ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(fact_254_lset__lappend1,axiom,
% 2.83/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coindu1112613586e_lset @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.83/1.64 ! [A8: $tType,A9: $tType] :
% 2.83/1.64 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 2.83/1.64 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.83/1.64 ! [A8: $tType,A9: $tType] :
% 2.83/1.64 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 2.83/1.64 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 2.83/1.64 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_Set_Oset___Lattices_Olattice_2,axiom,
% 2.83/1.64 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_3,axiom,
% 2.83/1.64 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.83/1.64 linorder @ $o @ ( type2 @ $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(tcon_HOL_Obool___Lattices_Olattice_4,axiom,
% 2.83/1.64 lattice @ $o @ ( type2 @ $o ) ).
% 2.83/1.64
% 2.83/1.64 thf(help_If_3_1_T,axiom,
% 2.83/1.64 ! [P: $o] :
% 2.83/1.64 ( ( P = $true )
% 2.83/1.64 | ( P = $false ) ) ).
% 2.83/1.64
% 2.83/1.64 thf(help_If_2_1_T,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Y: A] :
% 2.83/1.64 ( ( if @ A @ $false @ X @ Y )
% 2.83/1.64 = Y ) ).
% 2.83/1.64
% 2.83/1.64 thf(help_If_1_1_T,axiom,
% 2.83/1.64 ! [A: $tType,X: A,Y: A] :
% 2.83/1.64 ( ( if @ A @ $true @ X @ Y )
% 2.83/1.64 = X ) ).
% 2.83/1.64
% 2.83/1.64 thf(conj_0,conjecture,
% 2.83/1.64 coindu1696667936prefix @ a @ ( coindu268472904append @ a @ xs @ ys ) @ ( coindu268472904append @ a @ xs @ zs ) ).
% 2.83/1.64 ------------------------
% 2.83/1.68 % (29501)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_29397 for (2999ds/275Mi)
% 2.83/1.68 % (29499)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29397 for (2999ds/2Mi)
% 2.83/1.68 % (29498)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_29397 for (2999ds/27Mi)
% 2.83/1.68 % (29500)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_29397 for (2999ds/2Mi)
% 2.83/1.68 % (29496)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29397 for (2999ds/183Mi)
% 2.83/1.68 % (29497)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_29397 for (2999ds/4Mi)
% 2.83/1.68 % (29502)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29397 for (2999ds/18Mi)
% 2.83/1.68 % (29499)Instruction limit reached!
% 2.83/1.68 % (29499)------------------------------
% 2.83/1.68 % (29499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.68 % (29499)Termination reason: Unknown
% 2.83/1.68 % (29500)Instruction limit reached!
% 2.83/1.68 % (29500)------------------------------
% 2.83/1.68 % (29500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.68 % (29499)Termination phase: shuffling
% 2.83/1.68
% 2.83/1.68 % (29499)Memory used [KB]: 1279
% 2.83/1.68 % (29499)Time elapsed: 0.003 s
% 2.83/1.68 % (29499)Instructions burned: 2 (million)
% 2.83/1.68 % (29499)------------------------------
% 2.83/1.68 % (29499)------------------------------
% 2.83/1.68 % (29500)Termination reason: Unknown
% 2.83/1.68 % (29500)Termination phase: shuffling
% 2.83/1.68
% 2.83/1.68 % (29500)Memory used [KB]: 1279
% 2.83/1.68 % (29500)Time elapsed: 0.003 s
% 2.83/1.68 % (29500)Instructions burned: 2 (million)
% 2.83/1.68 % (29500)------------------------------
% 2.83/1.68 % (29500)------------------------------
% 2.83/1.68 % (29497)Instruction limit reached!
% 2.83/1.68 % (29497)------------------------------
% 2.83/1.68 % (29497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.68 % (29497)Termination reason: Unknown
% 2.83/1.68 % (29497)Termination phase: shuffling
% 2.83/1.68
% 2.83/1.68 % (29497)Memory used [KB]: 1407
% 2.83/1.68 % (29497)Time elapsed: 0.004 s
% 2.83/1.68 % (29497)Instructions burned: 4 (million)
% 2.83/1.68 % (29497)------------------------------
% 2.83/1.68 % (29497)------------------------------
% 2.83/1.69 % (29502)Instruction limit reached!
