%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT130^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 08:44:52 AM UTC 2026
% Result : Theorem 2.69s 1.61s
% Output : Refutation 2.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : DAT130^1 : TPTP v9.2.1. Released v7.0.0.
% 0.10/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n002.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 06:08:33 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.38 ---- Original DTF file ---
% 0.14/0.38 thf(spec,logic,$$dhol).
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 % File : DAT130^1 : TPTP v9.2.1. Released v7.0.0.
% 0.14/0.38 % Domain : Data Structures
% 0.14/0.38 % Problem : Coinductive list 3543
% 0.14/0.38 % Version : [Bla16] axioms : Especial.
% 0.14/0.38 % English :
% 0.14/0.38
% 0.14/0.38 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.14/0.38 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.14/0.38 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.14/0.38 % Source : [Bla16]
% 0.14/0.38 % Names : coinductive_list__3543.p [Bla16]
% 0.14/0.38
% 0.14/0.38 % Status : Theorem
% 0.14/0.38 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.14/0.38 % Syntax : Number of formulae : 308 ( 119 unt; 44 typ; 0 def)
% 0.14/0.38 % Number of atoms : 751 ( 251 equ; 0 cnn)
% 0.14/0.38 % Maximal formula atoms : 8 ( 2 avg)
% 0.14/0.38 % Number of connectives : 3848 ( 137 ~; 41 |; 76 &;3272 @)
% 0.14/0.38 % ( 0 <=>; 322 =>; 0 <=; 0 <~>)
% 0.14/0.38 % Maximal formula depth : 22 ( 8 avg)
% 0.14/0.38 % Number of types : 2 ( 1 usr)
% 0.14/0.38 % Number of type conns : 271 ( 271 >; 0 *; 0 +; 0 <<)
% 0.14/0.38 % Number of symbols : 46 ( 43 usr; 4 con; 0-7 aty)
% 0.14/0.38 % Number of variables : 955 ( 47 ^; 810 !; 58 ?; 955 :)
% 0.14/0.38 % ( 40 !>; 0 ?*; 0 @-; 0 @+)
% 0.14/0.38 % SPC : TH1_THM_EQU_NAR
% 0.14/0.38
% 0.14/0.38 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.14/0.38 % 2016-07-13 15:02:13.700
% 0.14/0.38 %------------------------------------------------------------------------------
% 0.14/0.38 %----Could-be-implicit typings (4)
% 0.14/0.38 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.14/0.38 coindu1593790203_llist: $tType > $tType ).
% 0.14/0.38
% 0.14/0.38 thf(ty_t_Set_Oset,type,
% 0.14/0.38 set: $tType > $tType ).
% 0.14/0.38
% 0.14/0.38 thf(ty_t_itself,type,
% 0.14/0.38 itself: $tType > $tType ).
% 0.14/0.38
% 0.14/0.38 thf(ty_tf_a,type,
% 0.14/0.38 a: $tType ).
% 0.14/0.38
% 0.14/0.38 %----Explicit typings (40)
% 0.14/0.38 thf(sy_cl_HOL_Otype,type,
% 0.14/0.38 type:
% 0.14/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_cl_Lattices_Olattice,type,
% 0.14/0.38 lattice:
% 0.14/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.14/0.38 semilattice_inf:
% 0.14/0.38 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix,type,
% 0.14/0.38 coindu1571841457prefix:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OlSup,type,
% 0.14/0.38 coindu526335360e_lSup:
% 0.14/0.38 !>[A: $tType] : ( ( set @ ( coindu1593790203_llist @ A ) ) > ( coindu1593790203_llist @ A ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.14/0.38 coindu268472904append:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oldistinct,type,
% 0.14/0.38 coindu6345450stinct:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.14/0.38 coindu1213758845finite:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast,type,
% 0.14/0.38 coindu2000965700_llast:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 0.14/0.38 coindu300403952lexord:
% 0.14/0.38 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.14/0.38 coindu1121789889_LCons:
% 0.14/0.38 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.14/0.38 coindu1598213697e_LNil:
% 0.14/0.38 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 0.14/0.38 coindu882539134_llist:
% 0.14/0.38 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.14/0.38 coindu1046438764le_lhd:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.14/0.38 coindu335574135_lnull:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 0.14/0.38 coindu1112613586e_lset:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.14/0.38 coindu1047225960le_ltl:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.14/0.38 coindu1696667936prefix:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.38
% 0.14/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.14/0.38 coindu574146665prefix:
% 0.14/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 0.14/0.39 coindu721411036eWhile:
% 0.14/0.39 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord_Olsorted,type,
% 0.14/0.39 coindu543932918sorted:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.14/0.39 coindu1599971794_llist:
% 0.14/0.39 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Complete__Partial__Order2_Ocompact,type,
% 0.14/0.39 comple2143767107ompact:
% 0.14/0.39 !>[A: $tType] : ( ( ( set @ A ) > A ) > ( A > A > $o ) > A > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Complete__Partial__Order2_Ocont,type,
% 0.14/0.39 comple1412571634l_cont:
% 0.14/0.39 !>[A: $tType,B: $tType] : ( ( ( set @ A ) > A ) > ( A > A > $o ) > ( ( set @ B ) > B ) > ( B > B > $o ) > ( A > B ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Complete__Partial__Order_Occpo_Oadmissible,type,
% 0.14/0.39 comple1986059218ssible:
% 0.14/0.39 !>[A: $tType] : ( ( ( set @ A ) > A ) > ( A > A > $o ) > ( A > $o ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Complete__Partial__Order_Ochain,type,
% 0.14/0.39 comple1193779247_chain:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Finite__Set_Ofinite,type,
% 0.14/0.39 finite_finite:
% 0.14/0.39 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_If,type,
% 0.14/0.39 if:
% 0.14/0.39 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.14/0.39 inf_inf:
% 0.14/0.39 !>[A: $tType] : ( A > A > A ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Orderings_Oord_Omax,type,
% 0.14/0.39 max:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Orderings_Oord_Omin,type,
% 0.14/0.39 min:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Pure_Otype,type,
% 0.14/0.39 type2:
% 0.14/0.39 !>[A: $tType] : ( itself @ A ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Set_OCollect,type,
% 0.14/0.39 collect:
% 0.14/0.39 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 0.14/0.39 set_atLeast:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Set__Interval_Oord_OatLeastAtMost,type,
% 0.14/0.39 set_atLeastAtMost:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > A > A > ( set @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 0.14/0.39 set_atMost:
% 0.14/0.39 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_c_member,type,
% 0.14/0.39 member:
% 0.14/0.39 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_v_Ya____,type,
% 0.14/0.39 ya: set @ ( coindu1593790203_llist @ a ) ).
% 0.14/0.39
% 0.14/0.39 thf(sy_v_less__eq,type,
% 0.14/0.39 less_eq: a > a > $o ).
% 0.14/0.39
% 0.14/0.39 thf(sy_v_xs____,type,
% 0.14/0.39 xs: coindu1593790203_llist @ a ).
% 0.14/0.39
% 0.14/0.39 %----Relevant facts (254)
% 0.14/0.39 thf(fact_0__092_060open_062xs_A_092_060in_062_AY_092_060close_062,axiom,
% 0.14/0.39 member @ ( coindu1593790203_llist @ a ) @ xs @ ya ).
% 0.14/0.39
% 0.14/0.39 % \<open>xs \<in> Y\<close>
% 0.14/0.39 thf(fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062,axiom,
% 0.14/0.39 less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % \<open>lhd xs \<le> lhd (ltl xs)\<close>
% 0.14/0.39 thf(fact_2_local_Oord__eq__le__trans,axiom,
% 0.14/0.39 ! [A2: a,B2: a,C: a] :
% 0.14/0.39 ( ( A2 = B2 )
% 0.14/0.39 => ( ( less_eq @ B2 @ C )
% 0.14/0.39 => ( less_eq @ A2 @ C ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.ord_eq_le_trans
% 0.14/0.39 thf(fact_3_local_Oord__le__eq__trans,axiom,
% 0.14/0.39 ! [A2: a,B2: a,C: a] :
% 0.14/0.39 ( ( less_eq @ A2 @ B2 )
% 0.14/0.39 => ( ( B2 = C )
% 0.14/0.39 => ( less_eq @ A2 @ C ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.ord_le_eq_trans
% 0.14/0.39 thf(fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062,axiom,
% 0.14/0.39 ( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
% 0.14/0.39 = ( coindu1046438764le_lhd @ a @ xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % \<open>lhd (lSup Y) = lhd xs\<close>
% 0.14/0.39 thf(fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062,axiom,
% 0.14/0.39 ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
% 0.14/0.39 = ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % \<open>lhd (ltl (lSup Y)) = lhd (ltl xs)\<close>
% 0.14/0.39 thf(fact_6_local_Omax__def,axiom,
% 0.14/0.39 ! [A2: a,B2: a] :
% 0.14/0.39 ( ( ( less_eq @ A2 @ B2 )
% 0.14/0.39 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.14/0.39 = B2 ) )
% 0.14/0.39 & ( ~ ( less_eq @ A2 @ B2 )
% 0.14/0.39 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.14/0.39 = A2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.max_def
% 0.14/0.39 thf(fact_7_local_Omin__def,axiom,
% 0.14/0.39 ! [A2: a,B2: a] :
% 0.14/0.39 ( ( ( less_eq @ A2 @ B2 )
% 0.14/0.39 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.14/0.39 = A2 ) )
% 0.14/0.39 & ( ~ ( less_eq @ A2 @ B2 )
% 0.14/0.39 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.14/0.39 = B2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.min_def
% 0.14/0.39 thf(fact_8_lsorted_I2_J,axiom,
% 0.14/0.39 ! [X: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ a ) @ X @ ya )
% 0.14/0.39 => ( coindu543932918sorted @ a @ less_eq @ X ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted(2)
% 0.14/0.39 thf(fact_9_lsorted_I3_J,axiom,
% 0.14/0.39 ~ ( coindu335574135_lnull @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted(3)
% 0.14/0.39 thf(fact_10_lsorted_I4_J,axiom,
% 0.14/0.39 ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted(4)
% 0.14/0.39 thf(fact_11__092_060open_062_092_060not_062_Alnull_A_Iltl_Axs_J_092_060close_062,axiom,
% 0.14/0.39 ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % \<open>\<not> lnull (ltl xs)\<close>
% 0.14/0.39 thf(fact_12_sorted,axiom,
% 0.14/0.39 ! [Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ a ) @ Xs @ ya )
% 0.14/0.39 => ( coindu543932918sorted @ a @ less_eq @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % sorted
% 0.14/0.39 thf(fact_13_lsorted__ltlI,axiom,
% 0.14/0.39 ! [Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( coindu543932918sorted @ a @ less_eq @ Xs )
% 0.14/0.39 => ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_ltlI
% 0.14/0.39 thf(fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062xs_A_092_060in_062_AY_059_A_092_060not_062_Alnull_Axs_059_A_092_060not_062_Alnull_A_Iltl_Axs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.14/0.39 ~ ! [Xs2: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ a ) @ Xs2 @ ya )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ a @ Xs2 )
% 0.14/0.39 => ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ Xs2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % \<open>\<And>thesis. (\<And>xs. \<lbrakk>xs \<in> Y; \<not> lnull xs; \<not> lnull (ltl xs)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.14/0.39 thf(fact_15_local_OatLeastAtMost__iff,axiom,
% 0.14/0.39 ! [I: a,L: a,U: a] :
% 0.14/0.39 ( ( member @ a @ I @ ( set_atLeastAtMost @ a @ less_eq @ L @ U ) )
% 0.14/0.39 = ( ( less_eq @ L @ I )
% 0.14/0.39 & ( less_eq @ I @ U ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.atLeastAtMost_iff
% 0.14/0.39 thf(fact_16__092_060open_062_092_060not_062_Alnull_Axs_092_060close_062,axiom,
% 0.14/0.39 ~ ( coindu335574135_lnull @ a @ xs ) ).
% 0.14/0.39
% 0.14/0.39 % \<open>\<not> lnull xs\<close>
% 0.14/0.39 thf(fact_17_local_OatLeast__iff,axiom,
% 0.14/0.39 ! [I: a,K: a] :
% 0.14/0.39 ( ( member @ a @ I @ ( set_atLeast @ a @ less_eq @ K ) )
% 0.14/0.39 = ( less_eq @ K @ I ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.atLeast_iff
% 0.14/0.39 thf(fact_18_local_OatMost__iff,axiom,
% 0.14/0.39 ! [I: a,K: a] :
% 0.14/0.39 ( ( member @ a @ I @ ( set_atMost @ a @ less_eq @ K ) )
% 0.14/0.39 = ( less_eq @ I @ K ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.atMost_iff
% 0.14/0.39 thf(fact_19_lsorted__coinduct_H,axiom,
% 0.14/0.39 ! [X2: ( coindu1593790203_llist @ a ) > $o,Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( X2 @ Xs )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( X2 @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ a @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ Xs2 ) )
% 0.14/0.39 => ( ( less_eq @ ( coindu1046438764le_lhd @ a @ Xs2 ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ Xs2 ) ) )
% 0.14/0.39 & ( ( X2 @ ( coindu1047225960le_ltl @ a @ Xs2 ) )
% 0.14/0.39 | ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ Xs2 ) ) ) ) ) ) )
% 0.14/0.39 => ( coindu543932918sorted @ a @ less_eq @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_coinduct'
% 0.14/0.39 thf(fact_20_lsorted__lhdD,axiom,
% 0.14/0.39 ! [Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( coindu543932918sorted @ a @ less_eq @ Xs )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ a @ Xs )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ Xs ) )
% 0.14/0.39 => ( less_eq @ ( coindu1046438764le_lhd @ a @ Xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ Xs ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_lhdD
% 0.14/0.39 thf(fact_21_chain,axiom,
% 0.14/0.39 comple1193779247_chain @ ( coindu1593790203_llist @ a ) @ ( coindu1696667936prefix @ a ) @ ya ).
% 0.14/0.39
% 0.14/0.39 % chain
% 0.14/0.39 thf(fact_22_llist_Oexpand,axiom,
% 0.14/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( coindu335574135_lnull @ A @ Llist )
% 0.14/0.39 = ( coindu335574135_lnull @ A @ Llist2 ) )
% 0.14/0.39 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Llist2 )
% 0.14/0.39 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Llist2 ) )
% 0.14/0.39 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 0.14/0.39 = ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) )
% 0.14/0.39 => ( Llist = Llist2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.expand
% 0.14/0.39 thf(fact_23_lprefix__refl,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_refl
% 0.14/0.39 thf(fact_24_llist_Oleq__refl,axiom,
% 0.14/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X3 @ X3 ) ).
% 0.14/0.39
% 0.14/0.39 % llist.leq_refl
% 0.14/0.39 thf(fact_25_lnull__lSup,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.14/0.39 = ( ! [X4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X4 @ A3 )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ X4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lnull_lSup
% 0.14/0.39 thf(fact_26_lzip_Oexhaust,axiom,
% 0.14/0.39 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.14/0.39 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.14/0.39 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lzip.exhaust
% 0.14/0.39 thf(fact_27_lnull__lprefix,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.14/0.39
% 0.14/0.39 % lnull_lprefix
% 0.14/0.39 thf(fact_28_lprefix__lnull,axiom,
% 0.14/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_lnull
% 0.14/0.39 thf(fact_29_lprefix__trans,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_trans
% 0.14/0.39 thf(fact_30_lprefix__lnullD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_lnullD
% 0.14/0.39 thf(fact_31_lappend_Oexhaust,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lappend.exhaust
% 0.14/0.39 thf(fact_32_llist_Oleq__trans,axiom,
% 0.14/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ X3 @ Z ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.leq_trans
% 0.14/0.39 thf(fact_33_lprefix__antisym,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.14/0.39 => ( Xs = Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_antisym
% 0.14/0.39 thf(fact_34_llist_Oleq__antisym,axiom,
% 0.14/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Y @ X3 )
% 0.14/0.39 => ( X3 = Y ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.leq_antisym
% 0.14/0.39 thf(fact_35_lprefix__not__lnullD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_not_lnullD
% 0.14/0.39 thf(fact_36_lprefix__down__linear,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_down_linear
% 0.14/0.39 thf(fact_37_chain__lprefix__lSup,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.14/0.39 => ( ( member @ ( coindu1593790203_llist @ A ) @ Xs @ A3 )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ Xs @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % chain_lprefix_lSup
% 0.14/0.39 thf(fact_38_chain__lSup__lprefix,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),Zs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ Xs2 @ A3 )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ Xs2 @ Zs ) )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ ( coindu526335360e_lSup @ A @ A3 ) @ Zs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % chain_lSup_lprefix
% 0.14/0.39 thf(fact_39_llist_Olub__upper,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),X3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.14/0.39 => ( ( member @ ( coindu1593790203_llist @ A ) @ X3 @ A3 )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ X3 @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.lub_upper
% 0.14/0.39 thf(fact_40_llist_Olub__least,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),Z: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ A3 )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ X5 @ Z ) )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ ( coindu526335360e_lSup @ A @ A3 ) @ Z ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.lub_least
% 0.14/0.39 thf(fact_41_lprefix__lhdD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_lhdD
% 0.14/0.39 thf(fact_42_lhd__lSup__eq,axiom,
% 0.14/0.39 ! [A: $tType,Y2: set @ ( coindu1593790203_llist @ A ),Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ Y2 )
% 0.14/0.39 => ( ( member @ ( coindu1593790203_llist @ A ) @ Xs @ Y2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( coindu1046438764le_lhd @ A @ ( coindu526335360e_lSup @ A @ Y2 ) )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lhd_lSup_eq
% 0.14/0.39 thf(fact_43_mem__Collect__eq,axiom,
% 0.14/0.39 ! [A: $tType,A2: A,P: A > $o] :
% 0.14/0.39 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.14/0.39 = ( P @ A2 ) ) ).
% 0.14/0.39
% 0.14/0.39 % mem_Collect_eq
% 0.14/0.39 thf(fact_44_Collect__mem__eq,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ A] :
% 0.14/0.39 ( ( collect @ A
% 0.14/0.39 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.14/0.39 = A3 ) ).
% 0.14/0.39
% 0.14/0.39 % Collect_mem_eq
% 0.14/0.39 thf(fact_45_Collect__cong,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.14/0.39 ( ! [X5: A] :
% 0.14/0.39 ( ( P @ X5 )
% 0.14/0.39 = ( Q @ X5 ) )
% 0.14/0.39 => ( ( collect @ A @ P )
% 0.14/0.39 = ( collect @ A @ Q ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Collect_cong
% 0.14/0.39 thf(fact_46_ext,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.14/0.39 ( ! [X5: A] :
% 0.14/0.39 ( ( F @ X5 )
% 0.14/0.39 = ( G @ X5 ) )
% 0.14/0.39 => ( F = G ) ) ).
% 0.14/0.39
% 0.14/0.39 % ext
% 0.14/0.39 thf(fact_47_lprefix__coinduct,axiom,
% 0.14/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( P @ Xs @ Ys )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( P @ Xs2 @ Ys2 )
% 0.14/0.39 => ( ( ( coindu335574135_lnull @ A @ Ys2 )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ Xs2 ) )
% 0.14/0.39 & ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Ys2 )
% 0.14/0.39 => ( ( ( coindu1046438764le_lhd @ A @ Xs2 )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Ys2 ) )
% 0.14/0.39 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys2 ) )
% 0.14/0.39 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys2 ) ) ) ) ) ) ) )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_coinduct
% 0.14/0.39 thf(fact_48_lprefix__expand,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.14/0.39 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.14/0.39 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_expand
% 0.14/0.39 thf(fact_49_lSup_Odisc__iff_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.14/0.39 = ( ! [X4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X4 @ A3 )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ X4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lSup.disc_iff(2)
% 0.14/0.39 thf(fact_50_lSup_Odisc_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ! [X5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ A3 )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ X5 ) )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lSup.disc(1)
% 0.14/0.39 thf(fact_51_lSup_Odisc_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ~ ! [X: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X @ A3 )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ X ) )
% 0.14/0.39 => ~ ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lSup.disc(2)
% 0.14/0.39 thf(fact_52_lnull__ltlI,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lnull_ltlI
% 0.14/0.39 thf(fact_53_ord_Olsorted__coinduct_H,axiom,
% 0.14/0.39 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 0.14/0.39 ( ( X2 @ Xs )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.14/0.39 => ( ( Less_eq @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ ( coindu1046438764le_lhd @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.14/0.39 & ( ( X2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.14/0.39 | ( coindu543932918sorted @ A @ Less_eq @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) ) ) ) ) )
% 0.14/0.39 => ( coindu543932918sorted @ A @ Less_eq @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_coinduct'
% 0.14/0.39 thf(fact_54_ord_Olsorted__lhdD,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ Xs )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.14/0.39 => ( Less_eq @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_lhdD
% 0.14/0.39 thf(fact_55_ltakeWhile_Oexhaust,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.14/0.39 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.exhaust
% 0.14/0.39 thf(fact_56_lprefix__ltlI,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_ltlI
% 0.14/0.39 thf(fact_57_ord_Olsorted__ltlI,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ Xs )
% 0.14/0.39 => ( coindu543932918sorted @ A @ Less_eq @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_ltlI
% 0.14/0.39 thf(fact_58_llist_Ocoinduct__strong,axiom,
% 0.14/0.39 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( R @ Llist @ Llist2 )
% 0.14/0.39 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( R @ Llist3 @ Llist4 )
% 0.14/0.39 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.14/0.39 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.14/0.39 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.14/0.39 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.14/0.39 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) )
% 0.14/0.39 | ( ( coindu1047225960le_ltl @ A @ Llist3 )
% 0.14/0.39 = ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) ) )
% 0.14/0.39 => ( Llist = Llist2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.coinduct_strong
% 0.14/0.39 thf(fact_59_llist_Ocoinduct,axiom,
% 0.14/0.39 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( R @ Llist @ Llist2 )
% 0.14/0.39 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( R @ Llist3 @ Llist4 )
% 0.14/0.39 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.14/0.39 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.14/0.39 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.14/0.39 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.14/0.39 & ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) )
% 0.14/0.39 => ( Llist = Llist2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.coinduct
% 0.14/0.39 thf(fact_60_local_OatLeastAtMost__def,axiom,
% 0.14/0.39 ! [L: a,U: a] :
% 0.14/0.39 ( ( set_atLeastAtMost @ a @ less_eq @ L @ U )
% 0.14/0.39 = ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ L ) @ ( set_atMost @ a @ less_eq @ U ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % local.atLeastAtMost_def
% 0.14/0.39 thf(fact_61_lsorted__LCons_H,axiom,
% 0.14/0.39 ! [X3: a,Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ Xs ) )
% 0.14/0.39 = ( ~ ( coindu335574135_lnull @ a @ Xs )
% 0.14/0.39 => ( ( less_eq @ X3 @ ( coindu1046438764le_lhd @ a @ Xs ) )
% 0.14/0.39 & ( coindu543932918sorted @ a @ less_eq @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_LCons'
% 0.14/0.39 thf(fact_62_LNil,axiom,
% 0.14/0.39 coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ) ).
% 0.14/0.39
% 0.14/0.39 % LNil
% 0.14/0.39 thf(fact_63_LCons__LCons,axiom,
% 0.14/0.39 ! [X3: a,Y: a,Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( less_eq @ X3 @ Y )
% 0.14/0.39 => ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y @ Xs ) )
% 0.14/0.39 => ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1121789889_LCons @ a @ Y @ Xs ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % LCons_LCons
% 0.14/0.39 thf(fact_64_ord_Omax__def,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( max @ A )
% 0.14/0.39 = ( ^ [Less_eq2: A > A > $o,A4: A,B3: A] : ( if @ A @ ( Less_eq2 @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.max_def
% 0.14/0.39 thf(fact_65_ord_Omin__def,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( min @ A )
% 0.14/0.39 = ( ^ [Less_eq2: A > A > $o,A4: A,B3: A] : ( if @ A @ ( Less_eq2 @ A4 @ B3 ) @ A4 @ B3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.min_def
% 0.14/0.39 thf(fact_66_unfold__llist__id,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 0.14/0.39 = Xs ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist_id
% 0.14/0.39 thf(fact_67_llist_Ocase__eq__if,axiom,
% 0.14/0.39 ! [A: $tType,B: $tType] :
% 0.14/0.39 ( ( coindu882539134_llist @ B @ A )
% 0.14/0.39 = ( ^ [F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist5: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist5 ) @ F1 @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist5 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.case_eq_if
% 0.14/0.39 thf(fact_68_ord_OatMost__iff,axiom,
% 0.14/0.39 ! [A: $tType,I: A,Less_eq: A > A > $o,K: A] :
% 0.14/0.39 ( ( member @ A @ I @ ( set_atMost @ A @ Less_eq @ K ) )
% 0.14/0.39 = ( Less_eq @ I @ K ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.atMost_iff
% 0.14/0.39 thf(fact_69_ord_OatLeast__iff,axiom,
% 0.14/0.39 ! [A: $tType,I: A,Less_eq: A > A > $o,K: A] :
% 0.14/0.39 ( ( member @ A @ I @ ( set_atLeast @ A @ Less_eq @ K ) )
% 0.14/0.39 = ( Less_eq @ K @ I ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.atLeast_iff
% 0.14/0.39 thf(fact_70_llist_Oinject,axiom,
% 0.14/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.14/0.39 = ( ( X21 = Y21 )
% 0.14/0.39 & ( X22 = Y22 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.inject
% 0.14/0.39 thf(fact_71_Singleton,axiom,
% 0.14/0.39 ! [X3: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1598213697e_LNil @ a ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Singleton
% 0.14/0.39 thf(fact_72_lsorted_Ocases,axiom,
% 0.14/0.39 ! [A2: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( coindu543932918sorted @ a @ less_eq @ A2 )
% 0.14/0.39 => ( ( A2
% 0.14/0.39 != ( coindu1598213697e_LNil @ a ) )
% 0.14/0.39 => ( ! [X5: a] :
% 0.14/0.39 ( A2
% 0.14/0.39 != ( coindu1121789889_LCons @ a @ X5 @ ( coindu1598213697e_LNil @ a ) ) )
% 0.14/0.39 => ~ ! [X5: a,Y3: a,Xs2: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ a @ X5 @ ( coindu1121789889_LCons @ a @ Y3 @ Xs2 ) ) )
% 0.14/0.39 => ( ( less_eq @ X5 @ Y3 )
% 0.14/0.39 => ~ ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted.cases
% 0.14/0.39 thf(fact_73_lsorted_Ocoinduct,axiom,
% 0.14/0.39 ! [X2: ( coindu1593790203_llist @ a ) > $o,X3: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( X2 @ X3 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( X2 @ X5 )
% 0.14/0.39 => ( ( X5
% 0.14/0.39 = ( coindu1598213697e_LNil @ a ) )
% 0.14/0.39 | ? [Xa: a] :
% 0.14/0.39 ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ a @ Xa @ ( coindu1598213697e_LNil @ a ) ) )
% 0.14/0.39 | ? [Xa: a,Y4: a,Xs3: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ a @ Xa @ ( coindu1121789889_LCons @ a @ Y4 @ Xs3 ) ) )
% 0.14/0.39 & ( less_eq @ Xa @ Y4 )
% 0.14/0.39 & ( ( X2 @ ( coindu1121789889_LCons @ a @ Y4 @ Xs3 ) )
% 0.14/0.39 | ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y4 @ Xs3 ) ) ) ) ) )
% 0.14/0.39 => ( coindu543932918sorted @ a @ less_eq @ X3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted.coinduct
% 0.14/0.39 thf(fact_74_lsorted_Osimps,axiom,
% 0.14/0.39 ! [A2: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( coindu543932918sorted @ a @ less_eq @ A2 )
% 0.14/0.39 = ( ( A2
% 0.14/0.39 = ( coindu1598213697e_LNil @ a ) )
% 0.14/0.39 | ? [X4: a] :
% 0.14/0.39 ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ a @ X4 @ ( coindu1598213697e_LNil @ a ) ) )
% 0.14/0.39 | ? [X4: a,Y5: a,Xs4: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ a @ X4 @ ( coindu1121789889_LCons @ a @ Y5 @ Xs4 ) ) )
% 0.14/0.39 & ( less_eq @ X4 @ Y5 )
% 0.14/0.39 & ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y5 @ Xs4 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted.simps
% 0.14/0.39 thf(fact_75_LCons__lprefix__LCons,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.14/0.39 = ( ( X3 = Y )
% 0.14/0.39 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % LCons_lprefix_LCons
% 0.14/0.39 thf(fact_76_lprefix__code_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_code(1)
% 0.14/0.39 thf(fact_77_unfold__llist__eq__LCons,axiom,
% 0.14/0.39 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( ~ ( IS_LNIL @ B2 )
% 0.14/0.39 & ( X3
% 0.14/0.39 = ( LHD @ B2 ) )
% 0.14/0.39 & ( Xs
% 0.14/0.39 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist_eq_LCons
% 0.14/0.39 thf(fact_78_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.14/0.39 = ( P2 @ A2 ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.disc_iff(1)
% 0.14/0.39 thf(fact_79_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.14/0.39 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) )
% 0.14/0.39 = ( ~ ( P2 @ A2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.disc_iff(2)
% 0.14/0.39 thf(fact_80_lprefix__LNil,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_LNil
% 0.14/0.39 thf(fact_81_lsorted__LCons__LCons,axiom,
% 0.14/0.39 ! [X3: a,Y: a,Xs: coindu1593790203_llist @ a] :
% 0.14/0.39 ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1121789889_LCons @ a @ Y @ Xs ) ) )
% 0.14/0.39 = ( ( less_eq @ X3 @ Y )
% 0.14/0.39 & ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_LCons_LCons
% 0.14/0.39 thf(fact_82_lhd__LCons__ltl,axiom,
% 0.14/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.14/0.39 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 0.14/0.39 = Llist ) ) ).