% 2.83/1.69 % (29502)------------------------------
% 2.83/1.69 % (29502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (29502)Termination reason: Unknown
% 2.83/1.69 % (29502)Termination phase: shuffling
% 2.83/1.69
% 2.83/1.69 % (29502)Memory used [KB]: 1663
% 2.83/1.69 % (29502)Time elapsed: 0.011 s
% 2.83/1.69 % (29502)Instructions burned: 18 (million)
% 2.83/1.69 % (29502)------------------------------
% 2.83/1.69 % (29502)------------------------------
% 2.83/1.69 % (29498)Instruction limit reached!
% 2.83/1.69 % (29498)------------------------------
% 2.83/1.69 % (29498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.69 % (29498)Termination reason: Unknown
% 2.83/1.69 % (29498)Termination phase: Property scanning
% 2.83/1.69
% 2.83/1.69 % (29498)Memory used [KB]: 1918
% 2.83/1.69 % (29498)Time elapsed: 0.016 s
% 2.83/1.69 % (29498)Instructions burned: 28 (million)
% 2.83/1.69 % (29498)------------------------------
% 2.83/1.69 % (29498)------------------------------
% 2.83/1.70 % (29503)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29397 for (2999ds/3Mi)
% 2.83/1.70 % (29504)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_29397 for (2999ds/37Mi)
% 2.88/1.70 % (29505)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_29397 for (2999ds/15Mi)
% 2.88/1.70 % (29503)Instruction limit reached!
% 2.88/1.70 % (29503)------------------------------
% 2.88/1.70 % (29503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.70 % (29503)Termination reason: Unknown
% 2.88/1.70 % (29503)Termination phase: shuffling
% 2.88/1.70
% 2.88/1.70 % (29503)Memory used [KB]: 1407
% 2.88/1.70 % (29503)Time elapsed: 0.003 s
% 2.88/1.70 % (29503)Instructions burned: 3 (million)
% 2.88/1.70 % (29503)------------------------------
% 2.88/1.70 % (29503)------------------------------
% 2.88/1.70 % (29506)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_29397 for (2999ds/3Mi)
% 2.88/1.70 % (29505)Instruction limit reached!
% 2.88/1.70 % (29505)------------------------------
% 2.88/1.70 % (29505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.70 % (29505)Termination reason: Unknown
% 2.88/1.70 % (29505)Termination phase: shuffling
% 2.88/1.70
% 2.88/1.70 % (29505)Memory used [KB]: 1663
% 2.88/1.70 % (29505)Time elapsed: 0.009 s
% 2.88/1.70 % (29505)Instructions burned: 15 (million)
% 2.88/1.70 % (29505)------------------------------
% 2.88/1.70 % (29505)------------------------------
% 2.88/1.71 % (29506)Instruction limit reached!
% 2.88/1.71 % (29506)------------------------------
% 2.88/1.71 % (29506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (29506)Termination reason: Unknown
% 2.88/1.71 % (29506)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (29506)Memory used [KB]: 1407
% 2.88/1.71 % (29506)Time elapsed: 0.003 s
% 2.88/1.71 % (29506)Instructions burned: 3 (million)
% 2.88/1.71 % (29506)------------------------------
% 2.88/1.71 % (29506)------------------------------
% 2.88/1.71 % (29507)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_29397 for (2999ds/1041Mi)
% 2.88/1.71 % (29508)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29397 for (2999ds/7Mi)
% 2.88/1.71 % (29504)Instruction limit reached!
% 2.88/1.71 % (29504)------------------------------
% 2.88/1.71 % (29504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.71 % (29504)Termination reason: Unknown
% 2.88/1.71 % (29504)Termination phase: shuffling
% 2.88/1.71
% 2.88/1.71 % (29504)Memory used [KB]: 2046
% 2.88/1.71 % (29504)Time elapsed: 0.019 s
% 2.88/1.71 % (29504)Instructions burned: 38 (million)
% 2.88/1.71 % (29504)------------------------------
% 2.88/1.71 % (29504)------------------------------
% 2.88/1.71 % (29501)First to succeed.
% 2.88/1.72 % (29508)Instruction limit reached!
% 2.88/1.72 % (29508)------------------------------
% 2.88/1.72 % (29508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.72 % (29508)Termination reason: Unknown
% 2.88/1.72 % (29508)Termination phase: shuffling
% 2.88/1.72
% 2.88/1.72 % (29508)Memory used [KB]: 1407
% 2.88/1.72 % (29508)Time elapsed: 0.005 s
% 2.88/1.72 % (29508)Instructions burned: 7 (million)
% 2.88/1.72 % (29508)------------------------------
% 2.88/1.72 % (29508)------------------------------
% 2.88/1.72 % (29501)Refutation found. Thanks to Tanya!
% 2.88/1.72 % SZS status Theorem for DTF2THF_29397
% 2.88/1.72 % SZS output start Proof for DTF2THF_29397
% 2.88/1.72 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.88/1.72 thf(type_def_7, type, set: ($tType) > $tType).
% 2.88/1.72 thf(type_def_8, type, coindu1593790203_llist: ($tType) > $tType).
% 2.88/1.72 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 2.88/1.72 thf(type_def_10, type, a: $tType).
% 2.88/1.72 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 2.88/1.72 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 2.88/1.72 thf(func_def_2, type, set: ($tType) > $tType).
% 2.88/1.72 thf(func_def_3, type, itself: ($tType) > $tType).
% 2.88/1.72 thf(func_def_4, type, a: $tType).
% 2.88/1.72 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.88/1.72 thf(func_def_6, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.88/1.72 thf(func_def_7, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.88/1.72 thf(func_def_8, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.88/1.72 thf(func_def_9, type, coindu1928975208n_lset: !>[X0: $tType]:(set @ X0 > coindu1593790203_llist @ X0 > set @ X0)).
% 2.88/1.72 thf(func_def_10, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_11, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.88/1.72 thf(func_def_12, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_13, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_14, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0)).
% 2.88/1.72 thf(func_def_15, type, coindu1244876290_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coindu1593790203_llist @ X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 2.88/1.72 thf(func_def_16, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.88/1.72 thf(func_def_17, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o)).
% 2.88/1.72 thf(func_def_18, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.88/1.72 thf(func_def_19, type, coindu1112613586e_lset: !>[X0: $tType]:(coindu1593790203_llist @ X0 > set @ X0)).
% 2.88/1.72 thf(func_def_20, type, coindu1047225960le_ltl: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_21, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 2.88/1.72 thf(func_def_22, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.88/1.72 thf(func_def_23, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 2.88/1.72 thf(func_def_24, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.88/1.72 thf(func_def_25, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.88/1.72 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.88/1.72 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 2.88/1.72 thf(func_def_28, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 2.88/1.72 thf(func_def_29, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 2.88/1.72 thf(func_def_30, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.88/1.72 thf(func_def_31, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.88/1.72 thf(func_def_32, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.88/1.72 thf(func_def_33, type, xs: coindu1593790203_llist @ a).
% 2.88/1.72 thf(func_def_34, type, ys: coindu1593790203_llist @ a).
% 2.88/1.72 thf(func_def_35, type, zs: coindu1593790203_llist @ a).
% 2.88/1.72 thf(func_def_53, type, sK0: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.88/1.72 thf(func_def_54, type, sK1: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_55, type, sK2: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_56, type, sK3: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_57, type, sK4: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_58, type, sK5: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_59, type, sK6: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_60, type, sK7: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.88/1.72 thf(func_def_61, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.88/1.72 thf(func_def_62, type, sK9: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_63, type, sK10: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 2.88/1.72 thf(func_def_64, type, sK11: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_65, type, sK12: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_66, type, sK13: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_67, type, sK14: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_68, type, sK15: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_69, type, sK16: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_70, type, sK17: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_71, type, sK18: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_72, type, sK19: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0)).
% 2.88/1.72 thf(func_def_73, type, sK20: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_74, type, sK21: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.88/1.72 thf(func_def_75, type, sK22: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_76, type, sK23: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.88/1.72 thf(func_def_77, type, sK24: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.88/1.72 thf(func_def_79, type, ph26: !>[X0: $tType]:(X0)).
% 2.88/1.72 thf(f1077,plain,(
% 2.88/1.72 $false),
% 2.88/1.72 inference(subsumption_resolution,[status(thm)],[f1065,f1023])).
% 2.88/1.72 thf(f1023,plain,(
% 2.88/1.72 ((coindu1213758845finite @ a @ xs) = $true)),
% 2.88/1.72 inference(subsumption_resolution,[status(thm)],[f995,f952])).
% 2.88/1.72 thf(f952,plain,(
% 2.88/1.72 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (((coindu1696667936prefix @ X0 @ X1 @ (coindu268472904append @ X0 @ X1 @ X2)) = $true)) )),
% 2.88/1.72 inference(cnf_transformation,[status(thm)],[f576])).