% 0.14/0.39
% 0.14/0.39 % lhd_LCons_ltl
% 0.14/0.39 thf(fact_83_lsorted__code_I1_J,axiom,
% 0.14/0.39 coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_code(1)
% 0.14/0.39 thf(fact_84_lsorted__code_I2_J,axiom,
% 0.14/0.39 ! [X3: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1598213697e_LNil @ a ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lsorted_code(2)
% 0.14/0.39 thf(fact_85_lprefix__code_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_code(2)
% 0.14/0.39 thf(fact_86_lprefix_Ocases,axiom,
% 0.14/0.39 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 0.14/0.39 => ( ( ( A1
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ! [Xs2: coindu1593790203_llist @ A] : ( A22 != Xs2 ) )
% 0.14/0.39 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X5: A] :
% 0.14/0.39 ( ( A1
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.14/0.39 => ( ( A22
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Ys2 ) )
% 0.14/0.39 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix.cases
% 0.14/0.39 thf(fact_87_lprefix_Osimps,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A )
% 0.14/0.39 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A12
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 & ( A23 = Xs4 ) )
% 0.14/0.39 | ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X4: A] :
% 0.14/0.39 ( ( A12
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.14/0.39 & ( A23
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Ys3 ) )
% 0.14/0.39 & ( coindu1696667936prefix @ A @ Xs4 @ Ys3 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix.simps
% 0.14/0.39 thf(fact_88_lprefix_Ocoinduct,axiom,
% 0.14/0.39 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ X3 @ Xa2 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ A,Xa3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ X5 @ Xa3 )
% 0.14/0.39 => ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 & ( Xa3 = Xs3 ) )
% 0.14/0.39 | ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Xs3 ) )
% 0.14/0.39 & ( Xa3
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 0.14/0.39 & ( ( X2 @ Xs3 @ Ys4 )
% 0.14/0.39 | ( coindu1696667936prefix @ A @ Xs3 @ Ys4 ) ) ) ) )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ X3 @ Xa2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix.coinduct
% 0.14/0.39 thf(fact_89_lprefix__LCons__conv,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.14/0.39 = ( ( Xs
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Xs
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.14/0.39 & ( coindu1696667936prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_LCons_conv
% 0.14/0.39 thf(fact_90_unfold__llist_Ocode,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType] :
% 0.14/0.39 ( ( coindu1599971794_llist @ A @ B )
% 0.14/0.39 = ( ^ [P3: A > $o,G212: A > B,G222: A > A,A4: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P3 @ A4 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A4 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.code
% 0.14/0.39 thf(fact_91_neq__LNil__conv,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Xs
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = ( ? [X4: A,Xs5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( Xs
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % neq_LNil_conv
% 0.14/0.39 thf(fact_92_llist_Oexhaust,axiom,
% 0.14/0.39 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Y
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.14/0.39 ( Y
% 0.14/0.39 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.exhaust
% 0.14/0.39 thf(fact_93_unfold__llist_Octr_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,B: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.14/0.39 ( ( P2 @ A2 )
% 0.14/0.39 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.14/0.39 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.ctr(1)
% 0.14/0.39 thf(fact_94_unfold__llist_Octr_I2_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.14/0.39 ( ~ ( P2 @ A2 )
% 0.14/0.39 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.14/0.39 = ( coindu1121789889_LCons @ B @ ( G21 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.ctr(2)
% 0.14/0.39 thf(fact_95_llist_Odistinct_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1598213697e_LNil @ A )
% 0.14/0.39 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.distinct(1)
% 0.14/0.39 thf(fact_96_llist_Osimps_I4_J,axiom,
% 0.14/0.39 ! [A: $tType,B: $tType,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B] :
% 0.14/0.39 ( ( coindu882539134_llist @ B @ A @ F12 @ F22 @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = F12 ) ).
% 0.14/0.39
% 0.14/0.39 % llist.simps(4)
% 0.14/0.39 thf(fact_97_llist_Osimps_I5_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu882539134_llist @ B @ A @ F12 @ F22 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.14/0.39 = ( F22 @ X21 @ X22 ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.simps(5)
% 0.14/0.39 thf(fact_98_ord_OSingleton,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,X3: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.Singleton
% 0.14/0.39 thf(fact_99_ord_Olsorted_Ocoinduct,axiom,
% 0.14/0.39 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 0.14/0.39 ( ( X2 @ X3 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ X5 )
% 0.14/0.39 => ( ( X5
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [Xa: A] :
% 0.14/0.39 ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu1598213697e_LNil @ A ) ) )
% 0.14/0.39 | ? [Xa: A,Y4: A,Xs3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu1121789889_LCons @ A @ Y4 @ Xs3 ) ) )
% 0.14/0.39 & ( Less_eq @ Xa @ Y4 )
% 0.14/0.39 & ( ( X2 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs3 ) )
% 0.14/0.39 | ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y4 @ Xs3 ) ) ) ) ) )
% 0.14/0.39 => ( coindu543932918sorted @ A @ Less_eq @ X3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted.coinduct
% 0.14/0.39 thf(fact_100_ord_Olsorted_Osimps,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu543932918sorted @ A )
% 0.14/0.39 = ( ^ [Less_eq2: A > A > $o,A4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A4
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [X4: A] :
% 0.14/0.39 ( A4
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.14/0.39 | ? [X4: A,Y5: A,Xs4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A4
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ ( coindu1121789889_LCons @ A @ Y5 @ Xs4 ) ) )
% 0.14/0.39 & ( Less_eq2 @ X4 @ Y5 )
% 0.14/0.39 & ( coindu543932918sorted @ A @ Less_eq2 @ ( coindu1121789889_LCons @ A @ Y5 @ Xs4 ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted.simps
% 0.14/0.39 thf(fact_101_ord_Olsorted_Ocases,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,A2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ A2 )
% 0.14/0.39 => ( ( A2
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( ! [X5: A] :
% 0.14/0.39 ( A2
% 0.14/0.39 != ( coindu1121789889_LCons @ A @ X5 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.14/0.39 => ~ ! [X5: A,Y3: A,Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) )
% 0.14/0.39 => ( ( Less_eq @ X5 @ Y3 )
% 0.14/0.39 => ~ ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted.cases
% 0.14/0.39 thf(fact_102_ord_Olsorted__code_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,X3: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_code(2)
% 0.14/0.39 thf(fact_103_ltl__unfold__llist,axiom,
% 0.14/0.39 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.14/0.39 ( ( ( IS_LNIL @ A2 )
% 0.14/0.39 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) )
% 0.14/0.39 & ( ~ ( IS_LNIL @ A2 )
% 0.14/0.39 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.14/0.39 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltl_unfold_llist
% 0.14/0.39 thf(fact_104_llist_Osplit__sel,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P: B > $o,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( P @ ( coindu882539134_llist @ B @ A @ F12 @ F22 @ Llist ) )
% 0.14/0.39 = ( ( ( Llist
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( P @ F12 ) )
% 0.14/0.39 & ( ( Llist
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.14/0.39 => ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.split_sel
% 0.14/0.39 thf(fact_105_llist_Osplit__sel__asm,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P: B > $o,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( P @ ( coindu882539134_llist @ B @ A @ F12 @ F22 @ Llist ) )
% 0.14/0.39 = ( ~ ( ( ( Llist
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 & ~ ( P @ F12 ) )
% 0.14/0.39 | ( ( Llist
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.14/0.39 & ~ ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.split_sel_asm
% 0.14/0.39 thf(fact_106_eq__LConsD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Xs
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.14/0.39 => ( ( Xs
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.14/0.39 = Y )
% 0.14/0.39 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 0.14/0.39 = Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % eq_LConsD
% 0.14/0.39 thf(fact_107_llist_Oexhaust__sel,axiom,
% 0.14/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Llist
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( Llist
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.exhaust_sel
% 0.14/0.39 thf(fact_108_LCons__lprefix__conv,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ Ys )
% 0.14/0.39 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Ys
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Ys5 ) )
% 0.14/0.39 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % LCons_lprefix_conv
% 0.14/0.39 thf(fact_109_Le__LCons,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X3: A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ X3 @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Le_LCons
% 0.14/0.39 thf(fact_110_not__lnull__conv,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.14/0.39 = ( ? [X4: A,Xs5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( Xs
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % not_lnull_conv
% 0.14/0.39 thf(fact_111_llist_OdiscI_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Llist
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.14/0.39 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.discI(2)
% 0.14/0.39 thf(fact_112_llist_Odisc_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.14/0.39 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.disc(2)
% 0.14/0.39 thf(fact_113_ltl__simps_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.14/0.39 = X22 ) ).
% 0.14/0.39
% 0.14/0.39 % ltl_simps(2)
% 0.14/0.39 thf(fact_114_LNil__lprefix,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.14/0.39
% 0.14/0.39 % LNil_lprefix
% 0.14/0.39 thf(fact_115_lhd__LCons,axiom,
% 0.14/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.14/0.39 = X21 ) ).
% 0.14/0.39
% 0.14/0.39 % lhd_LCons
% 0.14/0.39 thf(fact_116_lnull__def,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A )
% 0.14/0.39 = ( ^ [Llist5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( Llist5
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lnull_def
% 0.14/0.39 thf(fact_117_llist_Ocollapse_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ Llist )
% 0.14/0.39 => ( Llist
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.collapse(1)
% 0.14/0.39 thf(fact_118_llist_OdiscI_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Llist
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.discI(1)
% 0.14/0.39 thf(fact_119_llist_Odisc_I1_J,axiom,
% 0.14/0.39 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.disc(1)
% 0.14/0.39 thf(fact_120_ltl__simps_I1_J,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltl_simps(1)
% 0.14/0.39 thf(fact_121_ord_Olsorted__LCons__LCons,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,X3: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.14/0.39 = ( ( Less_eq @ X3 @ Y )
% 0.14/0.39 & ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_LCons_LCons
% 0.14/0.39 thf(fact_122_ord_OLCons__LCons,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,X3: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Less_eq @ X3 @ Y )
% 0.14/0.39 => ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) )
% 0.14/0.39 => ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.LCons_LCons
% 0.14/0.39 thf(fact_123_ord_OLNil,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.LNil
% 0.14/0.39 thf(fact_124_ord_Olsorted__code_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_code(1)
% 0.14/0.39 thf(fact_125_unfold__llist_Odisc_I1_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.14/0.39 ( ( P2 @ A2 )
% 0.14/0.39 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.disc(1)
% 0.14/0.39 thf(fact_126_unfold__llist_Odisc_I2_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.14/0.39 ( ~ ( P2 @ A2 )
% 0.14/0.39 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.disc(2)
% 0.14/0.39 thf(fact_127_unfold__llist_Osimps_I4_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.14/0.39 ( ~ ( P2 @ A2 )
% 0.14/0.39 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.14/0.39 = ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.simps(4)
% 0.14/0.39 thf(fact_128_unfold__llist_Osimps_I3_J,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.14/0.39 ( ~ ( P2 @ A2 )
% 0.14/0.39 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.14/0.39 = ( G21 @ A2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % unfold_llist.simps(3)
% 0.14/0.39 thf(fact_129_lSup_Octr_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ! [X5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ A3 )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ X5 ) )
% 0.14/0.39 => ( ( coindu526335360e_lSup @ A @ A3 )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lSup.ctr(1)
% 0.14/0.39 thf(fact_130_ord_OatLeastAtMost__def,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( set_atLeastAtMost @ A )
% 0.14/0.39 = ( ^ [Less_eq2: A > A > $o,L2: A,U2: A] : ( inf_inf @ ( set @ A ) @ ( set_atLeast @ A @ Less_eq2 @ L2 ) @ ( set_atMost @ A @ Less_eq2 @ U2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.atLeastAtMost_def
% 0.14/0.39 thf(fact_131_ord_Olsorted__LCons_H,axiom,
% 0.14/0.39 ! [A: $tType,Less_eq: A > A > $o,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( Less_eq @ X3 @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 & ( coindu543932918sorted @ A @ Less_eq @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.lsorted_LCons'
% 0.14/0.39 thf(fact_132_ord_OatLeastAtMost__iff,axiom,
% 0.14/0.39 ! [A: $tType,I: A,Less_eq: A > A > $o,L: A,U: A] :
% 0.14/0.39 ( ( member @ A @ I @ ( set_atLeastAtMost @ A @ Less_eq @ L @ U ) )
% 0.14/0.39 = ( ( Less_eq @ L @ I )
% 0.14/0.39 & ( Less_eq @ I @ U ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ord.atLeastAtMost_iff
% 0.14/0.39 thf(fact_133_Int__iff,axiom,
% 0.14/0.39 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.14/0.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.14/0.39 = ( ( member @ A @ C @ A3 )
% 0.14/0.39 & ( member @ A @ C @ B4 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Int_iff
% 0.14/0.39 thf(fact_134_IntI,axiom,
% 0.14/0.39 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.14/0.39 ( ( member @ A @ C @ A3 )
% 0.14/0.39 => ( ( member @ A @ C @ B4 )
% 0.14/0.39 => ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % IntI
% 0.14/0.39 thf(fact_135_inf__right__idem,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A] :
% 0.14/0.39 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y ) @ Y )
% 0.14/0.39 = ( inf_inf @ A @ X3 @ Y ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_right_idem
% 0.14/0.39 thf(fact_136_inf_Oright__idem,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [A2: A,B2: A] :
% 0.14/0.39 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.14/0.39 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf.right_idem
% 0.14/0.39 thf(fact_137_inf__left__idem,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A] :
% 0.14/0.39 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y ) )
% 0.14/0.39 = ( inf_inf @ A @ X3 @ Y ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_left_idem
% 0.14/0.39 thf(fact_138_inf_Oleft__idem,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [A2: A,B2: A] :
% 0.14/0.39 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.14/0.39 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf.left_idem
% 0.14/0.39 thf(fact_139_inf__idem,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A] :
% 0.14/0.39 ( ( inf_inf @ A @ X3 @ X3 )
% 0.14/0.39 = X3 ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_idem
% 0.14/0.39 thf(fact_140_inf__apply,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.14/0.39 => ( ( inf_inf @ ( A > B ) )
% 0.14/0.39 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( inf_inf @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_apply
% 0.14/0.39 thf(fact_141_inf_Oidem,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [A2: A] :
% 0.14/0.39 ( ( inf_inf @ A @ A2 @ A2 )
% 0.14/0.39 = A2 ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf.idem
% 0.14/0.39 thf(fact_142_inf__sup__aci_I4_J,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( lattice @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A] :
% 0.14/0.39 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y ) )
% 0.14/0.39 = ( inf_inf @ A @ X3 @ Y ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_sup_aci(4)
% 0.14/0.39 thf(fact_143_inf__sup__aci_I3_J,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( lattice @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A,Z: A] :
% 0.14/0.39 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) )
% 0.14/0.39 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X3 @ Z ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_sup_aci(3)
% 0.14/0.39 thf(fact_144_inf__sup__aci_I2_J,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( lattice @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A,Z: A] :
% 0.14/0.39 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y ) @ Z )
% 0.14/0.39 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_sup_aci(2)
% 0.14/0.39 thf(fact_145_inf__sup__aci_I1_J,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( lattice @ A @ ( type2 @ A ) )
% 0.14/0.39 => ( ( inf_inf @ A )
% 0.14/0.39 = ( ^ [X4: A,Y5: A] : ( inf_inf @ A @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_sup_aci(1)
% 0.14/0.39 thf(fact_146_inf__fun__def,axiom,
% 0.14/0.39 ! [B: $tType,A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.14/0.39 => ( ( inf_inf @ ( A > B ) )
% 0.14/0.39 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( inf_inf @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_fun_def
% 0.14/0.39 thf(fact_147_inf_Oassoc,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [A2: A,B2: A,C: A] :
% 0.14/0.39 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C )
% 0.14/0.39 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf.assoc
% 0.14/0.39 thf(fact_148_inf__assoc,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A,Z: A] :
% 0.14/0.39 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y ) @ Z )
% 0.14/0.39 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_assoc
% 0.14/0.39 thf(fact_149_inf_Ocommute,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ( ( inf_inf @ A )
% 0.14/0.39 = ( ^ [A4: A,B3: A] : ( inf_inf @ A @ B3 @ A4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf.commute
% 0.14/0.39 thf(fact_150_inf__commute,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ( ( inf_inf @ A )
% 0.14/0.39 = ( ^ [X4: A,Y5: A] : ( inf_inf @ A @ Y5 @ X4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_commute
% 0.14/0.39 thf(fact_151_inf_Oleft__commute,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [B2: A,A2: A,C: A] :
% 0.14/0.39 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C ) )
% 0.14/0.39 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf.left_commute
% 0.14/0.39 thf(fact_152_inf__left__commute,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.14/0.39 => ! [X3: A,Y: A,Z: A] :
% 0.14/0.39 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) )
% 0.14/0.39 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X3 @ Z ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % inf_left_commute
% 0.14/0.39 thf(fact_153_IntE,axiom,
% 0.14/0.39 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.14/0.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.14/0.39 => ~ ( ( member @ A @ C @ A3 )
% 0.14/0.39 => ~ ( member @ A @ C @ B4 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % IntE
% 0.14/0.39 thf(fact_154_IntD1,axiom,
% 0.14/0.39 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.14/0.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.14/0.39 => ( member @ A @ C @ A3 ) ) ).
% 0.14/0.39
% 0.14/0.39 % IntD1
% 0.14/0.39 thf(fact_155_IntD2,axiom,
% 0.14/0.39 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.14/0.39 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.14/0.39 => ( member @ A @ C @ B4 ) ) ).
% 0.14/0.39
% 0.14/0.39 % IntD2
% 0.14/0.39 thf(fact_156_Int__assoc,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 0.14/0.39 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ C2 )
% 0.14/0.39 = ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Int_assoc
% 0.14/0.39 thf(fact_157_Int__absorb,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ A] :
% 0.14/0.39 ( ( inf_inf @ ( set @ A ) @ A3 @ A3 )
% 0.14/0.39 = A3 ) ).
% 0.14/0.39
% 0.14/0.39 % Int_absorb
% 0.14/0.39 thf(fact_158_Int__commute,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( inf_inf @ ( set @ A ) )
% 0.14/0.39 = ( ^ [A5: set @ A,B5: set @ A] : ( inf_inf @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Int_commute
% 0.14/0.39 thf(fact_159_Int__left__absorb,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.14/0.39 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.14/0.39 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.14/0.39
% 0.14/0.39 % Int_left_absorb
% 0.14/0.39 thf(fact_160_Int__left__commute,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 0.14/0.39 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C2 ) )
% 0.14/0.39 = ( inf_inf @ ( set @ A ) @ B4 @ ( inf_inf @ ( set @ A ) @ A3 @ C2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Int_left_commute
% 0.14/0.39 thf(fact_161_compact__LCons__iff,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % compact_LCons_iff
% 0.14/0.39 thf(fact_162_ltakeWhile_Ocode,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu721411036eWhile @ A )
% 0.14/0.39 = ( ^ [P4: A > $o,Xs4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( if @ ( coindu1593790203_llist @ A )
% 0.14/0.39 @ ( ( coindu335574135_lnull @ A @ Xs4 )
% 0.14/0.39 | ~ ( P4 @ ( coindu1046438764le_lhd @ A @ Xs4 ) ) )
% 0.14/0.39 @ ( coindu1598213697e_LNil @ A )
% 0.14/0.39 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs4 ) @ ( coindu721411036eWhile @ A @ P4 @ ( coindu1047225960le_ltl @ A @ Xs4 ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.code
% 0.14/0.39 thf(fact_163_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.14/0.39 = ( ( Xs
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Xs
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.14/0.39 & ( coindu1571841457prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(3)
% 0.14/0.39 thf(fact_164_lstrict__prefix__code_I3_J,axiom,
% 0.14/0.39 ! [B: $tType,X3: B,Xs: coindu1593790203_llist @ B] :
% 0.14/0.39 ~ ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X3 @ Xs ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.14/0.39
% 0.14/0.39 % lstrict_prefix_code(3)
% 0.14/0.39 thf(fact_165_ltakeWhile__LNil,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o] :
% 0.14/0.39 ( ( coindu721411036eWhile @ A @ P @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile_LNil
% 0.14/0.39 thf(fact_166_lstrict__prefix__code_I4_J,axiom,
% 0.14/0.39 ! [B: $tType,X3: B,Xs: coindu1593790203_llist @ B,Y: B,Ys: coindu1593790203_llist @ B] :
% 0.14/0.39 ( ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X3 @ Xs ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 0.14/0.39 = ( ( X3 = Y )
% 0.14/0.39 & ( coindu574146665prefix @ B @ Xs @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lstrict_prefix_code(4)
% 0.14/0.39 thf(fact_167_lstrict__prefix__code_I1_J,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % lstrict_prefix_code(1)
% 0.14/0.39 thf(fact_168_ltakeWhile__LCons,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( P @ X3 )
% 0.14/0.39 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) )
% 0.14/0.39 & ( ~ ( P @ X3 )
% 0.14/0.39 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile_LCons
% 0.14/0.39 thf(fact_169_ltakeWhile_Odisc__iff_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 0.14/0.39 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 & ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.disc_iff(2)
% 0.14/0.39 thf(fact_170_ltakeWhile_Odisc__iff_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.disc_iff(1)
% 0.14/0.39 thf(fact_171_lnull__ltakeWhile,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lnull_ltakeWhile
% 0.14/0.39 thf(fact_172_lstrict__prefix__code_I2_J,axiom,
% 0.14/0.39 ! [B: $tType,Y: B,Ys: coindu1593790203_llist @ B] : ( coindu574146665prefix @ B @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) ) ).
% 0.14/0.39
% 0.14/0.39 % lstrict_prefix_code(2)
% 0.14/0.39 thf(fact_173_lprefix__ltakeWhile,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) @ Xs ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_ltakeWhile
% 0.14/0.39 thf(fact_174_llist__less__induct,axiom,
% 0.14/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ! [Ys4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu574146665prefix @ A @ Ys4 @ Xs2 )
% 0.14/0.39 => ( P @ Ys4 ) )
% 0.14/0.39 => ( P @ Xs2 ) )
% 0.14/0.39 => ( P @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist_less_induct
% 0.14/0.39 thf(fact_175_lstrict__prefix__def,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu574146665prefix @ A )
% 0.14/0.39 = ( ^ [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs4 @ Ys3 )
% 0.14/0.39 & ( Xs4 != Ys3 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lstrict_prefix_def
% 0.14/0.39 thf(fact_176_ltakeWhile_Odisc_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 => ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.disc(2)
% 0.14/0.39 thf(fact_177_ltakeWhile_Odisc_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.14/0.39 => ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.disc(1)
% 0.14/0.39 thf(fact_178_lhd__ltakeWhile,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 => ( ( coindu1046438764le_lhd @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lhd_ltakeWhile
% 0.14/0.39 thf(fact_179_ltakeWhile__eq__LNil__iff,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = ( ( Xs
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile_eq_LNil_iff
% 0.14/0.39 thf(fact_180_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu1571841457prefix @ A )
% 0.14/0.39 = ( coindu1696667936prefix @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_def
% 0.14/0.39 thf(fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 = ( Xs
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(1)
% 0.14/0.39 thf(fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1571841457prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.14/0.39
% 0.14/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(2)
% 0.14/0.39 thf(fact_183_ltakeWhile_Octr_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.14/0.39 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.ctr(1)
% 0.14/0.39 thf(fact_184_ltakeWhile_Osimps_I4_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.simps(4)
% 0.14/0.39 thf(fact_185_ltl__ltakeWhile,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) )
% 0.14/0.39 & ( ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltl_ltakeWhile
% 0.14/0.39 thf(fact_186_ltakeWhile_Octr_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.14/0.39 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile.ctr(2)
% 0.14/0.39 thf(fact_187_compact__LConsI,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X3: A] :
% 0.14/0.39 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs )
% 0.14/0.39 => ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % compact_LConsI
% 0.14/0.39 thf(fact_188_compact__LConsD,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 => ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % compact_LConsD
% 0.14/0.39 thf(fact_189_ldistinct__lSup,axiom,
% 0.14/0.39 ! [A: $tType,Y2: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ Y2 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ Y2 )
% 0.14/0.39 => ( coindu6345450stinct @ A @ X5 ) )
% 0.14/0.39 => ( coindu6345450stinct @ A @ ( coindu526335360e_lSup @ A @ Y2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_lSup
% 0.14/0.39 thf(fact_190_llast__singleton,axiom,
% 0.14/0.39 ! [A: $tType,X3: A] :
% 0.14/0.39 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.14/0.39 = X3 ) ).
% 0.14/0.39
% 0.14/0.39 % llast_singleton
% 0.14/0.39 thf(fact_191_cont__ltl,axiom,
% 0.14/0.39 ! [A: $tType] : ( comple1412571634l_cont @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1047225960le_ltl @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % cont_ltl
% 0.14/0.39 thf(fact_192_ldistinct__LNil__code,axiom,
% 0.14/0.39 ! [A: $tType] : ( coindu6345450stinct @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_LNil_code
% 0.14/0.39 thf(fact_193_llast__LCons2,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.14/0.39 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llast_LCons2
% 0.14/0.39 thf(fact_194_ldistinct__ltlI,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu6345450stinct @ A @ Xs )
% 0.14/0.39 => ( coindu6345450stinct @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_ltlI
% 0.14/0.39 thf(fact_195_ldistinct_OLNil,axiom,
% 0.14/0.39 ! [A: $tType] : ( coindu6345450stinct @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct.LNil
% 0.14/0.39 thf(fact_196_ldistinct__lprefix,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu6345450stinct @ A @ Xs )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.14/0.39 => ( coindu6345450stinct @ A @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_lprefix
% 0.14/0.39 thf(fact_197_llast__LCons,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X3: A] :
% 0.14/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = X3 ) )
% 0.14/0.39 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( coindu2000965700_llast @ A @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llast_LCons
% 0.14/0.39 thf(fact_198_ldistinct__lhdD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu6345450stinct @ A @ Xs )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ~ ( member @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_lhdD
% 0.14/0.39 thf(fact_199_ldistinct__coinduct,axiom,
% 0.14/0.39 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ Xs )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( ~ ( member @ A @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.14/0.39 & ( ( X2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.14/0.39 | ( coindu6345450stinct @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) ) ) ) )
% 0.14/0.39 => ( coindu6345450stinct @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_coinduct
% 0.14/0.39 thf(fact_200_ldistinct__LCons,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu6345450stinct @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( ~ ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 & ( coindu6345450stinct @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct_LCons
% 0.14/0.39 thf(fact_201_ldistinct_OLCons,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ~ ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( ( coindu6345450stinct @ A @ Xs )
% 0.14/0.39 => ( coindu6345450stinct @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct.LCons
% 0.14/0.39 thf(fact_202_llist_Oset__sel_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,A2: coindu1593790203_llist @ A,X3: A] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.14/0.39 => ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ A2 ) ) )
% 0.14/0.39 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.set_sel(2)
% 0.14/0.39 thf(fact_203_llist_Oset__sel_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.14/0.39 => ( member @ A @ ( coindu1046438764le_lhd @ A @ A2 ) @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.set_sel(1)
% 0.14/0.39 thf(fact_204_lset__intros_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,X6: A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lset_intros(2)
% 0.14/0.39 thf(fact_205_lset__intros_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lset_intros(1)
% 0.14/0.39 thf(fact_206_llist_Oset__intros_I2_J,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,A22: coindu1593790203_llist @ A,A1: A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ A22 ) )
% 0.14/0.39 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.set_intros(2)
% 0.14/0.39 thf(fact_207_llist_Oset__intros_I1_J,axiom,
% 0.14/0.39 ! [A: $tType,A1: A,A22: coindu1593790203_llist @ A] : ( member @ A @ A1 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.set_intros(1)
% 0.14/0.39 thf(fact_208_lset__cases,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( ! [Xs6: coindu1593790203_llist @ A] :
% 0.14/0.39 ( Xs
% 0.14/0.39 != ( coindu1121789889_LCons @ A @ X3 @ Xs6 ) )
% 0.14/0.39 => ~ ! [X7: A,Xs6: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( Xs
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X7 @ Xs6 ) )
% 0.14/0.39 => ~ ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs6 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lset_cases
% 0.14/0.39 thf(fact_209_lset__induct,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) )
% 0.14/0.39 => ( ! [X7: A,Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.14/0.39 => ( ( X3 != X7 )
% 0.14/0.39 => ( ( P @ Xs2 )
% 0.14/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X7 @ Xs2 ) ) ) ) )
% 0.14/0.39 => ( P @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lset_induct
% 0.14/0.39 thf(fact_210_lset__induct_H,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) )
% 0.14/0.39 => ( ! [X7: A,Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.14/0.39 => ( ( P @ Xs2 )
% 0.14/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X7 @ Xs2 ) ) ) )
% 0.14/0.39 => ( P @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lset_induct'
% 0.14/0.39 thf(fact_211_llist_Oset__cases,axiom,
% 0.14/0.39 ! [A: $tType,E: A,A2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.14/0.39 => ( ! [Z2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( A2
% 0.14/0.39 != ( coindu1121789889_LCons @ A @ E @ Z2 ) )
% 0.14/0.39 => ~ ! [Z1: A,Z2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.14/0.39 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.set_cases
% 0.14/0.39 thf(fact_212_llist_Oset__induct,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,A2: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.14/0.39 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.14/0.39 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A,Xa3: A] :
% 0.14/0.39 ( ( member @ A @ Xa3 @ ( coindu1112613586e_lset @ A @ Z2 ) )
% 0.14/0.39 => ( ( P @ Xa3 @ Z2 )
% 0.14/0.39 => ( P @ Xa3 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) ) ) )
% 0.14/0.39 => ( P @ X3 @ A2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist.set_induct
% 0.14/0.39 thf(fact_213_in__lset__ltlD,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) )
% 0.14/0.39 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % in_lset_ltlD
% 0.14/0.39 thf(fact_214_ltakeWhile__all,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.14/0.39 ( ! [X5: A] :
% 0.14/0.39 ( ( member @ A @ X5 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( P @ X5 ) )
% 0.14/0.39 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.14/0.39 = Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile_all
% 0.14/0.39 thf(fact_215_ltakeWhile__cong,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,P: A > $o,Q: A > $o] :
% 0.14/0.39 ( ( Xs = Ys )
% 0.14/0.39 => ( ! [X5: A] :
% 0.14/0.39 ( ( member @ A @ X5 @ ( coindu1112613586e_lset @ A @ Ys ) )
% 0.14/0.39 => ( ( P @ X5 )
% 0.14/0.39 = ( Q @ X5 ) ) )
% 0.14/0.39 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.14/0.39 = ( coindu721411036eWhile @ A @ Q @ Ys ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ltakeWhile_cong
% 0.14/0.39 thf(fact_216_lset__ltakeWhileD,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 0.14/0.39 => ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 & ( P @ X3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lset_ltakeWhileD
% 0.14/0.39 thf(fact_217_llist__set__induct,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.14/0.39 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( P @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ Xs2 ) )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,Y3: A] :
% 0.14/0.39 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( ( member @ A @ Y3 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.14/0.39 => ( ( P @ Y3 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.14/0.39 => ( P @ Y3 @ Xs2 ) ) ) )
% 0.14/0.39 => ( P @ X3 @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist_set_induct
% 0.14/0.39 thf(fact_218_ldistinct_Ocases,axiom,
% 0.14/0.39 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu6345450stinct @ A @ A2 )
% 0.14/0.39 => ( ( A2
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ~ ! [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.14/0.39 => ( ~ ( member @ A @ X5 @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.14/0.39 => ~ ( coindu6345450stinct @ A @ Xs2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct.cases
% 0.14/0.39 thf(fact_219_ldistinct_Osimps,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu6345450stinct @ A )
% 0.14/0.39 = ( ^ [A4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A4
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [X4: A,Xs4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A4
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.14/0.39 & ~ ( member @ A @ X4 @ ( coindu1112613586e_lset @ A @ Xs4 ) )
% 0.14/0.39 & ( coindu6345450stinct @ A @ Xs4 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct.simps
% 0.14/0.39 thf(fact_220_ldistinct_Ocoinduct,axiom,
% 0.14/0.39 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ X3 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ X5 )
% 0.14/0.39 => ( ( X5
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [Xa: A,Xs3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xa @ Xs3 ) )
% 0.14/0.39 & ~ ( member @ A @ Xa @ ( coindu1112613586e_lset @ A @ Xs3 ) )
% 0.14/0.39 & ( ( X2 @ Xs3 )
% 0.14/0.39 | ( coindu6345450stinct @ A @ Xs3 ) ) ) ) )
% 0.14/0.39 => ( coindu6345450stinct @ A @ X3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % ldistinct.coinduct
% 0.14/0.39 thf(fact_221_compact__eq__lfinite,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) )
% 0.14/0.39 = ( coindu1213758845finite @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % compact_eq_lfinite
% 0.14/0.39 thf(fact_222_llexord_Ocoinduct,axiom,
% 0.14/0.39 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A,R2: A > A > $o] :
% 0.14/0.39 ( ( X2 @ X3 @ Xa2 )
% 0.14/0.39 => ( ! [X5: coindu1593790203_llist @ A,Xa3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X2 @ X5 @ Xa3 )
% 0.14/0.39 => ( ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Xs3 ) )
% 0.14/0.39 & ( Xa3
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 0.14/0.39 & ( ( X2 @ Xs3 @ Ys4 )
% 0.14/0.39 | ( coindu300403952lexord @ A @ R2 @ Xs3 @ Ys4 ) ) )
% 0.14/0.39 | ? [Xb: A,Y4: A,Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Xs3 ) )
% 0.14/0.39 & ( Xa3
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y4 @ Ys4 ) )
% 0.14/0.39 & ( R2 @ Xb @ Y4 ) )
% 0.14/0.39 | ? [Ys4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( X5
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 & ( Xa3 = Ys4 ) ) ) )
% 0.14/0.39 => ( coindu300403952lexord @ A @ R2 @ X3 @ Xa2 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llexord.coinduct
% 0.14/0.39 thf(fact_223_lfinite__LCons,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.14/0.39 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_LCons
% 0.14/0.39 thf(fact_224_lfinite__code_I2_J,axiom,
% 0.14/0.39 ! [B: $tType,X3: B,Xs: coindu1593790203_llist @ B] :
% 0.14/0.39 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X3 @ Xs ) )
% 0.14/0.39 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_code(2)
% 0.14/0.39 thf(fact_225_lfinite__code_I1_J,axiom,
% 0.14/0.39 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_code(1)
% 0.14/0.39 thf(fact_226_lfinite__ltl,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.14/0.39 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_ltl
% 0.14/0.39 thf(fact_227_lfinite__ltakeWhile,axiom,
% 0.14/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.14/0.39 = ( ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 | ? [X4: A] :
% 0.14/0.39 ( ( member @ A @ X4 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.14/0.39 & ~ ( P @ X4 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_ltakeWhile
% 0.14/0.39 thf(fact_228_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A )
% 0.14/0.39 = ( ^ [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( ( coindu1213758845finite @ A @ Xs4 )
% 0.14/0.39 => ( coindu1571841457prefix @ A @ Xs4 @ Ys3 ) )
% 0.14/0.39 & ( ~ ( coindu1213758845finite @ A @ Xs4 )
% 0.14/0.39 => ( Xs4 = Ys3 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % Coinductive_List_Mirabelle_kmikjhschf.lprefix_nitpick_simps
% 0.14/0.39 thf(fact_229_lstrict__prefix__lfinite1,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % lstrict_prefix_lfinite1
% 0.14/0.39 thf(fact_230_lfinite__lSupD,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.14/0.39 => ! [X: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X @ A3 )
% 0.14/0.39 => ( coindu1213758845finite @ A @ X ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_lSupD
% 0.14/0.39 thf(fact_231_lfinite__LNil,axiom,
% 0.14/0.39 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_LNil
% 0.14/0.39 thf(fact_232_lnull__imp__lfinite,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.14/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % lnull_imp_lfinite
% 0.14/0.39 thf(fact_233_lfinite__LConsI,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X3: A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_LConsI
% 0.14/0.39 thf(fact_234_not__lfinite__lprefix__conv__eq,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 = ( Xs = Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % not_lfinite_lprefix_conv_eq
% 0.14/0.39 thf(fact_235_lprefix__lfiniteD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.14/0.39 => ( ( coindu1213758845finite @ A @ Ys )
% 0.14/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lprefix_lfiniteD
% 0.14/0.39 thf(fact_236_llexord__LNil,axiom,
% 0.14/0.39 ! [A: $tType,R2: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R2 @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.14/0.39
% 0.14/0.39 % llexord_LNil
% 0.14/0.39 thf(fact_237_llexord__LCons__less,axiom,
% 0.14/0.39 ! [A: $tType,R2: A > A > $o,X3: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( R2 @ X3 @ Y )
% 0.14/0.39 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llexord_LCons_less
% 0.14/0.39 thf(fact_238_llexord__LCons__eq,axiom,
% 0.14/0.39 ! [A: $tType,R2: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X3: A] :
% 0.14/0.39 ( ( coindu300403952lexord @ A @ R2 @ Xs @ Ys )
% 0.14/0.39 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ X3 @ Ys ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llexord_LCons_eq
% 0.14/0.39 thf(fact_239_lfinite__induct,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( P @ Xs2 ) )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.14/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.14/0.39 => ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.14/0.39 => ( P @ Xs2 ) ) ) )
% 0.14/0.39 => ( P @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_induct
% 0.14/0.39 thf(fact_240_lfinite_Oinducts,axiom,
% 0.14/0.39 ! [A: $tType,X3: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ X3 )
% 0.14/0.39 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,X5: A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.14/0.39 => ( ( P @ Xs2 )
% 0.14/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.14/0.39 => ( P @ X3 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite.inducts
% 0.14/0.39 thf(fact_241_lfinite_Osimps,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu1213758845finite @ A )
% 0.14/0.39 = ( ^ [A4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A4
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 | ? [Xs4: coindu1593790203_llist @ A,X4: A] :
% 0.14/0.39 ( ( A4
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.14/0.39 & ( coindu1213758845finite @ A @ Xs4 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite.simps
% 0.14/0.39 thf(fact_242_lfinite_Ocases,axiom,
% 0.14/0.39 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ A2 )
% 0.14/0.39 => ( ( A2
% 0.14/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ? [X5: A] :
% 0.14/0.39 ( A2
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.14/0.39 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite.cases
% 0.14/0.39 thf(fact_243_llimit__induct,axiom,
% 0.14/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( ! [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.14/0.39 => ( ( P @ Xs2 )
% 0.14/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.14/0.39 => ( ( ! [Ys4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu574146665prefix @ A @ Ys4 @ Xs )
% 0.14/0.39 => ( P @ Ys4 ) )
% 0.14/0.39 => ( P @ Xs ) )
% 0.14/0.39 => ( P @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llimit_induct
% 0.14/0.39 thf(fact_244_compact__lfiniteI,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 => ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % compact_lfiniteI
% 0.14/0.39 thf(fact_245_compact__lfiniteD,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs )
% 0.14/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.14/0.39
% 0.14/0.39 % compact_lfiniteD
% 0.14/0.39 thf(fact_246_llexord_Ocases,axiom,
% 0.14/0.39 ! [A: $tType,R2: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu300403952lexord @ A @ R2 @ A1 @ A22 )
% 0.14/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X5: A] :
% 0.14/0.39 ( ( A1
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.14/0.39 => ( ( A22
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Ys2 ) )
% 0.14/0.39 => ~ ( coindu300403952lexord @ A @ R2 @ Xs2 @ Ys2 ) ) )
% 0.14/0.39 => ( ! [X5: A] :
% 0.14/0.39 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( A1
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.14/0.39 => ! [Y3: A] :
% 0.14/0.39 ( ? [Ys2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( A22
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) )
% 0.14/0.39 => ~ ( R2 @ X5 @ Y3 ) ) )
% 0.14/0.39 => ~ ( ( A1
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ! [Ys2: coindu1593790203_llist @ A] : ( A22 != Ys2 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llexord.cases
% 0.14/0.39 thf(fact_247_llexord_Osimps,axiom,
% 0.14/0.39 ! [A: $tType] :
% 0.14/0.39 ( ( coindu300403952lexord @ A )
% 0.14/0.39 = ( ^ [R3: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X4: A] :
% 0.14/0.39 ( ( A12
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.14/0.39 & ( A23
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Ys3 ) )
% 0.14/0.39 & ( coindu300403952lexord @ A @ R3 @ Xs4 @ Ys3 ) )
% 0.14/0.39 | ? [X4: A,Y5: A,Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A12
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.14/0.39 & ( A23
% 0.14/0.39 = ( coindu1121789889_LCons @ A @ Y5 @ Ys3 ) )
% 0.14/0.39 & ( R3 @ X4 @ Y5 ) )
% 0.14/0.39 | ? [Ys3: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( A12
% 0.14/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 & ( A23 = Ys3 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llexord.simps
% 0.14/0.39 thf(fact_248_llist__induct,axiom,
% 0.14/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1986059218ssible @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ P )
% 0.14/0.39 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.14/0.39 => ( ! [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.14/0.39 => ( ( P @ Xs2 )
% 0.14/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.14/0.39 => ( P @ Xs ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist_induct
% 0.14/0.39 thf(fact_249_lfinite__lSup__chain,axiom,
% 0.14/0.39 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.14/0.39 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.14/0.39 => ( ( coindu1213758845finite @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.14/0.39 = ( ( finite_finite @ ( coindu1593790203_llist @ A ) @ A3 )
% 0.14/0.39 & ! [X4: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( member @ ( coindu1593790203_llist @ A ) @ X4 @ A3 )
% 0.14/0.39 => ( coindu1213758845finite @ A @ X4 ) ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_lSup_chain
% 0.14/0.39 thf(fact_250_lfinite__imp__finite__lset,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 => ( finite_finite @ A @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % lfinite_imp_finite_lset
% 0.14/0.39 thf(fact_251_llist__gen__induct,axiom,
% 0.14/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( comple1986059218ssible @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ P )
% 0.14/0.39 => ( ? [Zs2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Zs2 @ Xs )
% 0.14/0.39 & ( coindu1213758845finite @ A @ Zs2 )
% 0.14/0.39 & ! [Ys2: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1696667936prefix @ A @ Zs2 @ Ys2 )
% 0.14/0.39 => ( ( coindu1696667936prefix @ A @ Ys2 @ Xs )
% 0.14/0.39 => ( ( coindu1213758845finite @ A @ Ys2 )
% 0.14/0.39 => ( P @ Ys2 ) ) ) ) )
% 0.14/0.39 => ( P @ Xs ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llist_gen_induct
% 0.14/0.39 thf(fact_252_finite__Int,axiom,
% 0.14/0.39 ! [A: $tType,F4: set @ A,G3: set @ A] :
% 0.14/0.39 ( ( ( finite_finite @ A @ F4 )
% 0.14/0.39 | ( finite_finite @ A @ G3 ) )
% 0.14/0.39 => ( finite_finite @ A @ ( inf_inf @ ( set @ A ) @ F4 @ G3 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % finite_Int
% 0.14/0.39 thf(fact_253_llast__lappend__LCons,axiom,
% 0.14/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.14/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.14/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) )
% 0.14/0.39 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 % llast_lappend_LCons
% 0.14/0.39
% 0.14/0.39 %----Type constructors (6)
% 0.14/0.39 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.14/0.39 ! [A6: $tType,A7: $tType] :
% 0.14/0.39 ( ( semilattice_inf @ A7 @ ( type2 @ A7 ) )
% 0.14/0.39 => ( semilattice_inf @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.14/0.39 ! [A6: $tType,A7: $tType] :
% 0.14/0.39 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.14/0.39 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_1,axiom,
% 0.14/0.39 ! [A6: $tType] : ( semilattice_inf @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(tcon_Set_Oset___Lattices_Olattice_2,axiom,
% 0.14/0.39 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_3,axiom,
% 0.14/0.39 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.14/0.39
% 0.14/0.39 thf(tcon_HOL_Obool___Lattices_Olattice_4,axiom,
% 0.14/0.39 lattice @ $o @ ( type2 @ $o ) ).
% 0.14/0.39
% 0.14/0.39 %----Helper facts (3)
% 0.14/0.39 thf(help_If_3_1_T,axiom,
% 0.14/0.39 ! [P: $o] :
% 0.14/0.39 ( ( P = $true )
% 0.14/0.39 | ( P = $false ) ) ).
% 0.14/0.39
% 0.14/0.39 thf(help_If_2_1_T,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Y: A] :
% 0.14/0.39 ( ( if @ A @ $false @ X3 @ Y )
% 0.14/0.39 = Y ) ).
% 0.14/0.39
% 0.14/0.39 thf(help_If_1_1_T,axiom,
% 0.14/0.39 ! [A: $tType,X3: A,Y: A] :
% 0.14/0.39 ( ( if @ A @ $true @ X3 @ Y )
% 0.14/0.39 = X3 ) ).
% 0.14/0.39
% 0.14/0.39 %----Conjectures (1)
% 0.14/0.39 thf(conj_0,conjecture,
% 0.14/0.39 less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ).
% 0.14/0.39
% 0.14/0.39 %------------------------------------------------------------------------------
% 0.14/0.39 ------------------------
% 0.21/1.40 ---- Embedded in THF ---
% 0.21/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.21/1.40 %%% Generated on Tue Feb 24 06:08:34 EST 2026
% 0.21/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.21/1.40 %%% Logic specification used:
% 0.21/1.40 %%% thf(spec, logic, $$dhol).
% 0.21/1.40
% 0.21/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hgRkZ6IOB8/DTF2DTF15555.p
% 0.21/1.40 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 0.21/1.40 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.21/1.40 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.21/1.40 thf(ty_tf_a, type, a: $tType).
% 0.21/1.40 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.21/1.40 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.21/1.40 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix, type, coindu1571841457prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OlSup, type, coindu526335360e_lSup: (!> [A:$tType]: (((set @ (coindu1593790203_llist @ A)) > (coindu1593790203_llist @ A))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oldistinct, type, coindu6345450stinct: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast, type, coindu2000965700_llast: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord, type, coindu300403952lexord: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist, type, coindu882539134_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coindu1593790203_llist @ A) > B)) > ((coindu1593790203_llist @ A) > B)))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd, type, coindu1046438764le_lhd: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset, type, coindu1112613586e_lset: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (set @ A))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl, type, coindu1047225960le_ltl: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix, type, coindu574146665prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile, type, coindu721411036eWhile: (!> [A:$tType]: (((A > $o) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord_Olsorted, type, coindu543932918sorted: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > $o))))).
% 0.21/1.40 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist, type, coindu1599971794_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coindu1593790203_llist @ B)))))))).
% 0.21/1.40 thf(sy_c_Complete__Partial__Order2_Ocompact, type, comple2143767107ompact: (!> [A:$tType]: ((((set @ A) > A) > ((A > (A > $o)) > (A > $o)))))).
% 0.21/1.40 thf(sy_c_Complete__Partial__Order2_Ocont, type, comple1412571634l_cont: (!> [A:$tType,B:$tType]: ((((set @ A) > A) > ((A > (A > $o)) > (((set @ B) > B) > ((B > (B > $o)) > ((A > B) > $o)))))))).
% 0.21/1.40 thf(sy_c_Complete__Partial__Order_Occpo_Oadmissible, type, comple1986059218ssible: (!> [A:$tType]: ((((set @ A) > A) > ((A > (A > $o)) > ((A > $o) > $o)))))).
% 0.21/1.40 thf(sy_c_Complete__Partial__Order_Ochain, type, comple1193779247_chain: (!> [A:$tType]: (((A > (A > $o)) > ((set @ A) > $o))))).
% 0.21/1.40 thf(sy_c_Finite__Set_Ofinite, type, finite_finite: (!> [A:$tType]: (((set @ A) > $o)))).
% 0.21/1.40 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 0.21/1.40 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 0.21/1.40 thf(sy_c_Orderings_Oord_Omax, type, max: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 0.21/1.40 thf(sy_c_Orderings_Oord_Omin, type, min: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > A)))))).
% 0.21/1.40 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.21/1.40 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.21/1.40 thf(sy_c_Set__Interval_Oord_OatLeast, type, set_atLeast: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 0.21/1.40 thf(sy_c_Set__Interval_Oord_OatLeastAtMost, type, set_atLeastAtMost: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > (set @ A))))))).
% 0.21/1.40 thf(sy_c_Set__Interval_Oord_OatMost, type, set_atMost: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 0.21/1.40 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.21/1.40 thf(sy_v_Ya____, type, ya: (set @ (coindu1593790203_llist @ a))).
% 0.21/1.40 thf(sy_v_less__eq, type, less_eq: (a > (a > $o))).
% 0.21/1.40 thf(sy_v_xs____, type, xs: (coindu1593790203_llist @ a)).
% 0.21/1.40 thf(fact_0__092_060open_062xs_A_092_060in_062_AY_092_060close_062, axiom, (((member @ (coindu1593790203_llist @ a)) @ xs) @ ya)).
% 0.21/1.40 thf(fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062, axiom, ((less_eq @ ((coindu1046438764le_lhd @ a) @ xs)) @ ((coindu1046438764le_lhd @ a) @ ((coindu1047225960le_ltl @ a) @ xs)))).
% 0.21/1.40 thf(fact_2_local_Oord__eq__le__trans, axiom, (! [A2:a,B2:a,C:a]: (((A2 = B2) => (((less_eq @ B2) @ C) => ((less_eq @ A2) @ C)))))).
% 0.21/1.40 thf(fact_3_local_Oord__le__eq__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less_eq @ A2) @ B2) => ((B2 = C) => ((less_eq @ A2) @ C)))))).
% 0.21/1.40 thf(fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062, axiom, (((coindu1046438764le_lhd @ a) @ ((coindu526335360e_lSup @ a) @ ya)) = ((coindu1046438764le_lhd @ a) @ xs))).
% 0.21/1.40 thf(fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062, axiom, (((coindu1046438764le_lhd @ a) @ ((coindu1047225960le_ltl @ a) @ ((coindu526335360e_lSup @ a) @ ya))) = ((coindu1046438764le_lhd @ a) @ ((coindu1047225960le_ltl @ a) @ xs)))).