% 2.88/1.72 thf(f576,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X1 @ (coindu268472904append @ X0 @ X1 @ X2)) = $true)),
% 2.88/1.72 inference(fool_elimination,[status(thm)],[f575])).
% 2.88/1.72 thf(f575,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ X1 @ (coindu268472904append @ X0 @ X1 @ X2))),
% 2.88/1.72 inference(rectify,[status(thm)],[f6])).
% 2.88/1.72 thf(f6,axiom,(
% 2.88/1.72 ! [X0 : $tType,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ X4 @ (coindu268472904append @ X0 @ X4 @ X5))),
% 2.88/1.72 file('/export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2THF_29397.p',fact_5_lprefix__lappend)).
% 2.88/1.72 thf(f995,plain,(
% 2.88/1.72 ((coindu1213758845finite @ a @ xs) = $true) | ((coindu1696667936prefix @ a @ xs @ (coindu268472904append @ a @ xs @ zs)) != $true)),
% 2.88/1.72 inference(superposition,[status(thm)],[f960,f855])).
% 2.88/1.72 thf(f855,plain,(
% 2.88/1.72 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (((coindu268472904append @ X0 @ X1 @ X2) = X1) | ((coindu1213758845finite @ X0 @ X1) = $true)) )),
% 2.88/1.72 inference(cnf_transformation,[status(thm)],[f760])).
% 2.88/1.72 thf(f760,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (((coindu1213758845finite @ X0 @ X1) = $true) | ((coindu268472904append @ X0 @ X1 @ X2) = X1))),
% 2.88/1.72 inference(ennf_transformation,[status(thm)],[f740])).
% 2.88/1.72 thf(f740,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (((coindu1213758845finite @ X0 @ X1) != $true) => ((coindu268472904append @ X0 @ X1 @ X2) = X1))),
% 2.88/1.72 inference(flattening,[status(thm)],[f718])).
% 2.88/1.72 thf(f718,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~((coindu1213758845finite @ X0 @ X1) = $true) => ((coindu268472904append @ X0 @ X1 @ X2) = X1))),
% 2.88/1.72 inference(fool_elimination,[status(thm)],[f717])).
% 2.88/1.72 thf(f717,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~(coindu1213758845finite @ X0 @ X1) => ((coindu268472904append @ X0 @ X1 @ X2) = X1))),
% 2.88/1.72 inference(rectify,[status(thm)],[f13])).
% 2.88/1.72 thf(f13,axiom,(
% 2.88/1.72 ! [X0 : $tType,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0] : (~(coindu1213758845finite @ X0 @ X4) => ((coindu268472904append @ X0 @ X4 @ X5) = X4))),
% 2.88/1.72 file('/export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2THF_29397.p',fact_12_lappend__inf)).
% 2.88/1.72 thf(f960,plain,(
% 2.88/1.72 ((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs)) != $true)),
% 2.88/1.72 inference(cnf_transformation,[status(thm)],[f719])).
% 2.88/1.72 thf(f719,plain,(
% 2.88/1.72 ((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs)) != $true)),
% 2.88/1.72 inference(flattening,[status(thm)],[f394])).
% 2.88/1.72 thf(f394,plain,(
% 2.88/1.72 ~((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs)) = $true)),
% 2.88/1.72 inference(fool_elimination,[status(thm)],[f393])).
% 2.88/1.72 thf(f393,plain,(
% 2.88/1.72 ~(coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))),
% 2.88/1.72 inference(rectify,[status(thm)],[f267])).
% 2.88/1.72 thf(f267,negated_conjecture,(
% 2.88/1.72 ~(coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))),
% 2.88/1.72 inference(negated_conjecture,[status(cth)],[f266])).
% 2.88/1.72 thf(f266,conjecture,(
% 2.88/1.72 (coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))),
% 2.88/1.72 file('/export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2THF_29397.p',conj_0)).
% 2.88/1.72 thf(f1065,plain,(
% 2.88/1.72 ((coindu1213758845finite @ a @ xs) != $true)),
% 2.88/1.72 inference(trivial_inequality_removal,[status(thm)],[f1060])).
% 2.88/1.72 thf(f1060,plain,(
% 2.88/1.72 ($true != $true) | ((coindu1213758845finite @ a @ xs) != $true)),
% 2.88/1.72 inference(superposition,[status(thm)],[f1002,f900])).