% 0.21/1.40 thf(fact_6_local_Omax__def, axiom, (! [A2:a,B2:a]: (((((less_eq @ A2) @ B2) => (((((max @ a) @ less_eq) @ A2) @ B2) = B2)) & ((~ (((less_eq @ A2) @ B2))) => (((((max @ a) @ less_eq) @ A2) @ B2) = A2)))))).
% 0.21/1.40 thf(fact_7_local_Omin__def, axiom, (! [A2:a,B2:a]: (((((less_eq @ A2) @ B2) => (((((min @ a) @ less_eq) @ A2) @ B2) = A2)) & ((~ (((less_eq @ A2) @ B2))) => (((((min @ a) @ less_eq) @ A2) @ B2) = B2)))))).
% 0.21/1.40 thf(fact_8_lsorted_I2_J, axiom, (! [X:(coindu1593790203_llist @ a)]: (((((member @ (coindu1593790203_llist @ a)) @ X) @ ya) => (((coindu543932918sorted @ a) @ less_eq) @ X))))).
% 0.21/1.40 thf(fact_9_lsorted_I3_J, axiom, (~ (((coindu335574135_lnull @ a) @ ((coindu526335360e_lSup @ a) @ ya))))).
% 0.21/1.40 thf(fact_10_lsorted_I4_J, axiom, (~ (((coindu335574135_lnull @ a) @ ((coindu1047225960le_ltl @ a) @ ((coindu526335360e_lSup @ a) @ ya)))))).
% 0.21/1.40 thf(fact_11__092_060open_062_092_060not_062_Alnull_A_Iltl_Axs_J_092_060close_062, axiom, (~ (((coindu335574135_lnull @ a) @ ((coindu1047225960le_ltl @ a) @ xs))))).
% 0.21/1.40 thf(fact_12_sorted, axiom, (! [Xs:(coindu1593790203_llist @ a)]: (((((member @ (coindu1593790203_llist @ a)) @ Xs) @ ya) => (((coindu543932918sorted @ a) @ less_eq) @ Xs))))).
% 0.21/1.40 thf(fact_13_lsorted__ltlI, axiom, (! [Xs:(coindu1593790203_llist @ a)]: (((((coindu543932918sorted @ a) @ less_eq) @ Xs) => (((coindu543932918sorted @ a) @ less_eq) @ ((coindu1047225960le_ltl @ a) @ Xs)))))).
% 0.21/1.40 thf(fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062xs_A_092_060in_062_AY_059_A_092_060not_062_Alnull_Axs_059_A_092_060not_062_Alnull_A_Iltl_Axs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Xs2:(coindu1593790203_llist @ a)]: (((((member @ (coindu1593790203_llist @ a)) @ Xs2) @ ya) => ((~ (((coindu335574135_lnull @ a) @ Xs2))) => ((coindu335574135_lnull @ a) @ ((coindu1047225960le_ltl @ a) @ Xs2))))))))).
% 0.21/1.40 thf(fact_15_local_OatLeastAtMost__iff, axiom, (! [I:a,L:a,U:a]: (((((member @ a) @ I) @ ((((set_atLeastAtMost @ a) @ less_eq) @ L) @ U)) = (((less_eq @ L) @ I) & ((less_eq @ I) @ U)))))).
% 0.21/1.40 thf(fact_16__092_060open_062_092_060not_062_Alnull_Axs_092_060close_062, axiom, (~ (((coindu335574135_lnull @ a) @ xs)))).
% 0.21/1.40 thf(fact_17_local_OatLeast__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_atLeast @ a) @ less_eq) @ K)) = ((less_eq @ K) @ I))))).
% 0.21/1.40 thf(fact_18_local_OatMost__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_atMost @ a) @ less_eq) @ K)) = ((less_eq @ I) @ K))))).
% 0.21/1.40 thf(fact_19_lsorted__coinduct_H, axiom, (! [X2:((coindu1593790203_llist @ a) > $o),Xs:(coindu1593790203_llist @ a)]: (((X2 @ Xs) => ((! [Xs2:(coindu1593790203_llist @ a)]: (((X2 @ Xs2) => ((~ (((coindu335574135_lnull @ a) @ Xs2))) => ((~ (((coindu335574135_lnull @ a) @ ((coindu1047225960le_ltl @ a) @ Xs2)))) => (((less_eq @ ((coindu1046438764le_lhd @ a) @ Xs2)) @ ((coindu1046438764le_lhd @ a) @ ((coindu1047225960le_ltl @ a) @ Xs2))) & ((X2 @ ((coindu1047225960le_ltl @ a) @ Xs2)) | (((coindu543932918sorted @ a) @ less_eq) @ ((coindu1047225960le_ltl @ a) @ Xs2))))))))) => (((coindu543932918sorted @ a) @ less_eq) @ Xs)))))).
% 0.21/1.40 thf(fact_20_lsorted__lhdD, axiom, (! [Xs:(coindu1593790203_llist @ a)]: (((((coindu543932918sorted @ a) @ less_eq) @ Xs) => ((~ (((coindu335574135_lnull @ a) @ Xs))) => ((~ (((coindu335574135_lnull @ a) @ ((coindu1047225960le_ltl @ a) @ Xs)))) => ((less_eq @ ((coindu1046438764le_lhd @ a) @ Xs)) @ ((coindu1046438764le_lhd @ a) @ ((coindu1047225960le_ltl @ a) @ Xs))))))))).
% 0.21/1.40 thf(fact_21_chain, axiom, (((comple1193779247_chain @ (coindu1593790203_llist @ a)) @ (coindu1696667936prefix @ a)) @ ya)).
% 0.21/1.40 thf(fact_22_llist_Oexpand, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),Llist2:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Llist) = ((coindu335574135_lnull @ A) @ Llist2)) => (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((~ (((coindu335574135_lnull @ A) @ Llist2))) => ((((coindu1046438764le_lhd @ A) @ Llist) = ((coindu1046438764le_lhd @ A) @ Llist2)) & (((coindu1047225960le_ltl @ A) @ Llist) = ((coindu1047225960le_ltl @ A) @ Llist2))))) => (Llist = Llist2)))))).
% 0.21/1.40 thf(fact_23_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 0.21/1.40 thf(fact_24_llist_Oleq__refl, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ X3) @ X3)))).
% 0.21/1.40 thf(fact_25_lnull__lSup, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: ((((coindu335574135_lnull @ A) @ ((coindu526335360e_lSup @ A) @ A3)) = (! [X4:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X4) @ A3) => ((coindu335574135_lnull @ A) @ X4)))))))).
% 0.21/1.40 thf(fact_26_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((coindu335574135_lnull @ B) @ Ys)))))))).
% 0.21/1.40 thf(fact_27_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 0.21/1.40 thf(fact_28_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_29_lprefix__trans, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => (((coindu1696667936prefix @ A) @ Xs) @ Zs)))))).
% 0.21/1.40 thf(fact_30_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_31_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 0.21/1.40 thf(fact_32_llist_Oleq__trans, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A),Z:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X3) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ Z) => (((coindu1696667936prefix @ A) @ X3) @ Z)))))).
% 0.21/1.40 thf(fact_33_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 0.21/1.40 thf(fact_34_llist_Oleq__antisym, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X3) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ X3) => (X3 = Y)))))).
% 0.21/1.40 thf(fact_35_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 0.21/1.40 thf(fact_36_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Zs) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) | (((coindu1696667936prefix @ A) @ Ys) @ Xs))))))).
% 0.21/1.40 thf(fact_37_chain__lprefix__lSup, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A)),Xs:(coindu1593790203_llist @ A)]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ A3) => ((((member @ (coindu1593790203_llist @ A)) @ Xs) @ A3) => (((coindu1696667936prefix @ A) @ Xs) @ ((coindu526335360e_lSup @ A) @ A3))))))).
% 0.21/1.40 thf(fact_38_chain__lSup__lprefix, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A)),Zs:(coindu1593790203_llist @ A)]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ A3) => ((! [Xs2:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ Xs2) @ A3) => (((coindu1696667936prefix @ A) @ Xs2) @ Zs)))) => (((coindu1696667936prefix @ A) @ ((coindu526335360e_lSup @ A) @ A3)) @ Zs)))))).
% 0.21/1.40 thf(fact_39_llist_Olub__upper, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A)),X3:(coindu1593790203_llist @ A)]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ A3) => ((((member @ (coindu1593790203_llist @ A)) @ X3) @ A3) => (((coindu1696667936prefix @ A) @ X3) @ ((coindu526335360e_lSup @ A) @ A3))))))).
% 0.21/1.40 thf(fact_40_llist_Olub__least, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A)),Z:(coindu1593790203_llist @ A)]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ A3) => ((! [X5:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X5) @ A3) => (((coindu1696667936prefix @ A) @ X5) @ Z)))) => (((coindu1696667936prefix @ A) @ ((coindu526335360e_lSup @ A) @ A3)) @ Z)))))).
% 0.21/1.40 thf(fact_41_lprefix__lhdD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys))))))).
% 0.21/1.40 thf(fact_42_lhd__lSup__eq, axiom, (! [A:$tType,Y2:(set @ (coindu1593790203_llist @ A)),Xs:(coindu1593790203_llist @ A)]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ Y2) => ((((member @ (coindu1593790203_llist @ A)) @ Xs) @ Y2) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ ((coindu526335360e_lSup @ A) @ Y2)) = ((coindu1046438764le_lhd @ A) @ Xs)))))))).
% 0.21/1.40 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.21/1.40 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 0.21/1.40 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.21/1.40 thf(fact_46_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 0.21/1.40 thf(fact_47_lprefix__coinduct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((P @ Xs) @ Ys) => ((! [Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: ((((P @ Xs2) @ Ys2) => ((((coindu335574135_lnull @ A) @ Ys2) => ((coindu335574135_lnull @ A) @ Xs2)) & ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((~ (((coindu335574135_lnull @ A) @ Ys2))) => ((((coindu1046438764le_lhd @ A) @ Xs2) = ((coindu1046438764le_lhd @ A) @ Ys2)) & (((P @ ((coindu1047225960le_ltl @ A) @ Xs2)) @ ((coindu1047225960le_ltl @ A) @ Ys2)) | (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2)) @ ((coindu1047225960le_ltl @ A) @ Ys2)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 0.21/1.40 thf(fact_48_lprefix__expand, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ A) @ Ys))) & ((((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys)) & (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 0.21/1.40 thf(fact_49_lSup_Odisc__iff_I2_J, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: ((((coindu335574135_lnull @ A) @ ((coindu526335360e_lSup @ A) @ A3)) = (! [X4:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X4) @ A3) => ((coindu335574135_lnull @ A) @ X4)))))))).
% 0.21/1.40 thf(fact_50_lSup_Odisc_I1_J, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: (((! [X5:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X5) @ A3) => ((coindu335574135_lnull @ A) @ X5)))) => ((coindu335574135_lnull @ A) @ ((coindu526335360e_lSup @ A) @ A3)))))).
% 0.21/1.40 thf(fact_51_lSup_Odisc_I2_J, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: (((~ ((! [X:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X) @ A3) => ((coindu335574135_lnull @ A) @ X)))))) => (~ (((coindu335574135_lnull @ A) @ ((coindu526335360e_lSup @ A) @ A3)))))))).
% 0.21/1.40 thf(fact_52_lnull__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu335574135_lnull @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_53_ord_Olsorted__coinduct_H, axiom, (! [A:$tType,X2:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A),Less_eq:(A > (A > $o))]: (((X2 @ Xs) => ((! [Xs2:(coindu1593790203_llist @ A)]: (((X2 @ Xs2) => ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((~ (((coindu335574135_lnull @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2)))) => (((Less_eq @ ((coindu1046438764le_lhd @ A) @ Xs2)) @ ((coindu1046438764le_lhd @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2))) & ((X2 @ ((coindu1047225960le_ltl @ A) @ Xs2)) | (((coindu543932918sorted @ A) @ Less_eq) @ ((coindu1047225960le_ltl @ A) @ Xs2))))))))) => (((coindu543932918sorted @ A) @ Less_eq) @ Xs)))))).
% 0.21/1.40 thf(fact_54_ord_Olsorted__lhdD, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Xs:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ Xs) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))) => ((Less_eq @ ((coindu1046438764le_lhd @ A) @ Xs)) @ ((coindu1046438764le_lhd @ A) @ ((coindu1047225960le_ltl @ A) @ Xs))))))))).
% 0.21/1.40 thf(fact_55_ltakeWhile_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))))).
% 0.21/1.40 thf(fact_56_lprefix__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys)))))).
% 0.21/1.40 thf(fact_57_ord_Olsorted__ltlI, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Xs:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ Xs) => (((coindu543932918sorted @ A) @ Less_eq) @ ((coindu1047225960le_ltl @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_58_llist_Ocoinduct__strong, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist2:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist2) => ((! [Llist3:(coindu1593790203_llist @ A),Llist4:(coindu1593790203_llist @ A)]: ((((R @ Llist3) @ Llist4) => ((((coindu335574135_lnull @ A) @ Llist3) = ((coindu335574135_lnull @ A) @ Llist4)) & ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((((coindu1046438764le_lhd @ A) @ Llist3) = ((coindu1046438764le_lhd @ A) @ Llist4)) & (((R @ ((coindu1047225960le_ltl @ A) @ Llist3)) @ ((coindu1047225960le_ltl @ A) @ Llist4)) | (((coindu1047225960le_ltl @ A) @ Llist3) = ((coindu1047225960le_ltl @ A) @ Llist4)))))))))) => (Llist = Llist2)))))).
% 0.21/1.40 thf(fact_59_llist_Ocoinduct, axiom, (! [A:$tType,R:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist:(coindu1593790203_llist @ A),Llist2:(coindu1593790203_llist @ A)]: ((((R @ Llist) @ Llist2) => ((! [Llist3:(coindu1593790203_llist @ A),Llist4:(coindu1593790203_llist @ A)]: ((((R @ Llist3) @ Llist4) => ((((coindu335574135_lnull @ A) @ Llist3) = ((coindu335574135_lnull @ A) @ Llist4)) & ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((((coindu1046438764le_lhd @ A) @ Llist3) = ((coindu1046438764le_lhd @ A) @ Llist4)) & ((R @ ((coindu1047225960le_ltl @ A) @ Llist3)) @ ((coindu1047225960le_ltl @ A) @ Llist4))))))))) => (Llist = Llist2)))))).
% 0.21/1.40 thf(fact_60_local_OatLeastAtMost__def, axiom, (! [L:a,U:a]: ((((((set_atLeastAtMost @ a) @ less_eq) @ L) @ U) = (((inf_inf @ (set @ a)) @ (((set_atLeast @ a) @ less_eq) @ L)) @ (((set_atMost @ a) @ less_eq) @ U)))))).
% 0.21/1.40 thf(fact_61_lsorted__LCons_H, axiom, (! [X3:a,Xs:(coindu1593790203_llist @ a)]: (((((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ X3) @ Xs)) = ((~ (((coindu335574135_lnull @ a) @ Xs))) => (((less_eq @ X3) @ ((coindu1046438764le_lhd @ a) @ Xs)) & (((coindu543932918sorted @ a) @ less_eq) @ Xs))))))).
% 0.21/1.40 thf(fact_62_LNil, axiom, (((coindu543932918sorted @ a) @ less_eq) @ (coindu1598213697e_LNil @ a))).
% 0.21/1.40 thf(fact_63_LCons__LCons, axiom, (! [X3:a,Y:a,Xs:(coindu1593790203_llist @ a)]: ((((less_eq @ X3) @ Y) => ((((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ Y) @ Xs)) => (((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ X3) @ (((coindu1121789889_LCons @ a) @ Y) @ Xs)))))))).
% 0.21/1.40 thf(fact_64_ord_Omax__def, axiom, (! [A:$tType]: (((max @ A) = (^ [Less_eq2:(A > (A > $o)),A4:A,B3:A]: (((((if @ A) @ ((Less_eq2 @ A4) @ B3)) @ B3) @ A4))))))).
% 0.21/1.40 thf(fact_65_ord_Omin__def, axiom, (! [A:$tType]: (((min @ A) = (^ [Less_eq2:(A > (A > $o)),A4:A,B3:A]: (((((if @ A) @ ((Less_eq2 @ A4) @ B3)) @ A4) @ B3))))))).
% 0.21/1.40 thf(fact_66_unfold__llist__id, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((((((coindu1599971794_llist @ (coindu1593790203_llist @ A)) @ A) @ (coindu335574135_lnull @ A)) @ (coindu1046438764le_lhd @ A)) @ (coindu1047225960le_ltl @ A)) @ Xs) = Xs)))).
% 0.21/1.40 thf(fact_67_llist_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((coindu882539134_llist @ B) @ A) = (^ [F1:B,F2:(A > ((coindu1593790203_llist @ A) > B)),Llist5:(coindu1593790203_llist @ A)]: (((((if @ B) @ ((coindu335574135_lnull @ A) @ Llist5)) @ F1) @ ((F2 @ ((coindu1046438764le_lhd @ A) @ Llist5)) @ ((coindu1047225960le_ltl @ A) @ Llist5))))))))).
% 0.21/1.40 thf(fact_68_ord_OatMost__iff, axiom, (! [A:$tType,I:A,Less_eq:(A > (A > $o)),K:A]: (((((member @ A) @ I) @ (((set_atMost @ A) @ Less_eq) @ K)) = ((Less_eq @ I) @ K))))).
% 0.21/1.40 thf(fact_69_ord_OatLeast__iff, axiom, (! [A:$tType,I:A,Less_eq:(A > (A > $o)),K:A]: (((((member @ A) @ I) @ (((set_atLeast @ A) @ Less_eq) @ K)) = ((Less_eq @ K) @ I))))).
% 0.21/1.40 thf(fact_70_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 0.21/1.40 thf(fact_71_Singleton, axiom, (! [X3:a]: ((((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ X3) @ (coindu1598213697e_LNil @ a)))))).
% 0.21/1.40 thf(fact_72_lsorted_Ocases, axiom, (! [A2:(coindu1593790203_llist @ a)]: (((((coindu543932918sorted @ a) @ less_eq) @ A2) => ((A2 != (coindu1598213697e_LNil @ a)) => ((! [X5:a]: ((A2 != (((coindu1121789889_LCons @ a) @ X5) @ (coindu1598213697e_LNil @ a))))) => (~ ((! [X5:a,Y3:a,Xs2:(coindu1593790203_llist @ a)]: (((A2 = (((coindu1121789889_LCons @ a) @ X5) @ (((coindu1121789889_LCons @ a) @ Y3) @ Xs2))) => (((less_eq @ X5) @ Y3) => (~ ((((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ Y3) @ Xs2)))))))))))))))).
% 0.21/1.40 thf(fact_73_lsorted_Ocoinduct, axiom, (! [X2:((coindu1593790203_llist @ a) > $o),X3:(coindu1593790203_llist @ a)]: (((X2 @ X3) => ((! [X5:(coindu1593790203_llist @ a)]: (((X2 @ X5) => ((X5 = (coindu1598213697e_LNil @ a)) | ((? [Xa:a]: ((X5 = (((coindu1121789889_LCons @ a) @ Xa) @ (coindu1598213697e_LNil @ a))))) | (? [Xa:a,Y4:a,Xs3:(coindu1593790203_llist @ a)]: (((X5 = (((coindu1121789889_LCons @ a) @ Xa) @ (((coindu1121789889_LCons @ a) @ Y4) @ Xs3))) & (((less_eq @ Xa) @ Y4) & ((X2 @ (((coindu1121789889_LCons @ a) @ Y4) @ Xs3)) | (((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ Y4) @ Xs3)))))))))))) => (((coindu543932918sorted @ a) @ less_eq) @ X3)))))).
% 0.21/1.40 thf(fact_74_lsorted_Osimps, axiom, (! [A2:(coindu1593790203_llist @ a)]: (((((coindu543932918sorted @ a) @ less_eq) @ A2) = ((A2 = (coindu1598213697e_LNil @ a)) | ((? [X4:a]: ((A2 = (((coindu1121789889_LCons @ a) @ X4) @ (coindu1598213697e_LNil @ a))))) | (? [X4:a,Y5:a,Xs4:(coindu1593790203_llist @ a)]: (((A2 = (((coindu1121789889_LCons @ a) @ X4) @ (((coindu1121789889_LCons @ a) @ Y5) @ Xs4))) & (((less_eq @ X4) @ Y5) & (((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ Y5) @ Xs4)))))))))))).
% 0.21/1.40 thf(fact_75_LCons__lprefix__LCons, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X3 = Y) & (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 0.21/1.40 thf(fact_76_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 0.21/1.40 thf(fact_77_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B2:B,X3:A,Xs:(coindu1593790203_llist @ A)]: (((((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B2) = (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = ((~ ((IS_LNIL @ B2))) & ((X3 = (LHD @ B2)) & (Xs = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B2))))))))).
% 0.21/1.40 thf(fact_78_unfold__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),G21:(A > B),G22:(A > A),A2:A]: ((((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)) = (P2 @ A2))))).
% 0.21/1.40 thf(fact_79_unfold__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),G21:(A > B),G22:(A > A),A2:A]: (((~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)))) = (~ ((P2 @ A2))))))).
% 0.21/1.40 thf(fact_80_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 0.21/1.40 thf(fact_81_lsorted__LCons__LCons, axiom, (! [X3:a,Y:a,Xs:(coindu1593790203_llist @ a)]: (((((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ X3) @ (((coindu1121789889_LCons @ a) @ Y) @ Xs))) = (((less_eq @ X3) @ Y) & (((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ Y) @ Xs))))))).
% 0.21/1.40 thf(fact_82_lhd__LCons__ltl, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Llist))) => ((((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist)) = Llist))))).
% 0.21/1.40 thf(fact_83_lsorted__code_I1_J, axiom, (((coindu543932918sorted @ a) @ less_eq) @ (coindu1598213697e_LNil @ a))).
% 0.21/1.40 thf(fact_84_lsorted__code_I2_J, axiom, (! [X3:a]: ((((coindu543932918sorted @ a) @ less_eq) @ (((coindu1121789889_LCons @ a) @ X3) @ (coindu1598213697e_LNil @ a)))))).
% 0.21/1.40 thf(fact_85_lprefix__code_I2_J, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: ((~ ((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 0.21/1.40 thf(fact_86_lprefix_Ocases, axiom, (! [A:$tType,A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ A1) @ A22) => (((A1 = (coindu1598213697e_LNil @ A)) => (! [Xs2:(coindu1593790203_llist @ A)]: ((A22 != Xs2)))) => (~ ((! [Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),X5:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X5) @ Xs2)) => ((A22 = (((coindu1121789889_LCons @ A) @ X5) @ Ys2)) => (~ ((((coindu1696667936prefix @ A) @ Xs2) @ Ys2)))))))))))))).
% 0.21/1.40 thf(fact_87_lprefix_Osimps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs4:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Xs4)))) | (? [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X4:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X4) @ Xs4)) & ((A23 = (((coindu1121789889_LCons @ A) @ X4) @ Ys3)) & (((coindu1696667936prefix @ A) @ Xs4) @ Ys3)))))))))))).
% 0.21/1.40 thf(fact_88_lprefix_Ocoinduct, axiom, (! [A:$tType,X2:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X3:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X2 @ X3) @ Xa2) => ((! [X5:(coindu1593790203_llist @ A),Xa3:(coindu1593790203_llist @ A)]: ((((X2 @ X5) @ Xa3) => ((? [Xs3:(coindu1593790203_llist @ A)]: (((X5 = (coindu1598213697e_LNil @ A)) & (Xa3 = Xs3)))) | (? [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),Xb:A]: (((X5 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs3)) & ((Xa3 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys4)) & (((X2 @ Xs3) @ Ys4) | (((coindu1696667936prefix @ A) @ Xs3) @ Ys4)))))))))) => (((coindu1696667936prefix @ A) @ X3) @ Xa2)))))).
% 0.21/1.40 thf(fact_89_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs5:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs5)) & (((coindu1696667936prefix @ A) @ Xs5) @ Ys))))))))).
% 0.21/1.40 thf(fact_90_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1599971794_llist @ A) @ B) = (^ [P3:(A > $o),G212:(A > B),G222:(A > A),A4:A]: (((((if @ (coindu1593790203_llist @ B)) @ (P3 @ A4)) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ (G212 @ A4)) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G222) @ (G222 @ A4)))))))))).
% 0.21/1.40 thf(fact_91_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X4:A,Xs5:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X4) @ Xs5)))))))).
% 0.21/1.40 thf(fact_92_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 0.21/1.40 thf(fact_93_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P2 @ A2) => (((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2) = (coindu1598213697e_LNil @ B)))))).
% 0.21/1.40 thf(fact_94_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2) = (((coindu1121789889_LCons @ B) @ (G21 @ A2)) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A2)))))))).
% 0.21/1.40 thf(fact_95_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 0.21/1.40 thf(fact_96_llist_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F12:B,F22:(A > ((coindu1593790203_llist @ A) > B))]: (((((((coindu882539134_llist @ B) @ A) @ F12) @ F22) @ (coindu1598213697e_LNil @ A)) = F12)))).
% 0.21/1.40 thf(fact_97_llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F12:B,F22:(A > ((coindu1593790203_llist @ A) > B)),X21:A,X22:(coindu1593790203_llist @ A)]: (((((((coindu882539134_llist @ B) @ A) @ F12) @ F22) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = ((F22 @ X21) @ X22))))).
% 0.21/1.40 thf(fact_98_ord_OSingleton, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X3:A]: ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X3) @ (coindu1598213697e_LNil @ A)))))).
% 0.21/1.40 thf(fact_99_ord_Olsorted_Ocoinduct, axiom, (! [A:$tType,X2:((coindu1593790203_llist @ A) > $o),X3:(coindu1593790203_llist @ A),Less_eq:(A > (A > $o))]: (((X2 @ X3) => ((! [X5:(coindu1593790203_llist @ A)]: (((X2 @ X5) => ((X5 = (coindu1598213697e_LNil @ A)) | ((? [Xa:A]: ((X5 = (((coindu1121789889_LCons @ A) @ Xa) @ (coindu1598213697e_LNil @ A))))) | (? [Xa:A,Y4:A,Xs3:(coindu1593790203_llist @ A)]: (((X5 = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs3))) & (((Less_eq @ Xa) @ Y4) & ((X2 @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs3)) | (((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs3)))))))))))) => (((coindu543932918sorted @ A) @ Less_eq) @ X3)))))).
% 0.21/1.40 thf(fact_100_ord_Olsorted_Osimps, axiom, (! [A:$tType]: (((coindu543932918sorted @ A) = (^ [Less_eq2:(A > (A > $o)),A4:(coindu1593790203_llist @ A)]: (((A4 = (coindu1598213697e_LNil @ A)) | ((? [X4:A]: ((A4 = (((coindu1121789889_LCons @ A) @ X4) @ (coindu1598213697e_LNil @ A))))) | (? [X4:A,Y5:A,Xs4:(coindu1593790203_llist @ A)]: (((A4 = (((coindu1121789889_LCons @ A) @ X4) @ (((coindu1121789889_LCons @ A) @ Y5) @ Xs4))) & (((Less_eq2 @ X4) @ Y5) & (((coindu543932918sorted @ A) @ Less_eq2) @ (((coindu1121789889_LCons @ A) @ Y5) @ Xs4)))))))))))))).
% 0.21/1.40 thf(fact_101_ord_Olsorted_Ocases, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),A2:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ A2) => ((A2 != (coindu1598213697e_LNil @ A)) => ((! [X5:A]: ((A2 != (((coindu1121789889_LCons @ A) @ X5) @ (coindu1598213697e_LNil @ A))))) => (~ ((! [X5:A,Y3:A,Xs2:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X5) @ (((coindu1121789889_LCons @ A) @ Y3) @ Xs2))) => (((Less_eq @ X5) @ Y3) => (~ ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y3) @ Xs2)))))))))))))))).
% 0.21/1.40 thf(fact_102_ord_Olsorted__code_I2_J, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X3:A]: ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X3) @ (coindu1598213697e_LNil @ A)))))).
% 0.21/1.40 thf(fact_103_ltl__unfold__llist, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),A2:B,LHD:(B > A),LTL:(B > B)]: ((((IS_LNIL @ A2) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = (coindu1598213697e_LNil @ A))) & ((~ ((IS_LNIL @ A2))) => (((coindu1047225960le_ltl @ A) @ ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ A2)))))))).
% 0.21/1.40 thf(fact_104_llist_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F12:B,F22:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F12) @ F22) @ Llist)) = (((Llist = (coindu1598213697e_LNil @ A)) => (P @ F12)) & ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) => (P @ ((F22 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))).
% 0.21/1.40 thf(fact_105_llist_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F12:B,F22:(A > ((coindu1593790203_llist @ A) > B)),Llist:(coindu1593790203_llist @ A)]: (((P @ (((((coindu882539134_llist @ B) @ A) @ F12) @ F22) @ Llist)) = (~ ((((Llist = (coindu1598213697e_LNil @ A)) & (~ ((P @ F12)))) | ((Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))) & (~ ((P @ ((F22 @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))))))))).
% 0.21/1.40 thf(fact_106_eq__LConsD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) => ((Xs != (coindu1598213697e_LNil @ A)) & ((((coindu1046438764le_lhd @ A) @ Xs) = Y) & (((coindu1047225960le_ltl @ A) @ Xs) = Ys))))))).
% 0.21/1.40 thf(fact_107_llist_Oexhaust__sel, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist != (coindu1598213697e_LNil @ A)) => (Llist = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist)) @ ((coindu1047225960le_ltl @ A) @ Llist))))))).
% 0.21/1.40 thf(fact_108_LCons__lprefix__conv, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) @ Ys) = (? [Ys5:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ X3) @ Ys5)) & (((coindu1696667936prefix @ A) @ Xs) @ Ys5)))))))).
% 0.21/1.40 thf(fact_109_Le__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X3:A]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X3) @ Ys)))))).
% 0.21/1.40 thf(fact_110_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X4:A,Xs5:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X4) @ Xs5)))))))).
% 0.21/1.40 thf(fact_111_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist))))))).
% 0.21/1.40 thf(fact_112_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 0.21/1.40 thf(fact_113_ltl__simps_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1047225960le_ltl @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X22)))).
% 0.21/1.40 thf(fact_114_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 0.21/1.40 thf(fact_115_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1046438764le_lhd @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X21)))).
% 0.21/1.40 thf(fact_116_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist5:(coindu1593790203_llist @ A)]: ((Llist5 = (coindu1598213697e_LNil @ A)))))))).
% 0.21/1.40 thf(fact_117_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 0.21/1.40 thf(fact_118_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 0.21/1.40 thf(fact_119_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_120_ltl__simps_I1_J, axiom, (! [A:$tType]: ((((coindu1047225960le_ltl @ A) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_121_ord_Olsorted__LCons__LCons, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X3:A,Y:A,Xs:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X3) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))) = (((Less_eq @ X3) @ Y) & (((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))))))).
% 0.21/1.40 thf(fact_122_ord_OLCons__LCons, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X3:A,Y:A,Xs:(coindu1593790203_llist @ A)]: ((((Less_eq @ X3) @ Y) => ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)) => (((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X3) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)))))))).
% 0.21/1.40 thf(fact_123_ord_OLNil, axiom, (! [A:$tType,Less_eq:(A > (A > $o))]: ((((coindu543932918sorted @ A) @ Less_eq) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_124_ord_Olsorted__code_I1_J, axiom, (! [A:$tType,Less_eq:(A > (A > $o))]: ((((coindu543932918sorted @ A) @ Less_eq) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_125_unfold__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P2 @ A2) => ((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)))))).
% 0.21/1.40 thf(fact_126_unfold__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)))))))).
% 0.21/1.40 thf(fact_127_unfold__llist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (((coindu1047225960le_ltl @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)) = ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A2))))))).
% 0.21/1.40 thf(fact_128_unfold__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A2))) => (((coindu1046438764le_lhd @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A2)) = (G21 @ A2)))))).
% 0.21/1.40 thf(fact_129_lSup_Octr_I1_J, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: (((! [X5:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X5) @ A3) => ((coindu335574135_lnull @ A) @ X5)))) => (((coindu526335360e_lSup @ A) @ A3) = (coindu1598213697e_LNil @ A)))))).
% 0.21/1.40 thf(fact_130_ord_OatLeastAtMost__def, axiom, (! [A:$tType]: (((set_atLeastAtMost @ A) = (^ [Less_eq2:(A > (A > $o)),L2:A,U2:A]: ((((inf_inf @ (set @ A)) @ (((set_atLeast @ A) @ Less_eq2) @ L2)) @ (((set_atMost @ A) @ Less_eq2) @ U2)))))))).
% 0.21/1.40 thf(fact_131_ord_Olsorted__LCons_H, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X3:A,Xs:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((Less_eq @ X3) @ ((coindu1046438764le_lhd @ A) @ Xs)) & (((coindu543932918sorted @ A) @ Less_eq) @ Xs))))))).
% 0.21/1.40 thf(fact_132_ord_OatLeastAtMost__iff, axiom, (! [A:$tType,I:A,Less_eq:(A > (A > $o)),L:A,U:A]: (((((member @ A) @ I) @ ((((set_atLeastAtMost @ A) @ Less_eq) @ L) @ U)) = (((Less_eq @ L) @ I) & ((Less_eq @ I) @ U)))))).
% 0.21/1.40 thf(fact_133_Int__iff, axiom, (! [A:$tType,C:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = ((((member @ A) @ C) @ A3) & (((member @ A) @ C) @ B4)))))).
% 0.21/1.40 thf(fact_134_IntI, axiom, (! [A:$tType,C:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C) @ A3) => ((((member @ A) @ C) @ B4) => (((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B4))))))).
% 0.21/1.40 thf(fact_135_inf__right__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X3) @ Y)) @ Y) = (((inf_inf @ A) @ X3) @ Y)))))))).
% 0.21/1.40 thf(fact_136_inf_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 0.21/1.40 thf(fact_137_inf__left__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ X3) @ Y)) = (((inf_inf @ A) @ X3) @ Y)))))))).
% 0.21/1.40 thf(fact_138_inf_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 0.21/1.40 thf(fact_139_inf__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X3:A]: (((((inf_inf @ A) @ X3) @ X3) = X3))))))).
% 0.21/1.40 thf(fact_140_inf__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_inf @ B) @ (type2 @ B)) => ((inf_inf @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X4:A]: ((((inf_inf @ B) @ (F3 @ X4)) @ (G2 @ X4))))))))).
% 0.21/1.40 thf(fact_141_inf_Oidem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 0.21/1.40 thf(fact_142_inf__sup__aci_I4_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X3:A,Y:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ X3) @ Y)) = (((inf_inf @ A) @ X3) @ Y)))))))).
% 0.21/1.40 thf(fact_143_inf__sup__aci_I3_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ Y) @ (((inf_inf @ A) @ X3) @ Z))))))))).
% 0.21/1.40 thf(fact_144_inf__sup__aci_I2_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X3) @ Y)) @ Z) = (((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y) @ Z))))))))).
% 0.21/1.40 thf(fact_145_inf__sup__aci_I1_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [X4:A,Y5:A]: ((((inf_inf @ A) @ Y5) @ X4)))))))).
% 0.21/1.40 thf(fact_146_inf__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_inf @ B) @ (type2 @ B)) => ((inf_inf @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X4:A]: ((((inf_inf @ B) @ (F3 @ X4)) @ (G2 @ X4))))))))).
% 0.21/1.40 thf(fact_147_inf_Oassoc, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C))))))))).
% 0.21/1.40 thf(fact_148_inf__assoc, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X3) @ Y)) @ Z) = (((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y) @ Z))))))))).
% 0.21/1.40 thf(fact_149_inf_Ocommute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [A4:A,B3:A]: ((((inf_inf @ A) @ B3) @ A4)))))))).
% 0.21/1.40 thf(fact_150_inf__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [X4:A,Y5:A]: ((((inf_inf @ A) @ Y5) @ X4)))))))).
% 0.21/1.40 thf(fact_151_inf_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((inf_inf @ A) @ B2) @ (((inf_inf @ A) @ A2) @ C)) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C))))))))).
% 0.21/1.40 thf(fact_152_inf__left__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X3:A,Y:A,Z:A]: (((((inf_inf @ A) @ X3) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ Y) @ (((inf_inf @ A) @ X3) @ Z))))))))).
% 0.21/1.40 thf(fact_153_IntE, axiom, (! [A:$tType,C:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (~ (((((member @ A) @ C) @ A3) => (~ ((((member @ A) @ C) @ B4)))))))))).
% 0.21/1.40 thf(fact_154_IntD1, axiom, (! [A:$tType,C:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (((member @ A) @ C) @ A3))))).
% 0.21/1.40 thf(fact_155_IntD2, axiom, (! [A:$tType,C:A,A3:(set @ A),B4:(set @ A)]: (((((member @ A) @ C) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) => (((member @ A) @ C) @ B4))))).
% 0.21/1.40 thf(fact_156_Int__assoc, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:(set @ A)]: (((((inf_inf @ (set @ A)) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) @ C2) = (((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ B4) @ C2)))))).
% 0.21/1.40 thf(fact_157_Int__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ A3) = A3)))).
% 0.21/1.40 thf(fact_158_Int__commute, axiom, (! [A:$tType]: (((inf_inf @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((inf_inf @ (set @ A)) @ B5) @ A5))))))).
% 0.21/1.40 thf(fact_159_Int__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ A3) @ B4)) = (((inf_inf @ (set @ A)) @ A3) @ B4))))).
% 0.21/1.40 thf(fact_160_Int__left__commute, axiom, (! [A:$tType,A3:(set @ A),B4:(set @ A),C2:(set @ A)]: (((((inf_inf @ (set @ A)) @ A3) @ (((inf_inf @ (set @ A)) @ B4) @ C2)) = (((inf_inf @ (set @ A)) @ B4) @ (((inf_inf @ (set @ A)) @ A3) @ C2)))))).
% 0.21/1.40 thf(fact_161_compact__LCons__iff, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: ((((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = ((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ Xs))))).
% 0.21/1.40 thf(fact_162_ltakeWhile_Ocode, axiom, (! [A:$tType]: (((coindu721411036eWhile @ A) = (^ [P4:(A > $o),Xs4:(coindu1593790203_llist @ A)]: (((((if @ (coindu1593790203_llist @ A)) @ (((coindu335574135_lnull @ A) @ Xs4) | (~ ((P4 @ ((coindu1046438764le_lhd @ A) @ Xs4)))))) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs4)) @ (((coindu721411036eWhile @ A) @ P4) @ ((coindu1047225960le_ltl @ A) @ Xs4)))))))))).
% 0.21/1.40 thf(fact_163_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1571841457prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs5:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs5)) & (((coindu1571841457prefix @ A) @ Xs5) @ Ys))))))))).
% 0.21/1.40 thf(fact_164_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X3:B,Xs:(coindu1593790203_llist @ B)]: ((~ ((((coindu574146665prefix @ B) @ (((coindu1121789889_LCons @ B) @ X3) @ Xs)) @ (coindu1598213697e_LNil @ B))))))).
% 0.21/1.40 thf(fact_165_ltakeWhile__LNil, axiom, (! [A:$tType,P:(A > $o)]: (((((coindu721411036eWhile @ A) @ P) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_166_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X3:B,Xs:(coindu1593790203_llist @ B),Y:B,Ys:(coindu1593790203_llist @ B)]: (((((coindu574146665prefix @ B) @ (((coindu1121789889_LCons @ B) @ X3) @ Xs)) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys)) = ((X3 = Y) & (((coindu574146665prefix @ B) @ Xs) @ Ys)))))).
% 0.21/1.40 thf(fact_167_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu574146665prefix @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A))))))).
% 0.21/1.40 thf(fact_168_ltakeWhile__LCons, axiom, (! [A:$tType,P:(A > $o),X3:A,Xs:(coindu1593790203_llist @ A)]: ((((P @ X3) => ((((coindu721411036eWhile @ A) @ P) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = (((coindu1121789889_LCons @ A) @ X3) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))) & ((~ ((P @ X3))) => ((((coindu721411036eWhile @ A) @ P) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = (coindu1598213697e_LNil @ A))))))).
% 0.21/1.40 thf(fact_169_ltakeWhile_Odisc__iff_I2_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) & (P @ ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 0.21/1.40 thf(fact_170_ltakeWhile_Odisc__iff_I1_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))).
% 0.21/1.40 thf(fact_171_lnull__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))).
% 0.21/1.40 thf(fact_172_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coindu1593790203_llist @ B)]: ((((coindu574146665prefix @ B) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys))))).
% 0.21/1.40 thf(fact_173_lprefix__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) @ Xs)))).
% 0.21/1.40 thf(fact_174_llist__less__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((! [Xs2:(coindu1593790203_llist @ A)]: (((! [Ys4:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys4) @ Xs2) => (P @ Ys4)))) => (P @ Xs2)))) => (P @ Xs))))).
% 0.21/1.40 thf(fact_175_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu574146665prefix @ A) = (^ [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs4) @ Ys3) & (Xs4 != Ys3)))))))).
% 0.21/1.40 thf(fact_176_ltakeWhile_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (~ (((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs))))))))).
% 0.21/1.40 thf(fact_177_ltakeWhile_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))) => ((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))))).
% 0.21/1.40 thf(fact_178_lhd__ltakeWhile, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (((coindu1046438764le_lhd @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 0.21/1.40 thf(fact_179_ltakeWhile__eq__LNil__iff, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((((coindu721411036eWhile @ A) @ P) @ Xs) = (coindu1598213697e_LNil @ A)) = ((Xs != (coindu1598213697e_LNil @ A)) => (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))).
% 0.21/1.40 thf(fact_180_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def, axiom, (! [A:$tType]: (((coindu1571841457prefix @ A) = (coindu1696667936prefix @ A))))).
% 0.21/1.40 thf(fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1571841457prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = (Xs = (coindu1598213697e_LNil @ A)))))).
% 0.21/1.40 thf(fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1571841457prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 0.21/1.40 thf(fact_183_ltakeWhile_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 0.21/1.40 thf(fact_184_ltakeWhile_Osimps_I4_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (((coindu1047225960le_ltl @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu721411036eWhile @ A) @ P) @ ((coindu1047225960le_ltl @ A) @ Xs)))))))).
% 0.21/1.40 thf(fact_185_ltl__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (((coindu1047225960le_ltl @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu721411036eWhile @ A) @ P) @ ((coindu1047225960le_ltl @ A) @ Xs)))) & ((~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs)))) => (((coindu1047225960le_ltl @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (coindu1598213697e_LNil @ A))))))).
% 0.21/1.40 thf(fact_186_ltakeWhile_Octr_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ (((coindu721411036eWhile @ A) @ P) @ ((coindu1047225960le_ltl @ A) @ Xs))))))))).
% 0.21/1.40 thf(fact_187_compact__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X3:A]: ((((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ Xs) => ((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)))))).
% 0.21/1.40 thf(fact_188_compact__LConsD, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: ((((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) => ((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ Xs))))).
% 0.21/1.40 thf(fact_189_ldistinct__lSup, axiom, (! [A:$tType,Y2:(set @ (coindu1593790203_llist @ A))]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ Y2) => ((! [X5:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X5) @ Y2) => ((coindu6345450stinct @ A) @ X5)))) => ((coindu6345450stinct @ A) @ ((coindu526335360e_lSup @ A) @ Y2))))))).
% 0.21/1.40 thf(fact_190_llast__singleton, axiom, (! [A:$tType,X3:A]: ((((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ (coindu1598213697e_LNil @ A))) = X3)))).
% 0.21/1.40 thf(fact_191_cont__ltl, axiom, (! [A:$tType]: ((((((((comple1412571634l_cont @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ (coindu1047225960le_ltl @ A))))).
% 0.21/1.40 thf(fact_192_ldistinct__LNil__code, axiom, (! [A:$tType]: (((coindu6345450stinct @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_193_llast__LCons2, axiom, (! [A:$tType,X3:A,Y:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))) = ((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)))))).
% 0.21/1.40 thf(fact_194_ldistinct__ltlI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu6345450stinct @ A) @ Xs) => ((coindu6345450stinct @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_195_ldistinct_OLNil, axiom, (! [A:$tType]: (((coindu6345450stinct @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_196_ldistinct__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu6345450stinct @ A) @ Xs) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => ((coindu6345450stinct @ A) @ Ys)))))).
% 0.21/1.40 thf(fact_197_llast__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X3:A]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = X3)) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = ((coindu2000965700_llast @ A) @ Xs))))))).
% 0.21/1.40 thf(fact_198_ldistinct__lhdD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu6345450stinct @ A) @ Xs) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ ((((member @ A) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)))))))))).
% 0.21/1.40 thf(fact_199_ldistinct__coinduct, axiom, (! [A:$tType,X2:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((X2 @ Xs) => ((! [Xs2:(coindu1593790203_llist @ A)]: (((X2 @ Xs2) => ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((~ ((((member @ A) @ ((coindu1046438764le_lhd @ A) @ Xs2)) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2))))) & ((X2 @ ((coindu1047225960le_ltl @ A) @ Xs2)) | ((coindu6345450stinct @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2)))))))) => ((coindu6345450stinct @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_200_ldistinct__LCons, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu6345450stinct @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = ((~ ((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)))) & ((coindu6345450stinct @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_201_ldistinct_OLCons, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: (((~ ((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)))) => (((coindu6345450stinct @ A) @ Xs) => ((coindu6345450stinct @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs))))))).
% 0.21/1.40 thf(fact_202_llist_Oset__sel_I2_J, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A),X3:A]: (((~ (((coindu335574135_lnull @ A) @ A2))) => ((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ A2))) => (((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ A2))))))).
% 0.21/1.40 thf(fact_203_llist_Oset__sel_I1_J, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ A2))) => (((member @ A) @ ((coindu1046438764le_lhd @ A) @ A2)) @ ((coindu1112613586e_lset @ A) @ A2)))))).
% 0.21/1.40 thf(fact_204_lset__intros_I2_J, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A),X6:A]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)) => (((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X6) @ Xs))))))).
% 0.21/1.40 thf(fact_205_lset__intros_I1_J, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: ((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)))))).
% 0.21/1.40 thf(fact_206_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X3:A,A22:(coindu1593790203_llist @ A),A1:A]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ A22)) => (((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A1) @ A22))))))).
% 0.21/1.40 thf(fact_207_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coindu1593790203_llist @ A)]: ((((member @ A) @ A1) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A1) @ A22)))))).
% 0.21/1.40 thf(fact_208_lset__cases, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs6:(coindu1593790203_llist @ A)]: ((Xs != (((coindu1121789889_LCons @ A) @ X3) @ Xs6)))) => (~ ((! [X7:A,Xs6:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ X7) @ Xs6)) => (~ ((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs6)))))))))))))).
% 0.21/1.40 thf(fact_209_lset__induct, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X3) @ Xs2)))) => ((! [X7:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((X3 != X7) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X7) @ Xs2))))))) => (P @ Xs))))))).
% 0.21/1.40 thf(fact_210_lset__induct_H, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X3) @ Xs2)))) => ((! [X7:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X7) @ Xs2)))))) => (P @ Xs))))))).
% 0.21/1.40 thf(fact_211_llist_Oset__cases, axiom, (! [A:$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)))))))))))))).
% 0.21/1.40 thf(fact_212_llist_Oset__induct, axiom, (! [A:$tType,X3:A,A2:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ A2)) => ((! [Z1:A,Z2:(coindu1593790203_llist @ A)]: (((P @ Z1) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(coindu1593790203_llist @ A),Xa3:A]: (((((member @ A) @ Xa3) @ ((coindu1112613586e_lset @ A) @ Z2)) => (((P @ Xa3) @ Z2) => ((P @ Xa3) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z2)))))) => ((P @ X3) @ A2))))))).
% 0.21/1.40 thf(fact_213_in__lset__ltlD, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs))) => (((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_214_ltakeWhile__all, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((! [X5:A]: (((((member @ A) @ X5) @ ((coindu1112613586e_lset @ A) @ Xs)) => (P @ X5)))) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = Xs))))).
% 0.21/1.40 thf(fact_215_ltakeWhile__cong, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),P:(A > $o),Q:(A > $o)]: (((Xs = Ys) => ((! [X5:A]: (((((member @ A) @ X5) @ ((coindu1112613586e_lset @ A) @ Ys)) => ((P @ X5) = (Q @ X5))))) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (((coindu721411036eWhile @ A) @ Q) @ Ys))))))).
% 0.21/1.40 thf(fact_216_lset__ltakeWhileD, axiom, (! [A:$tType,X3:A,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs))) => ((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)) & (P @ X3)))))).
% 0.21/1.40 thf(fact_217_llist__set__induct, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X3) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs2)) @ Xs2)))) => ((! [Xs2:(coindu1593790203_llist @ A),Y3:A]: (((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((((member @ A) @ Y3) @ ((coindu1112613586e_lset @ A) @ ((coindu1047225960le_ltl @ A) @ Xs2))) => (((P @ Y3) @ ((coindu1047225960le_ltl @ A) @ Xs2)) => ((P @ Y3) @ Xs2)))))) => ((P @ X3) @ Xs))))))).
% 0.21/1.40 thf(fact_218_ldistinct_Ocases, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: ((((coindu6345450stinct @ A) @ A2) => ((A2 != (coindu1598213697e_LNil @ A)) => (~ ((! [X5:A,Xs2:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X5) @ Xs2)) => ((~ ((((member @ A) @ X5) @ ((coindu1112613586e_lset @ A) @ Xs2)))) => (~ (((coindu6345450stinct @ A) @ Xs2)))))))))))))).
% 0.21/1.40 thf(fact_219_ldistinct_Osimps, axiom, (! [A:$tType]: (((coindu6345450stinct @ A) = (^ [A4:(coindu1593790203_llist @ A)]: (((A4 = (coindu1598213697e_LNil @ A)) | (? [X4:A,Xs4:(coindu1593790203_llist @ A)]: (((A4 = (((coindu1121789889_LCons @ A) @ X4) @ Xs4)) & ((~ ((((member @ A) @ X4) @ ((coindu1112613586e_lset @ A) @ Xs4)))) & ((coindu6345450stinct @ A) @ Xs4)))))))))))).
% 0.21/1.40 thf(fact_220_ldistinct_Ocoinduct, axiom, (! [A:$tType,X2:((coindu1593790203_llist @ A) > $o),X3:(coindu1593790203_llist @ A)]: (((X2 @ X3) => ((! [X5:(coindu1593790203_llist @ A)]: (((X2 @ X5) => ((X5 = (coindu1598213697e_LNil @ A)) | (? [Xa:A,Xs3:(coindu1593790203_llist @ A)]: (((X5 = (((coindu1121789889_LCons @ A) @ Xa) @ Xs3)) & ((~ ((((member @ A) @ Xa) @ ((coindu1112613586e_lset @ A) @ Xs3)))) & ((X2 @ Xs3) | ((coindu6345450stinct @ A) @ Xs3)))))))))) => ((coindu6345450stinct @ A) @ X3)))))).
% 0.21/1.40 thf(fact_221_compact__eq__lfinite, axiom, (! [A:$tType]: (((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) = (coindu1213758845finite @ A))))).
% 0.21/1.40 thf(fact_222_llexord_Ocoinduct, axiom, (! [A:$tType,X2:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X3:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A),R2:(A > (A > $o))]: ((((X2 @ X3) @ Xa2) => ((! [X5:(coindu1593790203_llist @ A),Xa3:(coindu1593790203_llist @ A)]: ((((X2 @ X5) @ Xa3) => ((? [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),Xb:A]: (((X5 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs3)) & ((Xa3 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys4)) & (((X2 @ Xs3) @ Ys4) | ((((coindu300403952lexord @ A) @ R2) @ Xs3) @ Ys4)))))) | ((? [Xb:A,Y4:A,Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((X5 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs3)) & ((Xa3 = (((coindu1121789889_LCons @ A) @ Y4) @ Ys4)) & ((R2 @ Xb) @ Y4))))) | (? [Ys4:(coindu1593790203_llist @ A)]: (((X5 = (coindu1598213697e_LNil @ A)) & (Xa3 = Ys4))))))))) => ((((coindu300403952lexord @ A) @ R2) @ X3) @ Xa2)))))).
% 0.21/1.40 thf(fact_223_lfinite__LCons, axiom, (! [A:$tType,X3:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 0.21/1.40 thf(fact_224_lfinite__code_I2_J, axiom, (! [B:$tType,X3:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X3) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 0.21/1.40 thf(fact_225_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_226_lfinite__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 0.21/1.40 thf(fact_227_lfinite__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu1213758845finite @ A) @ Xs) | (? [X4:A]: (((((member @ A) @ X4) @ ((coindu1112613586e_lset @ A) @ Xs)) & (~ ((P @ X4))))))))))).
% 0.21/1.40 thf(fact_228_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((((coindu1213758845finite @ A) @ Xs4) => (((coindu1571841457prefix @ A) @ Xs4) @ Ys3)) & ((~ (((coindu1213758845finite @ A) @ Xs4))) => (Xs4 = Ys3))))))))).