% 2.88/1.72 thf(f900,plain,(
% 2.88/1.72 ((coindu1696667936prefix @ a @ ys @ zs) = $true) | ((coindu1213758845finite @ a @ xs) != $true)),
% 2.88/1.72 inference(cnf_transformation,[status(thm)],[f789])).
% 2.88/1.72 thf(f789,plain,(
% 2.88/1.72 ((coindu1696667936prefix @ a @ ys @ zs) = $true) | ((coindu1213758845finite @ a @ xs) != $true)),
% 2.88/1.72 inference(ennf_transformation,[status(thm)],[f356])).
% 2.88/1.72 thf(f356,plain,(
% 2.88/1.72 ((coindu1213758845finite @ a @ xs) = $true) => ((coindu1696667936prefix @ a @ ys @ zs) = $true)),
% 2.88/1.72 inference(fool_elimination,[status(thm)],[f355])).
% 2.88/1.72 thf(f355,plain,(
% 2.88/1.72 (coindu1213758845finite @ a @ xs) => (coindu1696667936prefix @ a @ ys @ zs)),
% 2.88/1.72 inference(rectify,[status(thm)],[f2])).
% 2.88/1.72 thf(f2,axiom,(
% 2.88/1.72 (coindu1213758845finite @ a @ xs) => (coindu1696667936prefix @ a @ ys @ zs)),
% 2.88/1.72 file('/export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2THF_29397.p',fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062)).
% 2.88/1.72 thf(f1002,plain,(
% 2.88/1.72 ((coindu1696667936prefix @ a @ ys @ zs) != $true)),
% 2.88/1.72 inference(trivial_inequality_removal,[status(thm)],[f996])).
% 2.88/1.72 thf(f996,plain,(
% 2.88/1.72 ((coindu1696667936prefix @ a @ ys @ zs) != $true) | ($true != $true)),
% 2.88/1.72 inference(superposition,[status(thm)],[f960,f941])).
% 2.88/1.72 thf(f941,plain,(
% 2.88/1.72 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X3 @ X1) @ (coindu268472904append @ X0 @ X3 @ X2))) | ((coindu1696667936prefix @ X0 @ X1 @ X2) != $true)) )),
% 2.88/1.72 inference(cnf_transformation,[status(thm)],[f753])).
% 2.88/1.72 thf(f753,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : (((coindu1696667936prefix @ X0 @ X1 @ X2) != $true) | ($true = (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X3 @ X1) @ (coindu268472904append @ X0 @ X3 @ X2))))),
% 2.88/1.72 inference(ennf_transformation,[status(thm)],[f522])).
% 2.88/1.72 thf(f522,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : (((coindu1696667936prefix @ X0 @ X1 @ X2) = $true) => ($true = (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X3 @ X1) @ (coindu268472904append @ X0 @ X3 @ X2))))),
% 2.88/1.72 inference(fool_elimination,[status(thm)],[f521])).
% 2.88/1.72 thf(f521,plain,(
% 2.88/1.72 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X1 @ X2) => (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X3 @ X1) @ (coindu268472904append @ X0 @ X3 @ X2)))),
% 2.88/1.72 inference(rectify,[status(thm)],[f8])).
% 2.88/1.72 thf(f8,axiom,(
% 2.88/1.72 ! [X0 : $tType,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0,X6 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X4 @ X5) => (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X6 @ X4) @ (coindu268472904append @ X0 @ X6 @ X5)))),
% 2.88/1.72 file('/export/starexec/sandbox2/tmp/tmp.wOQ1i1l4x8/DTF2THF_29397.p',fact_7_lprefix__lappend__sameI)).
% 2.88/1.72 % SZS output end Proof for DTF2THF_29397
% 2.88/1.72 % (29501)------------------------------
% 2.88/1.72 % (29501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.88/1.72 % (29501)Termination reason: Refutation
% 2.88/1.72
% 2.88/1.72 % (29501)Memory used [KB]: 6652
% 2.88/1.72 % (29501)Time elapsed: 0.039 s
% 2.88/1.72 % (29501)Instructions burned: 70 (million)
% 2.88/1.72 % (29501)------------------------------
% 2.88/1.72 % (29501)------------------------------
% 2.88/1.72 % (29495)Success in time 0.067 s
%------------------------------------------------------------------------------