% 0.21/1.40 thf(fact_229_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Xs) @ Ys) => ((coindu1213758845finite @ A) @ Xs))))).
% 0.21/1.40 thf(fact_230_lfinite__lSupD, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: ((((coindu1213758845finite @ A) @ ((coindu526335360e_lSup @ A) @ A3)) => (! [X:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X) @ A3) => ((coindu1213758845finite @ A) @ X)))))))).
% 0.21/1.40 thf(fact_231_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 0.21/1.40 thf(fact_232_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 0.21/1.40 thf(fact_233_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X3:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)))))).
% 0.21/1.40 thf(fact_234_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 0.21/1.40 thf(fact_235_lprefix__lfiniteD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1213758845finite @ A) @ Ys) => ((coindu1213758845finite @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_236_llexord__LNil, axiom, (! [A:$tType,R2:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R2) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 0.21/1.40 thf(fact_237_llexord__LCons__less, axiom, (! [A:$tType,R2:(A > (A > $o)),X3:A,Y:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((R2 @ X3) @ Y) => ((((coindu300403952lexord @ A) @ R2) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 0.21/1.40 thf(fact_238_llexord__LCons__eq, axiom, (! [A:$tType,R2:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X3:A]: ((((((coindu300403952lexord @ A) @ R2) @ Xs) @ Ys) => ((((coindu300403952lexord @ A) @ R2) @ (((coindu1121789889_LCons @ A) @ X3) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X3) @ Ys)))))).
% 0.21/1.40 thf(fact_239_lfinite__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs2) => (P @ Xs2)))) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((~ (((coindu335574135_lnull @ A) @ Xs2))) => ((P @ ((coindu1047225960le_ltl @ A) @ Xs2)) => (P @ Xs2)))))) => (P @ Xs))))))).
% 0.21/1.40 thf(fact_240_lfinite_Oinducts, axiom, (! [A:$tType,X3:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X3) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs2:(coindu1593790203_llist @ A),X5:A]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X5) @ Xs2)))))) => (P @ X3))))))).
% 0.21/1.40 thf(fact_241_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A4:(coindu1593790203_llist @ A)]: (((A4 = (coindu1598213697e_LNil @ A)) | (? [Xs4:(coindu1593790203_llist @ A),X4:A]: (((A4 = (((coindu1121789889_LCons @ A) @ X4) @ Xs4)) & ((coindu1213758845finite @ A) @ Xs4))))))))))).
% 0.21/1.40 thf(fact_242_lfinite_Ocases, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ A2) => ((A2 != (coindu1598213697e_LNil @ A)) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X5:A]: ((A2 = (((coindu1121789889_LCons @ A) @ X5) @ Xs2)))) => (~ (((coindu1213758845finite @ A) @ Xs2))))))))))))).
% 0.21/1.40 thf(fact_243_llimit__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((P @ (coindu1598213697e_LNil @ A)) => ((! [X5:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X5) @ Xs2)))))) => (((! [Ys4:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys4) @ Xs) => (P @ Ys4)))) => (P @ Xs)) => (P @ Xs))))))).
% 0.21/1.40 thf(fact_244_compact__lfiniteI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => ((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ Xs))))).
% 0.21/1.40 thf(fact_245_compact__lfiniteD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((((comple2143767107ompact @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 0.21/1.40 thf(fact_246_llexord_Ocases, axiom, (! [A:$tType,R2:(A > (A > $o)),A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R2) @ A1) @ A22) => ((! [Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),X5:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X5) @ Xs2)) => ((A22 = (((coindu1121789889_LCons @ A) @ X5) @ Ys2)) => (~ (((((coindu300403952lexord @ A) @ R2) @ Xs2) @ Ys2))))))) => ((! [X5:A]: (((? [Xs2:(coindu1593790203_llist @ A)]: ((A1 = (((coindu1121789889_LCons @ A) @ X5) @ Xs2)))) => (! [Y3:A]: (((? [Ys2:(coindu1593790203_llist @ A)]: ((A22 = (((coindu1121789889_LCons @ A) @ Y3) @ Ys2)))) => (~ (((R2 @ X5) @ Y3))))))))) => (~ (((A1 = (coindu1598213697e_LNil @ A)) => (! [Ys2:(coindu1593790203_llist @ A)]: ((A22 != Ys2)))))))))))).
% 0.21/1.40 thf(fact_247_llexord_Osimps, axiom, (! [A:$tType]: (((coindu300403952lexord @ A) = (^ [R3:(A > (A > $o)),A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X4:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X4) @ Xs4)) & ((A23 = (((coindu1121789889_LCons @ A) @ X4) @ Ys3)) & ((((coindu300403952lexord @ A) @ R3) @ Xs4) @ Ys3))))) | ((? [X4:A,Y5:A,Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((A12 = (((coindu1121789889_LCons @ A) @ X4) @ Xs4)) & ((A23 = (((coindu1121789889_LCons @ A) @ Y5) @ Ys3)) & ((R3 @ X4) @ Y5))))) | (? [Ys3:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Ys3)))))))))))).
% 0.21/1.40 thf(fact_248_llist__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: ((((((comple1986059218ssible @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ P) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [X5:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X5) @ Xs2)))))) => (P @ Xs))))))).
% 0.21/1.40 thf(fact_249_lfinite__lSup__chain, axiom, (! [A:$tType,A3:(set @ (coindu1593790203_llist @ A))]: (((((comple1193779247_chain @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A)) @ A3) => (((coindu1213758845finite @ A) @ ((coindu526335360e_lSup @ A) @ A3)) = (((finite_finite @ (coindu1593790203_llist @ A)) @ A3) & (! [X4:(coindu1593790203_llist @ A)]: (((((member @ (coindu1593790203_llist @ A)) @ X4) @ A3) => ((coindu1213758845finite @ A) @ X4)))))))))).
% 0.21/1.40 thf(fact_250_lfinite__imp__finite__lset, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => ((finite_finite @ A) @ ((coindu1112613586e_lset @ A) @ Xs)))))).
% 0.21/1.40 thf(fact_251_llist__gen__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: ((((((comple1986059218ssible @ (coindu1593790203_llist @ A)) @ (coindu526335360e_lSup @ A)) @ (coindu1696667936prefix @ A)) @ P) => ((? [Zs2:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Zs2) @ Xs) & (((coindu1213758845finite @ A) @ Zs2) & (! [Ys2:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Zs2) @ Ys2) => ((((coindu1696667936prefix @ A) @ Ys2) @ Xs) => (((coindu1213758845finite @ A) @ Ys2) => (P @ Ys2)))))))))) => (P @ Xs)))))).
% 0.21/1.40 thf(fact_252_finite__Int, axiom, (! [A:$tType,F4:(set @ A),G3:(set @ A)]: (((((finite_finite @ A) @ F4) | ((finite_finite @ A) @ G3)) => ((finite_finite @ A) @ (((inf_inf @ (set @ A)) @ F4) @ G3)))))).
% 0.21/1.40 thf(fact_253_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys))) = ((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys))))))).
% 0.21/1.40 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A6:$tType,A7:$tType]: ((((semilattice_inf @ A7) @ (type2 @ A7)) => ((semilattice_inf @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.21/1.40 thf(tcon_fun___Lattices_Olattice, axiom, (! [A6:$tType,A7:$tType]: ((((lattice @ A7) @ (type2 @ A7)) => ((lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.21/1.40 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_1, axiom, (! [A6:$tType]: (((semilattice_inf @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.21/1.40 thf(tcon_Set_Oset___Lattices_Olattice_2, axiom, (! [A6:$tType]: (((lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 0.21/1.40 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_3, axiom, ((semilattice_inf @ $o) @ (type2 @ $o))).
% 0.21/1.40 thf(tcon_HOL_Obool___Lattices_Olattice_4, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 0.21/1.40 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 0.21/1.40 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 0.21/1.40 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 0.21/1.40 thf(conj_0, conjecture, ((less_eq @ ((coindu1046438764le_lhd @ a) @ ((coindu526335360e_lSup @ a) @ ya))) @ ((coindu1046438764le_lhd @ a) @ ((coindu1047225960le_ltl @ a) @ ((coindu526335360e_lSup @ a) @ ya))))).
% 0.21/1.40 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.hgRkZ6IOB8/DTF2DTF15555.p
% 0.21/1.40 ------------------------
% 0.21/1.45 ---- Cleaned THF ---
% 0.21/1.45 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.21/1.45 coindu1593790203_llist: $tType > $tType ).
% 0.21/1.45
% 0.21/1.45 thf(ty_t_Set_Oset,type,
% 0.21/1.45 set: $tType > $tType ).
% 0.21/1.45
% 0.21/1.45 thf(ty_t_itself,type,
% 0.21/1.45 itself: $tType > $tType ).
% 0.21/1.45
% 0.21/1.45 thf(ty_tf_a,type,
% 0.21/1.45 a: $tType ).
% 0.21/1.45
% 0.21/1.45 thf(sy_cl_HOL_Otype,type,
% 0.21/1.45 type:
% 0.21/1.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_cl_Lattices_Olattice,type,
% 0.21/1.45 lattice:
% 0.21/1.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.21/1.45 semilattice_inf:
% 0.21/1.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix,type,
% 0.21/1.45 coindu1571841457prefix:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OlSup,type,
% 0.21/1.45 coindu526335360e_lSup:
% 0.21/1.45 !>[A: $tType] : ( ( set @ ( coindu1593790203_llist @ A ) ) > ( coindu1593790203_llist @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.21/1.45 coindu268472904append:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oldistinct,type,
% 0.21/1.45 coindu6345450stinct:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.21/1.45 coindu1213758845finite:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast,type,
% 0.21/1.45 coindu2000965700_llast:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 0.21/1.45 coindu300403952lexord:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.21/1.45 coindu1121789889_LCons:
% 0.21/1.45 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.21/1.45 coindu1598213697e_LNil:
% 0.21/1.45 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocase__llist,type,
% 0.21/1.45 coindu882539134_llist:
% 0.21/1.45 !>[B: $tType,A: $tType] : ( B > ( A > ( coindu1593790203_llist @ A ) > B ) > ( coindu1593790203_llist @ A ) > B ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.21/1.45 coindu1046438764le_lhd:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.21/1.45 coindu335574135_lnull:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 0.21/1.45 coindu1112613586e_lset:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.21/1.45 coindu1047225960le_ltl:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.21/1.45 coindu1696667936prefix:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.21/1.45 coindu574146665prefix:
% 0.21/1.45 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 0.21/1.45 coindu721411036eWhile:
% 0.21/1.45 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord_Olsorted,type,
% 0.21/1.45 coindu543932918sorted:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.21/1.45 coindu1599971794_llist:
% 0.21/1.45 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Complete__Partial__Order2_Ocompact,type,
% 0.21/1.45 comple2143767107ompact:
% 0.21/1.45 !>[A: $tType] : ( ( ( set @ A ) > A ) > ( A > A > $o ) > A > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Complete__Partial__Order2_Ocont,type,
% 0.21/1.45 comple1412571634l_cont:
% 0.21/1.45 !>[A: $tType,B: $tType] : ( ( ( set @ A ) > A ) > ( A > A > $o ) > ( ( set @ B ) > B ) > ( B > B > $o ) > ( A > B ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Complete__Partial__Order_Occpo_Oadmissible,type,
% 0.21/1.45 comple1986059218ssible:
% 0.21/1.45 !>[A: $tType] : ( ( ( set @ A ) > A ) > ( A > A > $o ) > ( A > $o ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Complete__Partial__Order_Ochain,type,
% 0.21/1.45 comple1193779247_chain:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > ( set @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Finite__Set_Ofinite,type,
% 0.21/1.45 finite_finite:
% 0.21/1.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_If,type,
% 0.21/1.45 if:
% 0.21/1.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.21/1.45 inf_inf:
% 0.21/1.45 !>[A: $tType] : ( A > A > A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Orderings_Oord_Omax,type,
% 0.21/1.45 max:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Orderings_Oord_Omin,type,
% 0.21/1.45 min:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > A > A > A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Pure_Otype,type,
% 0.21/1.45 type2:
% 0.21/1.45 !>[A: $tType] : ( itself @ A ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Set_OCollect,type,
% 0.21/1.45 collect:
% 0.21/1.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Set__Interval_Oord_OatLeast,type,
% 0.21/1.45 set_atLeast:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Set__Interval_Oord_OatLeastAtMost,type,
% 0.21/1.45 set_atLeastAtMost:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > A > A > ( set @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_Set__Interval_Oord_OatMost,type,
% 0.21/1.45 set_atMost:
% 0.21/1.45 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_c_member,type,
% 0.21/1.45 member:
% 0.21/1.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_v_Ya____,type,
% 0.21/1.45 ya: set @ ( coindu1593790203_llist @ a ) ).
% 0.21/1.45
% 0.21/1.45 thf(sy_v_less__eq,type,
% 0.21/1.45 less_eq: a > a > $o ).
% 0.21/1.45
% 0.21/1.45 thf(sy_v_xs____,type,
% 0.21/1.45 xs: coindu1593790203_llist @ a ).
% 0.21/1.45
% 0.21/1.45 thf(fact_0__092_060open_062xs_A_092_060in_062_AY_092_060close_062,axiom,
% 0.21/1.45 member @ ( coindu1593790203_llist @ a ) @ xs @ ya ).
% 0.21/1.45
% 0.21/1.45 thf(fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062,axiom,
% 0.21/1.45 less_eq @ ( coindu1046438764le_lhd @ a @ xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_2_local_Oord__eq__le__trans,axiom,
% 0.21/1.45 ! [A2: a,B2: a,C: a] :
% 0.21/1.45 ( ( A2 = B2 )
% 0.21/1.45 => ( ( less_eq @ B2 @ C )
% 0.21/1.45 => ( less_eq @ A2 @ C ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_3_local_Oord__le__eq__trans,axiom,
% 0.21/1.45 ! [A2: a,B2: a,C: a] :
% 0.21/1.45 ( ( less_eq @ A2 @ B2 )
% 0.21/1.45 => ( ( B2 = C )
% 0.21/1.45 => ( less_eq @ A2 @ C ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062,axiom,
% 0.21/1.45 ( ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) )
% 0.21/1.45 = ( coindu1046438764le_lhd @ a @ xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062,axiom,
% 0.21/1.45 ( ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) )
% 0.21/1.45 = ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_6_local_Omax__def,axiom,
% 0.21/1.45 ! [A2: a,B2: a] :
% 0.21/1.45 ( ( ( less_eq @ A2 @ B2 )
% 0.21/1.45 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.21/1.45 = B2 ) )
% 0.21/1.45 & ( ~ ( less_eq @ A2 @ B2 )
% 0.21/1.45 => ( ( max @ a @ less_eq @ A2 @ B2 )
% 0.21/1.45 = A2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_7_local_Omin__def,axiom,
% 0.21/1.45 ! [A2: a,B2: a] :
% 0.21/1.45 ( ( ( less_eq @ A2 @ B2 )
% 0.21/1.45 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.21/1.45 = A2 ) )
% 0.21/1.45 & ( ~ ( less_eq @ A2 @ B2 )
% 0.21/1.45 => ( ( min @ a @ less_eq @ A2 @ B2 )
% 0.21/1.45 = B2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_8_lsorted_I2_J,axiom,
% 0.21/1.45 ! [X: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ a ) @ X @ ya )
% 0.21/1.45 => ( coindu543932918sorted @ a @ less_eq @ X ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_9_lsorted_I3_J,axiom,
% 0.21/1.45 ~ ( coindu335574135_lnull @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_10_lsorted_I4_J,axiom,
% 0.21/1.45 ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_11__092_060open_062_092_060not_062_Alnull_A_Iltl_Axs_J_092_060close_062,axiom,
% 0.21/1.45 ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_12_sorted,axiom,
% 0.21/1.45 ! [Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ a ) @ Xs @ ya )
% 0.21/1.45 => ( coindu543932918sorted @ a @ less_eq @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_13_lsorted__ltlI,axiom,
% 0.21/1.45 ! [Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( coindu543932918sorted @ a @ less_eq @ Xs )
% 0.21/1.45 => ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062xs_A_092_060in_062_AY_059_A_092_060not_062_Alnull_Axs_059_A_092_060not_062_Alnull_A_Iltl_Axs_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.21/1.45 ~ ! [Xs2: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ a ) @ Xs2 @ ya )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ a @ Xs2 )
% 0.21/1.45 => ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ Xs2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_15_local_OatLeastAtMost__iff,axiom,
% 0.21/1.45 ! [I: a,L: a,U: a] :
% 0.21/1.45 ( ( member @ a @ I @ ( set_atLeastAtMost @ a @ less_eq @ L @ U ) )
% 0.21/1.45 = ( ( less_eq @ L @ I )
% 0.21/1.45 & ( less_eq @ I @ U ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_16__092_060open_062_092_060not_062_Alnull_Axs_092_060close_062,axiom,
% 0.21/1.45 ~ ( coindu335574135_lnull @ a @ xs ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_17_local_OatLeast__iff,axiom,
% 0.21/1.45 ! [I: a,K: a] :
% 0.21/1.45 ( ( member @ a @ I @ ( set_atLeast @ a @ less_eq @ K ) )
% 0.21/1.45 = ( less_eq @ K @ I ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_18_local_OatMost__iff,axiom,
% 0.21/1.45 ! [I: a,K: a] :
% 0.21/1.45 ( ( member @ a @ I @ ( set_atMost @ a @ less_eq @ K ) )
% 0.21/1.45 = ( less_eq @ I @ K ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_19_lsorted__coinduct_H,axiom,
% 0.21/1.45 ! [X2: ( coindu1593790203_llist @ a ) > $o,Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( X2 @ Xs )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( X2 @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ a @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ Xs2 ) )
% 0.21/1.45 => ( ( less_eq @ ( coindu1046438764le_lhd @ a @ Xs2 ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ Xs2 ) ) )
% 0.21/1.45 & ( ( X2 @ ( coindu1047225960le_ltl @ a @ Xs2 ) )
% 0.21/1.45 | ( coindu543932918sorted @ a @ less_eq @ ( coindu1047225960le_ltl @ a @ Xs2 ) ) ) ) ) ) )
% 0.21/1.45 => ( coindu543932918sorted @ a @ less_eq @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_20_lsorted__lhdD,axiom,
% 0.21/1.45 ! [Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( coindu543932918sorted @ a @ less_eq @ Xs )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ a @ Xs )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ a @ ( coindu1047225960le_ltl @ a @ Xs ) )
% 0.21/1.45 => ( less_eq @ ( coindu1046438764le_lhd @ a @ Xs ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ Xs ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_21_chain,axiom,
% 0.21/1.45 comple1193779247_chain @ ( coindu1593790203_llist @ a ) @ ( coindu1696667936prefix @ a ) @ ya ).
% 0.21/1.45
% 0.21/1.45 thf(fact_22_llist_Oexpand,axiom,
% 0.21/1.45 ! [A: $tType,Llist: coindu1593790203_llist @ A,Llist2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( coindu335574135_lnull @ A @ Llist )
% 0.21/1.45 = ( coindu335574135_lnull @ A @ Llist2 ) )
% 0.21/1.45 => ( ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Llist2 )
% 0.21/1.45 => ( ( ( coindu1046438764le_lhd @ A @ Llist )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Llist2 ) )
% 0.21/1.45 & ( ( coindu1047225960le_ltl @ A @ Llist )
% 0.21/1.45 = ( coindu1047225960le_ltl @ A @ Llist2 ) ) ) ) )
% 0.21/1.45 => ( Llist = Llist2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_23_lprefix__refl,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_24_llist_Oleq__refl,axiom,
% 0.21/1.45 ! [A: $tType,X3: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X3 @ X3 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_25_lnull__lSup,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.21/1.45 = ( ! [X4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X4 @ A3 )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ X4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_26_lzip_Oexhaust,axiom,
% 0.21/1.45 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.21/1.45 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.21/1.45 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_27_lnull__lprefix,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_28_lprefix__lnull,axiom,
% 0.21/1.45 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ Ys )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_29_lprefix__trans,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_30_lprefix__lnullD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_31_lappend_Oexhaust,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_32_llist_Oleq__trans,axiom,
% 0.21/1.45 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ X3 @ Z ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_33_lprefix__antisym,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.21/1.45 => ( Xs = Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_34_llist_Oleq__antisym,axiom,
% 0.21/1.45 ! [A: $tType,X3: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ X3 @ Y )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Y @ X3 )
% 0.21/1.45 => ( X3 = Y ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_35_lprefix__not__lnullD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_36_lprefix__down__linear,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_37_chain__lprefix__lSup,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.21/1.45 => ( ( member @ ( coindu1593790203_llist @ A ) @ Xs @ A3 )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ Xs @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_38_chain__lSup__lprefix,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),Zs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ Xs2 @ A3 )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ Xs2 @ Zs ) )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ ( coindu526335360e_lSup @ A @ A3 ) @ Zs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_39_llist_Olub__upper,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),X3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.21/1.45 => ( ( member @ ( coindu1593790203_llist @ A ) @ X3 @ A3 )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ X3 @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_40_llist_Olub__least,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A ),Z: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ A3 )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ X5 @ Z ) )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ ( coindu526335360e_lSup @ A @ A3 ) @ Z ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_41_lprefix__lhdD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_42_lhd__lSup__eq,axiom,
% 0.21/1.45 ! [A: $tType,Y2: set @ ( coindu1593790203_llist @ A ),Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ Y2 )
% 0.21/1.45 => ( ( member @ ( coindu1593790203_llist @ A ) @ Xs @ Y2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( coindu1046438764le_lhd @ A @ ( coindu526335360e_lSup @ A @ Y2 ) )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_43_mem__Collect__eq,axiom,
% 0.21/1.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.21/1.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.21/1.45 = ( P @ A2 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_44_Collect__mem__eq,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ A] :
% 0.21/1.45 ( ( collect @ A
% 0.21/1.45 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.21/1.45 = A3 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_45_Collect__cong,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/1.45 ( ! [X5: A] :
% 0.21/1.45 ( ( P @ X5 )
% 0.21/1.45 = ( Q @ X5 ) )
% 0.21/1.45 => ( ( collect @ A @ P )
% 0.21/1.45 = ( collect @ A @ Q ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_46_ext,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.21/1.45 ( ! [X5: A] :
% 0.21/1.45 ( ( F @ X5 )
% 0.21/1.45 = ( G @ X5 ) )
% 0.21/1.45 => ( F = G ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_47_lprefix__coinduct,axiom,
% 0.21/1.45 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( P @ Xs @ Ys )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( P @ Xs2 @ Ys2 )
% 0.21/1.45 => ( ( ( coindu335574135_lnull @ A @ Ys2 )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ Xs2 ) )
% 0.21/1.45 & ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Ys2 )
% 0.21/1.45 => ( ( ( coindu1046438764le_lhd @ A @ Xs2 )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Ys2 ) )
% 0.21/1.45 & ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys2 ) )
% 0.21/1.45 | ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) @ ( coindu1047225960le_ltl @ A @ Ys2 ) ) ) ) ) ) ) )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_48_lprefix__expand,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.21/1.45 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.21/1.45 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_49_lSup_Odisc__iff_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.21/1.45 = ( ! [X4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X4 @ A3 )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ X4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_50_lSup_Odisc_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ! [X5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ A3 )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ X5 ) )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_51_lSup_Odisc_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ~ ! [X: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X @ A3 )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ X ) )
% 0.21/1.45 => ~ ( coindu335574135_lnull @ A @ ( coindu526335360e_lSup @ A @ A3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_52_lnull__ltlI,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_53_ord_Olsorted__coinduct_H,axiom,
% 0.21/1.45 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 0.21/1.45 ( ( X2 @ Xs )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.21/1.45 => ( ( Less_eq @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ ( coindu1046438764le_lhd @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.21/1.45 & ( ( X2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.21/1.45 | ( coindu543932918sorted @ A @ Less_eq @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) ) ) ) ) )
% 0.21/1.45 => ( coindu543932918sorted @ A @ Less_eq @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_54_ord_Olsorted__lhdD,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu543932918sorted @ A @ Less_eq @ Xs )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.21/1.45 => ( Less_eq @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_55_ltakeWhile_Oexhaust,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.21/1.45 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_56_lprefix__ltlI,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_57_ord_Olsorted__ltlI,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu543932918sorted @ A @ Less_eq @ Xs )
% 0.21/1.45 => ( coindu543932918sorted @ A @ Less_eq @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_58_llist_Ocoinduct__strong,axiom,
% 0.21/1.45 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( R @ Llist @ Llist2 )
% 0.21/1.45 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( R @ Llist3 @ Llist4 )
% 0.21/1.45 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.21/1.45 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.21/1.45 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.21/1.45 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.21/1.45 & ( ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) )
% 0.21/1.45 | ( ( coindu1047225960le_ltl @ A @ Llist3 )
% 0.21/1.45 = ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) ) )
% 0.21/1.45 => ( Llist = Llist2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_59_llist_Ocoinduct,axiom,
% 0.21/1.45 ! [A: $tType,R: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist: coindu1593790203_llist @ A,Llist2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( R @ Llist @ Llist2 )
% 0.21/1.45 => ( ! [Llist3: coindu1593790203_llist @ A,Llist4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( R @ Llist3 @ Llist4 )
% 0.21/1.45 => ( ( ( coindu335574135_lnull @ A @ Llist3 )
% 0.21/1.45 = ( coindu335574135_lnull @ A @ Llist4 ) )
% 0.21/1.45 & ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.21/1.45 => ( ( ( coindu1046438764le_lhd @ A @ Llist3 )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Llist4 ) )
% 0.21/1.45 & ( R @ ( coindu1047225960le_ltl @ A @ Llist3 ) @ ( coindu1047225960le_ltl @ A @ Llist4 ) ) ) ) ) ) )
% 0.21/1.45 => ( Llist = Llist2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_60_local_OatLeastAtMost__def,axiom,
% 0.21/1.45 ! [L: a,U: a] :
% 0.21/1.45 ( ( set_atLeastAtMost @ a @ less_eq @ L @ U )
% 0.21/1.45 = ( inf_inf @ ( set @ a ) @ ( set_atLeast @ a @ less_eq @ L ) @ ( set_atMost @ a @ less_eq @ U ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_61_lsorted__LCons_H,axiom,
% 0.21/1.45 ! [X3: a,Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ Xs ) )
% 0.21/1.45 = ( ~ ( coindu335574135_lnull @ a @ Xs )
% 0.21/1.45 => ( ( less_eq @ X3 @ ( coindu1046438764le_lhd @ a @ Xs ) )
% 0.21/1.45 & ( coindu543932918sorted @ a @ less_eq @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_62_LNil,axiom,
% 0.21/1.45 coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_63_LCons__LCons,axiom,
% 0.21/1.45 ! [X3: a,Y: a,Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( less_eq @ X3 @ Y )
% 0.21/1.45 => ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y @ Xs ) )
% 0.21/1.45 => ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1121789889_LCons @ a @ Y @ Xs ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_64_ord_Omax__def,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( max @ A )
% 0.21/1.45 = ( ^ [Less_eq2: A > A > $o,A4: A,B3: A] : ( if @ A @ ( Less_eq2 @ A4 @ B3 ) @ B3 @ A4 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_65_ord_Omin__def,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( min @ A )
% 0.21/1.45 = ( ^ [Less_eq2: A > A > $o,A4: A,B3: A] : ( if @ A @ ( Less_eq2 @ A4 @ B3 ) @ A4 @ B3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_66_unfold__llist__id,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1599971794_llist @ ( coindu1593790203_llist @ A ) @ A @ ( coindu335574135_lnull @ A ) @ ( coindu1046438764le_lhd @ A ) @ ( coindu1047225960le_ltl @ A ) @ Xs )
% 0.21/1.45 = Xs ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_67_llist_Ocase__eq__if,axiom,
% 0.21/1.45 ! [A: $tType,B: $tType] :
% 0.21/1.45 ( ( coindu882539134_llist @ B @ A )
% 0.21/1.45 = ( ^ [F1: B,F2: A > ( coindu1593790203_llist @ A ) > B,Llist5: coindu1593790203_llist @ A] : ( if @ B @ ( coindu335574135_lnull @ A @ Llist5 ) @ F1 @ ( F2 @ ( coindu1046438764le_lhd @ A @ Llist5 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_68_ord_OatMost__iff,axiom,
% 0.21/1.45 ! [A: $tType,I: A,Less_eq: A > A > $o,K: A] :
% 0.21/1.45 ( ( member @ A @ I @ ( set_atMost @ A @ Less_eq @ K ) )
% 0.21/1.45 = ( Less_eq @ I @ K ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_69_ord_OatLeast__iff,axiom,
% 0.21/1.45 ! [A: $tType,I: A,Less_eq: A > A > $o,K: A] :
% 0.21/1.45 ( ( member @ A @ I @ ( set_atLeast @ A @ Less_eq @ K ) )
% 0.21/1.45 = ( Less_eq @ K @ I ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_70_llist_Oinject,axiom,
% 0.21/1.45 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.21/1.45 = ( ( X21 = Y21 )
% 0.21/1.45 & ( X22 = Y22 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_71_Singleton,axiom,
% 0.21/1.45 ! [X3: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1598213697e_LNil @ a ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_72_lsorted_Ocases,axiom,
% 0.21/1.45 ! [A2: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( coindu543932918sorted @ a @ less_eq @ A2 )
% 0.21/1.45 => ( ( A2
% 0.21/1.45 != ( coindu1598213697e_LNil @ a ) )
% 0.21/1.45 => ( ! [X5: a] :
% 0.21/1.45 ( A2
% 0.21/1.45 != ( coindu1121789889_LCons @ a @ X5 @ ( coindu1598213697e_LNil @ a ) ) )
% 0.21/1.45 => ~ ! [X5: a,Y3: a,Xs2: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ a @ X5 @ ( coindu1121789889_LCons @ a @ Y3 @ Xs2 ) ) )
% 0.21/1.45 => ( ( less_eq @ X5 @ Y3 )
% 0.21/1.45 => ~ ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_73_lsorted_Ocoinduct,axiom,
% 0.21/1.45 ! [X2: ( coindu1593790203_llist @ a ) > $o,X3: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( X2 @ X3 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( X2 @ X5 )
% 0.21/1.45 => ( ( X5
% 0.21/1.45 = ( coindu1598213697e_LNil @ a ) )
% 0.21/1.45 | ? [Xa: a] :
% 0.21/1.45 ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ a @ Xa @ ( coindu1598213697e_LNil @ a ) ) )
% 0.21/1.45 | ? [Xa: a,Y4: a,Xs3: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ a @ Xa @ ( coindu1121789889_LCons @ a @ Y4 @ Xs3 ) ) )
% 0.21/1.45 & ( less_eq @ Xa @ Y4 )
% 0.21/1.45 & ( ( X2 @ ( coindu1121789889_LCons @ a @ Y4 @ Xs3 ) )
% 0.21/1.45 | ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y4 @ Xs3 ) ) ) ) ) )
% 0.21/1.45 => ( coindu543932918sorted @ a @ less_eq @ X3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_74_lsorted_Osimps,axiom,
% 0.21/1.45 ! [A2: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( coindu543932918sorted @ a @ less_eq @ A2 )
% 0.21/1.45 = ( ( A2
% 0.21/1.45 = ( coindu1598213697e_LNil @ a ) )
% 0.21/1.45 | ? [X4: a] :
% 0.21/1.45 ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ a @ X4 @ ( coindu1598213697e_LNil @ a ) ) )
% 0.21/1.45 | ? [X4: a,Y5: a,Xs4: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ a @ X4 @ ( coindu1121789889_LCons @ a @ Y5 @ Xs4 ) ) )
% 0.21/1.45 & ( less_eq @ X4 @ Y5 )
% 0.21/1.45 & ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y5 @ Xs4 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_75_LCons__lprefix__LCons,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.21/1.45 = ( ( X3 = Y )
% 0.21/1.45 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_76_lprefix__code_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_77_unfold__llist__eq__LCons,axiom,
% 0.21/1.45 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( ~ ( IS_LNIL @ B2 )
% 0.21/1.45 & ( X3
% 0.21/1.45 = ( LHD @ B2 ) )
% 0.21/1.45 & ( Xs
% 0.21/1.45 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_78_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.21/1.45 = ( P2 @ A2 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_79_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.21/1.45 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) )
% 0.21/1.45 = ( ~ ( P2 @ A2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_80_lprefix__LNil,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_81_lsorted__LCons__LCons,axiom,
% 0.21/1.45 ! [X3: a,Y: a,Xs: coindu1593790203_llist @ a] :
% 0.21/1.45 ( ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1121789889_LCons @ a @ Y @ Xs ) ) )
% 0.21/1.45 = ( ( less_eq @ X3 @ Y )
% 0.21/1.45 & ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ Y @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_82_lhd__LCons__ltl,axiom,
% 0.21/1.45 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Llist )
% 0.21/1.45 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) )
% 0.21/1.45 = Llist ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_83_lsorted__code_I1_J,axiom,
% 0.21/1.45 coindu543932918sorted @ a @ less_eq @ ( coindu1598213697e_LNil @ a ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_84_lsorted__code_I2_J,axiom,
% 0.21/1.45 ! [X3: a] : ( coindu543932918sorted @ a @ less_eq @ ( coindu1121789889_LCons @ a @ X3 @ ( coindu1598213697e_LNil @ a ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_85_lprefix__code_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_86_lprefix_Ocases,axiom,
% 0.21/1.45 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 0.21/1.45 => ( ( ( A1
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ! [Xs2: coindu1593790203_llist @ A] : ( A22 != Xs2 ) )
% 0.21/1.45 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X5: A] :
% 0.21/1.45 ( ( A1
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.21/1.45 => ( ( A22
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Ys2 ) )
% 0.21/1.45 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_87_lprefix_Osimps,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A )
% 0.21/1.45 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A12
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 & ( A23 = Xs4 ) )
% 0.21/1.45 | ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X4: A] :
% 0.21/1.45 ( ( A12
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.21/1.45 & ( A23
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Ys3 ) )
% 0.21/1.45 & ( coindu1696667936prefix @ A @ Xs4 @ Ys3 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_88_lprefix_Ocoinduct,axiom,
% 0.21/1.45 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ X3 @ Xa2 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ A,Xa3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ X5 @ Xa3 )
% 0.21/1.45 => ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 & ( Xa3 = Xs3 ) )
% 0.21/1.45 | ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xb @ Xs3 ) )
% 0.21/1.45 & ( Xa3
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 0.21/1.45 & ( ( X2 @ Xs3 @ Ys4 )
% 0.21/1.45 | ( coindu1696667936prefix @ A @ Xs3 @ Ys4 ) ) ) ) )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ X3 @ Xa2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_89_lprefix__LCons__conv,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.21/1.45 = ( ( Xs
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Xs
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.21/1.45 & ( coindu1696667936prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_90_unfold__llist_Ocode,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType] :
% 0.21/1.45 ( ( coindu1599971794_llist @ A @ B )
% 0.21/1.45 = ( ^ [P3: A > $o,G212: A > B,G222: A > A,A4: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P3 @ A4 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A4 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_91_neq__LNil__conv,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Xs
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = ( ? [X4: A,Xs5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( Xs
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_92_llist_Oexhaust,axiom,
% 0.21/1.45 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Y
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.21/1.45 ( Y
% 0.21/1.45 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_93_unfold__llist_Octr_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,B: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.21/1.45 ( ( P2 @ A2 )
% 0.21/1.45 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.21/1.45 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_94_unfold__llist_Octr_I2_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.21/1.45 ( ~ ( P2 @ A2 )
% 0.21/1.45 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 )
% 0.21/1.45 = ( coindu1121789889_LCons @ B @ ( G21 @ A2 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_95_llist_Odistinct_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1598213697e_LNil @ A )
% 0.21/1.45 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_96_llist_Osimps_I4_J,axiom,
% 0.21/1.45 ! [A: $tType,B: $tType,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B] :
% 0.21/1.45 ( ( coindu882539134_llist @ B @ A @ F12 @ F22 @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = F12 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_97_llist_Osimps_I5_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu882539134_llist @ B @ A @ F12 @ F22 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.21/1.45 = ( F22 @ X21 @ X22 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_98_ord_OSingleton,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,X3: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_99_ord_Olsorted_Ocoinduct,axiom,
% 0.21/1.45 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 0.21/1.45 ( ( X2 @ X3 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ X5 )
% 0.21/1.45 => ( ( X5
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [Xa: A] :
% 0.21/1.45 ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu1598213697e_LNil @ A ) ) )
% 0.21/1.45 | ? [Xa: A,Y4: A,Xs3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu1121789889_LCons @ A @ Y4 @ Xs3 ) ) )
% 0.21/1.45 & ( Less_eq @ Xa @ Y4 )
% 0.21/1.45 & ( ( X2 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs3 ) )
% 0.21/1.45 | ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y4 @ Xs3 ) ) ) ) ) )
% 0.21/1.45 => ( coindu543932918sorted @ A @ Less_eq @ X3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_100_ord_Olsorted_Osimps,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu543932918sorted @ A )
% 0.21/1.45 = ( ^ [Less_eq2: A > A > $o,A4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A4
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [X4: A] :
% 0.21/1.45 ( A4
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.21/1.45 | ? [X4: A,Y5: A,Xs4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A4
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ ( coindu1121789889_LCons @ A @ Y5 @ Xs4 ) ) )
% 0.21/1.45 & ( Less_eq2 @ X4 @ Y5 )
% 0.21/1.45 & ( coindu543932918sorted @ A @ Less_eq2 @ ( coindu1121789889_LCons @ A @ Y5 @ Xs4 ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_101_ord_Olsorted_Ocases,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,A2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu543932918sorted @ A @ Less_eq @ A2 )
% 0.21/1.45 => ( ( A2
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( ! [X5: A] :
% 0.21/1.45 ( A2
% 0.21/1.45 != ( coindu1121789889_LCons @ A @ X5 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.21/1.45 => ~ ! [X5: A,Y3: A,Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) )
% 0.21/1.45 => ( ( Less_eq @ X5 @ Y3 )
% 0.21/1.45 => ~ ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_102_ord_Olsorted__code_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,X3: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_103_ltl__unfold__llist,axiom,
% 0.21/1.45 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.21/1.45 ( ( ( IS_LNIL @ A2 )
% 0.21/1.45 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) )
% 0.21/1.45 & ( ~ ( IS_LNIL @ A2 )
% 0.21/1.45 => ( ( coindu1047225960le_ltl @ A @ ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.21/1.45 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_104_llist_Osplit__sel,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P: B > $o,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( P @ ( coindu882539134_llist @ B @ A @ F12 @ F22 @ Llist ) )
% 0.21/1.45 = ( ( ( Llist
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( P @ F12 ) )
% 0.21/1.45 & ( ( Llist
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.21/1.45 => ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_105_llist_Osplit__sel__asm,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P: B > $o,F12: B,F22: A > ( coindu1593790203_llist @ A ) > B,Llist: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( P @ ( coindu882539134_llist @ B @ A @ F12 @ F22 @ Llist ) )
% 0.21/1.45 = ( ~ ( ( ( Llist
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 & ~ ( P @ F12 ) )
% 0.21/1.45 | ( ( Llist
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) )
% 0.21/1.45 & ~ ( P @ ( F22 @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_106_eq__LConsD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Xs
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.21/1.45 => ( ( Xs
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.21/1.45 = Y )
% 0.21/1.45 & ( ( coindu1047225960le_ltl @ A @ Xs )
% 0.21/1.45 = Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_107_llist_Oexhaust__sel,axiom,
% 0.21/1.45 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Llist
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( Llist
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist ) @ ( coindu1047225960le_ltl @ A @ Llist ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_108_LCons__lprefix__conv,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ Ys )
% 0.21/1.45 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Ys
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X3 @ Ys5 ) )
% 0.21/1.45 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_109_Le__LCons,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X3: A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ X3 @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_110_not__lnull__conv,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.21/1.45 = ( ? [X4: A,Xs5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( Xs
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_111_llist_OdiscI_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Llist
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.21/1.45 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_112_llist_Odisc_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.21/1.45 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_113_ltl__simps_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1047225960le_ltl @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.21/1.45 = X22 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_114_LNil__lprefix,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_115_lhd__LCons,axiom,
% 0.21/1.45 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.21/1.45 = X21 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_116_lnull__def,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A )
% 0.21/1.45 = ( ^ [Llist5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( Llist5
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_117_llist_Ocollapse_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ Llist )
% 0.21/1.45 => ( Llist
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_118_llist_OdiscI_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Llist
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_119_llist_Odisc_I1_J,axiom,
% 0.21/1.45 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_120_ltl__simps_I1_J,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu1047225960le_ltl @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_121_ord_Olsorted__LCons__LCons,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,X3: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.21/1.45 = ( ( Less_eq @ X3 @ Y )
% 0.21/1.45 & ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_122_ord_OLCons__LCons,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,X3: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Less_eq @ X3 @ Y )
% 0.21/1.45 => ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) )
% 0.21/1.45 => ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_123_ord_OLNil,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_124_ord_Olsorted__code_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_125_unfold__llist_Odisc_I1_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.21/1.45 ( ( P2 @ A2 )
% 0.21/1.45 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_126_unfold__llist_Odisc_I2_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.21/1.45 ( ~ ( P2 @ A2 )
% 0.21/1.45 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_127_unfold__llist_Osimps_I4_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.21/1.45 ( ~ ( P2 @ A2 )
% 0.21/1.45 => ( ( coindu1047225960le_ltl @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.21/1.45 = ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_128_unfold__llist_Osimps_I3_J,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType,P2: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.21/1.45 ( ~ ( P2 @ A2 )
% 0.21/1.45 => ( ( coindu1046438764le_lhd @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A2 ) )
% 0.21/1.45 = ( G21 @ A2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_129_lSup_Octr_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ! [X5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ A3 )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ X5 ) )
% 0.21/1.45 => ( ( coindu526335360e_lSup @ A @ A3 )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_130_ord_OatLeastAtMost__def,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( set_atLeastAtMost @ A )
% 0.21/1.45 = ( ^ [Less_eq2: A > A > $o,L2: A,U2: A] : ( inf_inf @ ( set @ A ) @ ( set_atLeast @ A @ Less_eq2 @ L2 ) @ ( set_atMost @ A @ Less_eq2 @ U2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_131_ord_Olsorted__LCons_H,axiom,
% 0.21/1.45 ! [A: $tType,Less_eq: A > A > $o,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( Less_eq @ X3 @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 & ( coindu543932918sorted @ A @ Less_eq @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_132_ord_OatLeastAtMost__iff,axiom,
% 0.21/1.45 ! [A: $tType,I: A,Less_eq: A > A > $o,L: A,U: A] :
% 0.21/1.45 ( ( member @ A @ I @ ( set_atLeastAtMost @ A @ Less_eq @ L @ U ) )
% 0.21/1.45 = ( ( Less_eq @ L @ I )
% 0.21/1.45 & ( Less_eq @ I @ U ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_133_Int__iff,axiom,
% 0.21/1.45 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.21/1.45 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.21/1.45 = ( ( member @ A @ C @ A3 )
% 0.21/1.45 & ( member @ A @ C @ B4 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_134_IntI,axiom,
% 0.21/1.45 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.21/1.45 ( ( member @ A @ C @ A3 )
% 0.21/1.45 => ( ( member @ A @ C @ B4 )
% 0.21/1.45 => ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_135_inf__right__idem,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A] :
% 0.21/1.45 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y ) @ Y )
% 0.21/1.45 = ( inf_inf @ A @ X3 @ Y ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_136_inf_Oright__idem,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [A2: A,B2: A] :
% 0.21/1.45 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.21/1.45 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_137_inf__left__idem,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A] :
% 0.21/1.45 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y ) )
% 0.21/1.45 = ( inf_inf @ A @ X3 @ Y ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_138_inf_Oleft__idem,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [A2: A,B2: A] :
% 0.21/1.45 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.21/1.45 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_139_inf__idem,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A] :
% 0.21/1.45 ( ( inf_inf @ A @ X3 @ X3 )
% 0.21/1.45 = X3 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_140_inf__apply,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.21/1.45 => ( ( inf_inf @ ( A > B ) )
% 0.21/1.45 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( inf_inf @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_141_inf_Oidem,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [A2: A] :
% 0.21/1.45 ( ( inf_inf @ A @ A2 @ A2 )
% 0.21/1.45 = A2 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_142_inf__sup__aci_I4_J,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A] :
% 0.21/1.45 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ X3 @ Y ) )
% 0.21/1.45 = ( inf_inf @ A @ X3 @ Y ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_143_inf__sup__aci_I3_J,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A,Z: A] :
% 0.21/1.45 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) )
% 0.21/1.45 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X3 @ Z ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_144_inf__sup__aci_I2_J,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A,Z: A] :
% 0.21/1.45 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y ) @ Z )
% 0.21/1.45 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_145_inf__sup__aci_I1_J,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( lattice @ A @ ( type2 @ A ) )
% 0.21/1.45 => ( ( inf_inf @ A )
% 0.21/1.45 = ( ^ [X4: A,Y5: A] : ( inf_inf @ A @ Y5 @ X4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_146_inf__fun__def,axiom,
% 0.21/1.45 ! [B: $tType,A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.21/1.45 => ( ( inf_inf @ ( A > B ) )
% 0.21/1.45 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( inf_inf @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_147_inf_Oassoc,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [A2: A,B2: A,C: A] :
% 0.21/1.45 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C )
% 0.21/1.45 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_148_inf__assoc,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A,Z: A] :
% 0.21/1.45 ( ( inf_inf @ A @ ( inf_inf @ A @ X3 @ Y ) @ Z )
% 0.21/1.45 = ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_149_inf_Ocommute,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ( ( inf_inf @ A )
% 0.21/1.45 = ( ^ [A4: A,B3: A] : ( inf_inf @ A @ B3 @ A4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_150_inf__commute,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ( ( inf_inf @ A )
% 0.21/1.45 = ( ^ [X4: A,Y5: A] : ( inf_inf @ A @ Y5 @ X4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_151_inf_Oleft__commute,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [B2: A,A2: A,C: A] :
% 0.21/1.45 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C ) )
% 0.21/1.45 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_152_inf__left__commute,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.21/1.45 => ! [X3: A,Y: A,Z: A] :
% 0.21/1.45 ( ( inf_inf @ A @ X3 @ ( inf_inf @ A @ Y @ Z ) )
% 0.21/1.45 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X3 @ Z ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_153_IntE,axiom,
% 0.21/1.45 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.21/1.45 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.21/1.45 => ~ ( ( member @ A @ C @ A3 )
% 0.21/1.45 => ~ ( member @ A @ C @ B4 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_154_IntD1,axiom,
% 0.21/1.45 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.21/1.45 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.21/1.45 => ( member @ A @ C @ A3 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_155_IntD2,axiom,
% 0.21/1.45 ! [A: $tType,C: A,A3: set @ A,B4: set @ A] :
% 0.21/1.45 ( ( member @ A @ C @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.21/1.45 => ( member @ A @ C @ B4 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_156_Int__assoc,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 0.21/1.45 ( ( inf_inf @ ( set @ A ) @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) @ C2 )
% 0.21/1.45 = ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_157_Int__absorb,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ A] :
% 0.21/1.45 ( ( inf_inf @ ( set @ A ) @ A3 @ A3 )
% 0.21/1.45 = A3 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_158_Int__commute,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( inf_inf @ ( set @ A ) )
% 0.21/1.45 = ( ^ [A5: set @ A,B5: set @ A] : ( inf_inf @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_159_Int__left__absorb,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ A,B4: set @ A] :
% 0.21/1.45 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ A3 @ B4 ) )
% 0.21/1.45 = ( inf_inf @ ( set @ A ) @ A3 @ B4 ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_160_Int__left__commute,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ A,B4: set @ A,C2: set @ A] :
% 0.21/1.45 ( ( inf_inf @ ( set @ A ) @ A3 @ ( inf_inf @ ( set @ A ) @ B4 @ C2 ) )
% 0.21/1.45 = ( inf_inf @ ( set @ A ) @ B4 @ ( inf_inf @ ( set @ A ) @ A3 @ C2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_161_compact__LCons__iff,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_162_ltakeWhile_Ocode,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu721411036eWhile @ A )
% 0.21/1.45 = ( ^ [P4: A > $o,Xs4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( if @ ( coindu1593790203_llist @ A )
% 0.21/1.45 @ ( ( coindu335574135_lnull @ A @ Xs4 )
% 0.21/1.45 | ~ ( P4 @ ( coindu1046438764le_lhd @ A @ Xs4 ) ) )
% 0.21/1.45 @ ( coindu1598213697e_LNil @ A )
% 0.21/1.45 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs4 ) @ ( coindu721411036eWhile @ A @ P4 @ ( coindu1047225960le_ltl @ A @ Xs4 ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_163_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.21/1.45 = ( ( Xs
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Xs
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.21/1.45 & ( coindu1571841457prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_164_lstrict__prefix__code_I3_J,axiom,
% 0.21/1.45 ! [B: $tType,X3: B,Xs: coindu1593790203_llist @ B] :
% 0.21/1.45 ~ ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X3 @ Xs ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_165_ltakeWhile__LNil,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o] :
% 0.21/1.45 ( ( coindu721411036eWhile @ A @ P @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_166_lstrict__prefix__code_I4_J,axiom,
% 0.21/1.45 ! [B: $tType,X3: B,Xs: coindu1593790203_llist @ B,Y: B,Ys: coindu1593790203_llist @ B] :
% 0.21/1.45 ( ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X3 @ Xs ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 0.21/1.45 = ( ( X3 = Y )
% 0.21/1.45 & ( coindu574146665prefix @ B @ Xs @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_167_lstrict__prefix__code_I1_J,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_168_ltakeWhile__LCons,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( P @ X3 )
% 0.21/1.45 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) )
% 0.21/1.45 & ( ~ ( P @ X3 )
% 0.21/1.45 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_169_ltakeWhile_Odisc__iff_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 0.21/1.45 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 & ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_170_ltakeWhile_Odisc__iff_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_171_lnull__ltakeWhile,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_172_lstrict__prefix__code_I2_J,axiom,
% 0.21/1.45 ! [B: $tType,Y: B,Ys: coindu1593790203_llist @ B] : ( coindu574146665prefix @ B @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_173_lprefix__ltakeWhile,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) @ Xs ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_174_llist__less__induct,axiom,
% 0.21/1.45 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ! [Ys4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu574146665prefix @ A @ Ys4 @ Xs2 )
% 0.21/1.45 => ( P @ Ys4 ) )
% 0.21/1.45 => ( P @ Xs2 ) )
% 0.21/1.45 => ( P @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_175_lstrict__prefix__def,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu574146665prefix @ A )
% 0.21/1.45 = ( ^ [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs4 @ Ys3 )
% 0.21/1.45 & ( Xs4 != Ys3 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_176_ltakeWhile_Odisc_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 => ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_177_ltakeWhile_Odisc_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.21/1.45 => ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_178_lhd__ltakeWhile,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 => ( ( coindu1046438764le_lhd @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_179_ltakeWhile__eq__LNil__iff,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = ( ( Xs
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_180_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu1571841457prefix @ A )
% 0.21/1.45 = ( coindu1696667936prefix @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 = ( Xs
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1571841457prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_183_ltakeWhile_Octr_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.21/1.45 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_184_ltakeWhile_Osimps_I4_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_185_ltl__ltakeWhile,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) )
% 0.21/1.45 & ( ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 => ( ( coindu1047225960le_ltl @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_186_ltakeWhile_Octr_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.21/1.45 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_187_compact__LConsI,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,X3: A] :
% 0.21/1.45 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs )
% 0.21/1.45 => ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_188_compact__LConsD,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 => ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_189_ldistinct__lSup,axiom,
% 0.21/1.45 ! [A: $tType,Y2: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ Y2 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X5 @ Y2 )
% 0.21/1.45 => ( coindu6345450stinct @ A @ X5 ) )
% 0.21/1.45 => ( coindu6345450stinct @ A @ ( coindu526335360e_lSup @ A @ Y2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_190_llast__singleton,axiom,
% 0.21/1.45 ! [A: $tType,X3: A] :
% 0.21/1.45 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.21/1.45 = X3 ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_191_cont__ltl,axiom,
% 0.21/1.45 ! [A: $tType] : ( comple1412571634l_cont @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ ( coindu1047225960le_ltl @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_192_ldistinct__LNil__code,axiom,
% 0.21/1.45 ! [A: $tType] : ( coindu6345450stinct @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_193_llast__LCons2,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.21/1.45 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_194_ldistinct__ltlI,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu6345450stinct @ A @ Xs )
% 0.21/1.45 => ( coindu6345450stinct @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_195_ldistinct_OLNil,axiom,
% 0.21/1.45 ! [A: $tType] : ( coindu6345450stinct @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_196_ldistinct__lprefix,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu6345450stinct @ A @ Xs )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.21/1.45 => ( coindu6345450stinct @ A @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_197_llast__LCons,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,X3: A] :
% 0.21/1.45 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = X3 ) )
% 0.21/1.45 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( coindu2000965700_llast @ A @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_198_ldistinct__lhdD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu6345450stinct @ A @ Xs )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ~ ( member @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_199_ldistinct__coinduct,axiom,
% 0.21/1.45 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ Xs )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( ~ ( member @ A @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.21/1.45 & ( ( X2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.21/1.45 | ( coindu6345450stinct @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) ) ) ) )
% 0.21/1.45 => ( coindu6345450stinct @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_200_ldistinct__LCons,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu6345450stinct @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( ~ ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 & ( coindu6345450stinct @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_201_ldistinct_OLCons,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ~ ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( ( coindu6345450stinct @ A @ Xs )
% 0.21/1.45 => ( coindu6345450stinct @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_202_llist_Oset__sel_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,A2: coindu1593790203_llist @ A,X3: A] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.21/1.45 => ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ A2 ) ) )
% 0.21/1.45 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_203_llist_Oset__sel_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.21/1.45 => ( member @ A @ ( coindu1046438764le_lhd @ A @ A2 ) @ ( coindu1112613586e_lset @ A @ A2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_204_lset__intros_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,X6: A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_205_lset__intros_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_206_llist_Oset__intros_I2_J,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,A22: coindu1593790203_llist @ A,A1: A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ A22 ) )
% 0.21/1.45 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_207_llist_Oset__intros_I1_J,axiom,
% 0.21/1.45 ! [A: $tType,A1: A,A22: coindu1593790203_llist @ A] : ( member @ A @ A1 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_208_lset__cases,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( ! [Xs6: coindu1593790203_llist @ A] :
% 0.21/1.45 ( Xs
% 0.21/1.45 != ( coindu1121789889_LCons @ A @ X3 @ Xs6 ) )
% 0.21/1.45 => ~ ! [X7: A,Xs6: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( Xs
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X7 @ Xs6 ) )
% 0.21/1.45 => ~ ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs6 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_209_lset__induct,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) )
% 0.21/1.45 => ( ! [X7: A,Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.21/1.45 => ( ( X3 != X7 )
% 0.21/1.45 => ( ( P @ Xs2 )
% 0.21/1.45 => ( P @ ( coindu1121789889_LCons @ A @ X7 @ Xs2 ) ) ) ) )
% 0.21/1.45 => ( P @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_210_lset__induct_H,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) )
% 0.21/1.45 => ( ! [X7: A,Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.21/1.45 => ( ( P @ Xs2 )
% 0.21/1.45 => ( P @ ( coindu1121789889_LCons @ A @ X7 @ Xs2 ) ) ) )
% 0.21/1.45 => ( P @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_211_llist_Oset__cases,axiom,
% 0.21/1.45 ! [A: $tType,E: A,A2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.21/1.45 => ( ! [Z2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( A2
% 0.21/1.45 != ( coindu1121789889_LCons @ A @ E @ Z2 ) )
% 0.21/1.45 => ~ ! [Z1: A,Z2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.21/1.45 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_212_llist_Oset__induct,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,A2: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ A2 ) )
% 0.21/1.45 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.21/1.45 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A,Xa3: A] :
% 0.21/1.45 ( ( member @ A @ Xa3 @ ( coindu1112613586e_lset @ A @ Z2 ) )
% 0.21/1.45 => ( ( P @ Xa3 @ Z2 )
% 0.21/1.45 => ( P @ Xa3 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) ) ) )
% 0.21/1.45 => ( P @ X3 @ A2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_213_in__lset__ltlD,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs ) ) )
% 0.21/1.45 => ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_214_ltakeWhile__all,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.21/1.45 ( ! [X5: A] :
% 0.21/1.45 ( ( member @ A @ X5 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( P @ X5 ) )
% 0.21/1.45 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.21/1.45 = Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_215_ltakeWhile__cong,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,P: A > $o,Q: A > $o] :
% 0.21/1.45 ( ( Xs = Ys )
% 0.21/1.45 => ( ! [X5: A] :
% 0.21/1.45 ( ( member @ A @ X5 @ ( coindu1112613586e_lset @ A @ Ys ) )
% 0.21/1.45 => ( ( P @ X5 )
% 0.21/1.45 = ( Q @ X5 ) ) )
% 0.21/1.45 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.21/1.45 = ( coindu721411036eWhile @ A @ Q @ Ys ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_216_lset__ltakeWhileD,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 0.21/1.45 => ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 & ( P @ X3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_217_llist__set__induct,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.21/1.45 ( ( member @ A @ X3 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( P @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ Xs2 ) )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A,Y3: A] :
% 0.21/1.45 ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( ( member @ A @ Y3 @ ( coindu1112613586e_lset @ A @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) )
% 0.21/1.45 => ( ( P @ Y3 @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.21/1.45 => ( P @ Y3 @ Xs2 ) ) ) )
% 0.21/1.45 => ( P @ X3 @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_218_ldistinct_Ocases,axiom,
% 0.21/1.45 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu6345450stinct @ A @ A2 )
% 0.21/1.45 => ( ( A2
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ~ ! [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.21/1.45 => ( ~ ( member @ A @ X5 @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.21/1.45 => ~ ( coindu6345450stinct @ A @ Xs2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_219_ldistinct_Osimps,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu6345450stinct @ A )
% 0.21/1.45 = ( ^ [A4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A4
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [X4: A,Xs4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A4
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.21/1.45 & ~ ( member @ A @ X4 @ ( coindu1112613586e_lset @ A @ Xs4 ) )
% 0.21/1.45 & ( coindu6345450stinct @ A @ Xs4 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_220_ldistinct_Ocoinduct,axiom,
% 0.21/1.45 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ X3 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ X5 )
% 0.21/1.45 => ( ( X5
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [Xa: A,Xs3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xa @ Xs3 ) )
% 0.21/1.45 & ~ ( member @ A @ Xa @ ( coindu1112613586e_lset @ A @ Xs3 ) )
% 0.21/1.45 & ( ( X2 @ Xs3 )
% 0.21/1.45 | ( coindu6345450stinct @ A @ Xs3 ) ) ) ) )
% 0.21/1.45 => ( coindu6345450stinct @ A @ X3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_221_compact__eq__lfinite,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) )
% 0.21/1.45 = ( coindu1213758845finite @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_222_llexord_Ocoinduct,axiom,
% 0.21/1.45 ! [A: $tType,X2: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X3: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A,R2: A > A > $o] :
% 0.21/1.45 ( ( X2 @ X3 @ Xa2 )
% 0.21/1.45 => ( ! [X5: coindu1593790203_llist @ A,Xa3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X2 @ X5 @ Xa3 )
% 0.21/1.45 => ( ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,Xb: A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xb @ Xs3 ) )
% 0.21/1.45 & ( Xa3
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xb @ Ys4 ) )
% 0.21/1.45 & ( ( X2 @ Xs3 @ Ys4 )
% 0.21/1.45 | ( coindu300403952lexord @ A @ R2 @ Xs3 @ Ys4 ) ) )
% 0.21/1.45 | ? [Xb: A,Y4: A,Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Xb @ Xs3 ) )
% 0.21/1.45 & ( Xa3
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y4 @ Ys4 ) )
% 0.21/1.45 & ( R2 @ Xb @ Y4 ) )
% 0.21/1.45 | ? [Ys4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( X5
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 & ( Xa3 = Ys4 ) ) ) )
% 0.21/1.45 => ( coindu300403952lexord @ A @ R2 @ X3 @ Xa2 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_223_lfinite__LCons,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) )
% 0.21/1.45 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_224_lfinite__code_I2_J,axiom,
% 0.21/1.45 ! [B: $tType,X3: B,Xs: coindu1593790203_llist @ B] :
% 0.21/1.45 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X3 @ Xs ) )
% 0.21/1.45 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_225_lfinite__code_I1_J,axiom,
% 0.21/1.45 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_226_lfinite__ltl,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.21/1.45 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_227_lfinite__ltakeWhile,axiom,
% 0.21/1.45 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.21/1.45 = ( ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 | ? [X4: A] :
% 0.21/1.45 ( ( member @ A @ X4 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.21/1.45 & ~ ( P @ X4 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_228_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A )
% 0.21/1.45 = ( ^ [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( ( coindu1213758845finite @ A @ Xs4 )
% 0.21/1.45 => ( coindu1571841457prefix @ A @ Xs4 @ Ys3 ) )
% 0.21/1.45 & ( ~ ( coindu1213758845finite @ A @ Xs4 )
% 0.21/1.45 => ( Xs4 = Ys3 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_229_lstrict__prefix__lfinite1,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_230_lfinite__lSupD,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.21/1.45 => ! [X: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X @ A3 )
% 0.21/1.45 => ( coindu1213758845finite @ A @ X ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_231_lfinite__LNil,axiom,
% 0.21/1.45 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_232_lnull__imp__lfinite,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ Xs )
% 0.21/1.45 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_233_lfinite__LConsI,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,X3: A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_234_not__lfinite__lprefix__conv__eq,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 = ( Xs = Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_235_lprefix__lfiniteD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.21/1.45 => ( ( coindu1213758845finite @ A @ Ys )
% 0.21/1.45 => ( coindu1213758845finite @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_236_llexord__LNil,axiom,
% 0.21/1.45 ! [A: $tType,R2: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R2 @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_237_llexord__LCons__less,axiom,
% 0.21/1.45 ! [A: $tType,R2: A > A > $o,X3: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( R2 @ X3 @ Y )
% 0.21/1.45 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_238_llexord__LCons__eq,axiom,
% 0.21/1.45 ! [A: $tType,R2: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X3: A] :
% 0.21/1.45 ( ( coindu300403952lexord @ A @ R2 @ Xs @ Ys )
% 0.21/1.45 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X3 @ Xs ) @ ( coindu1121789889_LCons @ A @ X3 @ Ys ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_239_lfinite__induct,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( P @ Xs2 ) )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.21/1.45 => ( ~ ( coindu335574135_lnull @ A @ Xs2 )
% 0.21/1.45 => ( ( P @ ( coindu1047225960le_ltl @ A @ Xs2 ) )
% 0.21/1.45 => ( P @ Xs2 ) ) ) )
% 0.21/1.45 => ( P @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_240_lfinite_Oinducts,axiom,
% 0.21/1.45 ! [A: $tType,X3: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ X3 )
% 0.21/1.45 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A,X5: A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.21/1.45 => ( ( P @ Xs2 )
% 0.21/1.45 => ( P @ ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.21/1.45 => ( P @ X3 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_241_lfinite_Osimps,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu1213758845finite @ A )
% 0.21/1.45 = ( ^ [A4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A4
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 | ? [Xs4: coindu1593790203_llist @ A,X4: A] :
% 0.21/1.45 ( ( A4
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.21/1.45 & ( coindu1213758845finite @ A @ Xs4 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_242_lfinite_Ocases,axiom,
% 0.21/1.45 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ A2 )
% 0.21/1.45 => ( ( A2
% 0.21/1.45 != ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ? [X5: A] :
% 0.21/1.45 ( A2
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.21/1.45 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_243_llimit__induct,axiom,
% 0.21/1.45 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( ! [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.21/1.45 => ( ( P @ Xs2 )
% 0.21/1.45 => ( P @ ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.21/1.45 => ( ( ! [Ys4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu574146665prefix @ A @ Ys4 @ Xs )
% 0.21/1.45 => ( P @ Ys4 ) )
% 0.21/1.45 => ( P @ Xs ) )
% 0.21/1.45 => ( P @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_244_compact__lfiniteI,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 => ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_245_compact__lfiniteD,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple2143767107ompact @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ Xs )
% 0.21/1.45 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_246_llexord_Ocases,axiom,
% 0.21/1.45 ! [A: $tType,R2: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu300403952lexord @ A @ R2 @ A1 @ A22 )
% 0.21/1.45 => ( ! [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X5: A] :
% 0.21/1.45 ( ( A1
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.21/1.45 => ( ( A22
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Ys2 ) )
% 0.21/1.45 => ~ ( coindu300403952lexord @ A @ R2 @ Xs2 @ Ys2 ) ) )
% 0.21/1.45 => ( ! [X5: A] :
% 0.21/1.45 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( A1
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) )
% 0.21/1.45 => ! [Y3: A] :
% 0.21/1.45 ( ? [Ys2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( A22
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) )
% 0.21/1.45 => ~ ( R2 @ X5 @ Y3 ) ) )
% 0.21/1.45 => ~ ( ( A1
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ! [Ys2: coindu1593790203_llist @ A] : ( A22 != Ys2 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_247_llexord_Osimps,axiom,
% 0.21/1.45 ! [A: $tType] :
% 0.21/1.45 ( ( coindu300403952lexord @ A )
% 0.21/1.45 = ( ^ [R3: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X4: A] :
% 0.21/1.45 ( ( A12
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.21/1.45 & ( A23
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Ys3 ) )
% 0.21/1.45 & ( coindu300403952lexord @ A @ R3 @ Xs4 @ Ys3 ) )
% 0.21/1.45 | ? [X4: A,Y5: A,Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A12
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ X4 @ Xs4 ) )
% 0.21/1.45 & ( A23
% 0.21/1.45 = ( coindu1121789889_LCons @ A @ Y5 @ Ys3 ) )
% 0.21/1.45 & ( R3 @ X4 @ Y5 ) )
% 0.21/1.45 | ? [Ys3: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( A12
% 0.21/1.45 = ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 & ( A23 = Ys3 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_248_llist__induct,axiom,
% 0.21/1.45 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1986059218ssible @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ P )
% 0.21/1.45 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.21/1.45 => ( ! [X5: A,Xs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.21/1.45 => ( ( P @ Xs2 )
% 0.21/1.45 => ( P @ ( coindu1121789889_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.21/1.45 => ( P @ Xs ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_249_lfinite__lSup__chain,axiom,
% 0.21/1.45 ! [A: $tType,A3: set @ ( coindu1593790203_llist @ A )] :
% 0.21/1.45 ( ( comple1193779247_chain @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) @ A3 )
% 0.21/1.45 => ( ( coindu1213758845finite @ A @ ( coindu526335360e_lSup @ A @ A3 ) )
% 0.21/1.45 = ( ( finite_finite @ ( coindu1593790203_llist @ A ) @ A3 )
% 0.21/1.45 & ! [X4: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( member @ ( coindu1593790203_llist @ A ) @ X4 @ A3 )
% 0.21/1.45 => ( coindu1213758845finite @ A @ X4 ) ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_250_lfinite__imp__finite__lset,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 => ( finite_finite @ A @ ( coindu1112613586e_lset @ A @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_251_llist__gen__induct,axiom,
% 0.21/1.45 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( comple1986059218ssible @ ( coindu1593790203_llist @ A ) @ ( coindu526335360e_lSup @ A ) @ ( coindu1696667936prefix @ A ) @ P )
% 0.21/1.45 => ( ? [Zs2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Zs2 @ Xs )
% 0.21/1.45 & ( coindu1213758845finite @ A @ Zs2 )
% 0.21/1.45 & ! [Ys2: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1696667936prefix @ A @ Zs2 @ Ys2 )
% 0.21/1.45 => ( ( coindu1696667936prefix @ A @ Ys2 @ Xs )
% 0.21/1.45 => ( ( coindu1213758845finite @ A @ Ys2 )
% 0.21/1.45 => ( P @ Ys2 ) ) ) ) )
% 0.21/1.45 => ( P @ Xs ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_252_finite__Int,axiom,
% 0.21/1.45 ! [A: $tType,F4: set @ A,G3: set @ A] :
% 0.21/1.45 ( ( ( finite_finite @ A @ F4 )
% 0.21/1.45 | ( finite_finite @ A @ G3 ) )
% 0.21/1.45 => ( finite_finite @ A @ ( inf_inf @ ( set @ A ) @ F4 @ G3 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(fact_253_llast__lappend__LCons,axiom,
% 0.21/1.45 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.21/1.45 ( ( coindu1213758845finite @ A @ Xs )
% 0.21/1.45 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) )
% 0.21/1.45 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.21/1.45 ! [A6: $tType,A7: $tType] :
% 0.21/1.45 ( ( semilattice_inf @ A7 @ ( type2 @ A7 ) )
% 0.21/1.45 => ( semilattice_inf @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.21/1.45 ! [A6: $tType,A7: $tType] :
% 0.21/1.45 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.21/1.45 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(tcon_Set_Oset___Lattices_Osemilattice__inf_1,axiom,
% 0.21/1.45 ! [A6: $tType] : ( semilattice_inf @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(tcon_Set_Oset___Lattices_Olattice_2,axiom,
% 0.21/1.45 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_3,axiom,
% 0.21/1.45 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(tcon_HOL_Obool___Lattices_Olattice_4,axiom,
% 0.21/1.45 lattice @ $o @ ( type2 @ $o ) ).
% 0.21/1.45
% 0.21/1.45 thf(help_If_3_1_T,axiom,
% 0.21/1.45 ! [P: $o] :
% 0.21/1.45 ( ( P = $true )
% 0.21/1.45 | ( P = $false ) ) ).
% 0.21/1.45
% 0.21/1.45 thf(help_If_2_1_T,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Y: A] :
% 0.21/1.45 ( ( if @ A @ $false @ X3 @ Y )
% 0.21/1.45 = Y ) ).
% 0.21/1.45
% 0.21/1.45 thf(help_If_1_1_T,axiom,
% 0.21/1.45 ! [A: $tType,X3: A,Y: A] :
% 0.21/1.45 ( ( if @ A @ $true @ X3 @ Y )
% 0.21/1.45 = X3 ) ).
% 0.21/1.45
% 0.21/1.45 thf(conj_0,conjecture,
% 0.21/1.45 less_eq @ ( coindu1046438764le_lhd @ a @ ( coindu526335360e_lSup @ a @ ya ) ) @ ( coindu1046438764le_lhd @ a @ ( coindu1047225960le_ltl @ a @ ( coindu526335360e_lSup @ a @ ya ) ) ) ).
% 0.21/1.45 ------------------------
% 0.21/1.47 % (15665)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/183Mi)
% 0.21/1.48 % (15666)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_15555 for (2999ds/4Mi)
% 0.21/1.48 % (15669)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_15555 for (2999ds/2Mi)
% 0.21/1.48 % (15668)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/2Mi)
% 0.21/1.48 % (15667)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_15555 for (2999ds/27Mi)
% 0.21/1.48 % (15671)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/18Mi)
% 0.21/1.48 % (15670)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_15555 for (2999ds/275Mi)
% 0.21/1.48 % (15666)Instruction limit reached!
% 0.21/1.48 % (15666)------------------------------
% 0.21/1.48 % (15666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/1.48 % (15666)Termination reason: Unknown
% 0.21/1.48 % (15666)Termination phase: shuffling
% 0.21/1.48
% 0.21/1.48 % (15666)Memory used [KB]: 1407
% 0.21/1.48 % (15666)Time elapsed: 0.003 s
% 0.21/1.48 % (15666)Instructions burned: 4 (million)
% 0.21/1.48 % (15666)------------------------------
% 0.21/1.48 % (15666)------------------------------
% 0.21/1.48 % (15668)Instruction limit reached!
% 0.21/1.48 % (15668)------------------------------
% 0.21/1.48 % (15668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/1.48 % (15668)Termination reason: Unknown
% 0.21/1.48 % (15668)Termination phase: shuffling
% 0.21/1.48
% 0.21/1.48 % (15668)Memory used [KB]: 1407
% 0.21/1.48 % (15668)Time elapsed: 0.003 s
% 0.21/1.48 % (15668)Instructions burned: 3 (million)
% 0.21/1.48 % (15668)------------------------------
% 0.21/1.48 % (15668)------------------------------
% 0.21/1.48 % (15669)Instruction limit reached!
% 0.21/1.48 % (15669)------------------------------
% 0.21/1.48 % (15669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/1.48 % (15669)Termination reason: Unknown
% 0.21/1.48 % (15669)Termination phase: shuffling
% 0.21/1.48
% 0.21/1.48 % (15669)Memory used [KB]: 1407
% 0.21/1.48 % (15669)Time elapsed: 0.003 s
% 0.21/1.48 % (15669)Instructions burned: 4 (million)
% 0.21/1.48 % (15669)------------------------------
% 0.21/1.48 % (15669)------------------------------
% 0.21/1.49 % (15671)Instruction limit reached!
% 0.21/1.49 % (15671)------------------------------
% 0.21/1.49 % (15671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/1.49 % (15671)Termination reason: Unknown
% 0.21/1.49 % (15671)Termination phase: shuffling
% 0.21/1.49
% 0.21/1.49 % (15671)Memory used [KB]: 1663
% 0.21/1.49 % (15671)Time elapsed: 0.011 s
% 0.21/1.49 % (15671)Instructions burned: 18 (million)
% 0.21/1.49 % (15671)------------------------------
% 0.21/1.49 % (15671)------------------------------
% 0.21/1.49 % (15667)Instruction limit reached!
% 0.21/1.49 % (15667)------------------------------
% 0.21/1.49 % (15667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.21/1.49 % (15667)Termination reason: Unknown
% 0.21/1.49 % (15667)Termination phase: Property scanning
% 0.21/1.49
% 0.21/1.49 % (15667)Memory used [KB]: 1791
% 0.21/1.49 % (15667)Time elapsed: 0.016 s
% 0.21/1.49 % (15667)Instructions burned: 28 (million)
% 0.21/1.49 % (15667)------------------------------
% 0.21/1.49 % (15667)------------------------------
% 0.21/1.49 % (15674)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_15555 for (2999ds/15Mi)
% 0.21/1.49 % (15672)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/3Mi)
% 0.21/1.49 % (15673)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_15555 for (2999ds/37Mi)
% 2.69/1.50 % (15672)Instruction limit reached!
% 2.69/1.50 % (15672)------------------------------
% 2.69/1.50 % (15672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.50 % (15672)Termination reason: Unknown
% 2.69/1.50 % (15672)Termination phase: shuffling
% 2.69/1.50
% 2.69/1.50 % (15672)Memory used [KB]: 1407
% 2.69/1.50 % (15672)Time elapsed: 0.003 s
% 2.69/1.50 % (15672)Instructions burned: 3 (million)
% 2.69/1.50 % (15672)------------------------------
% 2.69/1.50 % (15672)------------------------------
% 2.69/1.50 % (15674)Instruction limit reached!
% 2.69/1.50 % (15674)------------------------------
% 2.69/1.50 % (15674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.50 % (15674)Termination reason: Unknown
% 2.69/1.50 % (15674)Termination phase: shuffling
% 2.69/1.50
% 2.69/1.50 % (15674)Memory used [KB]: 1663
% 2.69/1.50 % (15674)Time elapsed: 0.010 s
% 2.69/1.50 % (15674)Instructions burned: 16 (million)
% 2.69/1.50 % (15674)------------------------------
% 2.69/1.50 % (15674)------------------------------
% 2.69/1.50 % (15675)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_15555 for (2999ds/3Mi)
% 2.69/1.50 % (15675)Instruction limit reached!
% 2.69/1.50 % (15675)------------------------------
% 2.69/1.50 % (15675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.50 % (15675)Termination reason: Unknown
% 2.69/1.50 % (15675)Termination phase: shuffling
% 2.69/1.50
% 2.69/1.50 % (15675)Memory used [KB]: 1407
% 2.69/1.50 % (15675)Time elapsed: 0.003 s
% 2.69/1.50 % (15675)Instructions burned: 3 (million)
% 2.69/1.50 % (15675)------------------------------
% 2.69/1.50 % (15675)------------------------------
% 2.69/1.51 % (15676)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_15555 for (2999ds/1041Mi)
% 2.69/1.51 % (15677)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/7Mi)
% 2.69/1.51 % (15673)Instruction limit reached!
% 2.69/1.51 % (15673)------------------------------
% 2.69/1.51 % (15673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.51 % (15673)Termination reason: Unknown
% 2.69/1.51 % (15673)Termination phase: shuffling
% 2.69/1.51
% 2.69/1.51 % (15673)Memory used [KB]: 2046
% 2.69/1.51 % (15673)Time elapsed: 0.019 s
% 2.69/1.51 % (15673)Instructions burned: 37 (million)
% 2.69/1.51 % (15673)------------------------------
% 2.69/1.51 % (15673)------------------------------
% 2.69/1.52 % (15677)Instruction limit reached!
% 2.69/1.52 % (15677)------------------------------
% 2.69/1.52 % (15677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (15677)Termination reason: Unknown
% 2.69/1.52 % (15677)Termination phase: shuffling
% 2.69/1.52
% 2.69/1.52 % (15677)Memory used [KB]: 1407
% 2.69/1.52 % (15677)Time elapsed: 0.005 s
% 2.69/1.52 % (15677)Instructions burned: 7 (million)
% 2.69/1.52 % (15677)------------------------------
% 2.69/1.52 % (15677)------------------------------
% 2.69/1.52 % (15678)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/16Mi)
% 2.69/1.52 % (15679)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/3Mi)
% 2.69/1.52 % (15679)Instruction limit reached!
% 2.69/1.52 % (15679)------------------------------
% 2.69/1.52 % (15679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (15679)Termination reason: Unknown
% 2.69/1.52 % (15679)Termination phase: shuffling
% 2.69/1.52
% 2.69/1.52 % (15679)Memory used [KB]: 1407
% 2.69/1.52 % (15679)Time elapsed: 0.003 s
% 2.69/1.52 % (15679)Instructions burned: 3 (million)
% 2.69/1.52 % (15679)------------------------------
% 2.69/1.52 % (15679)------------------------------
% 2.69/1.52 % (15665)Instruction limit reached!
% 2.69/1.52 % (15665)------------------------------
% 2.69/1.52 % (15665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.52 % (15665)Termination reason: Unknown
% 2.69/1.52 % (15665)Termination phase: Saturation
% 2.69/1.52
% 2.69/1.52 % (15665)Memory used [KB]: 7164
% 2.69/1.52 % (15665)Time elapsed: 0.054 s
% 2.69/1.52 % (15665)Instructions burned: 185 (million)
% 2.69/1.52 % (15665)------------------------------
% 2.69/1.52 % (15665)------------------------------
% 2.69/1.53 % (15678)Instruction limit reached!
% 2.69/1.53 % (15678)------------------------------
% 2.69/1.53 % (15678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.53 % (15678)Termination reason: Unknown
% 2.69/1.53 % (15678)Termination phase: shuffling
% 2.69/1.53
% 2.69/1.53 % (15678)Memory used [KB]: 1663
% 2.69/1.53 % (15678)Time elapsed: 0.010 s
% 2.69/1.53 % (15678)Instructions burned: 16 (million)
% 2.69/1.53 % (15678)------------------------------
% 2.69/1.53 % (15678)------------------------------
% 2.69/1.53 % (15680)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/3Mi)
% 2.69/1.53 % (15680)Instruction limit reached!
% 2.69/1.53 % (15680)------------------------------
% 2.69/1.53 % (15680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.53 % (15680)Termination reason: Unknown
% 2.69/1.53 % (15680)Termination phase: shuffling
% 2.69/1.53
% 2.69/1.53 % (15680)Memory used [KB]: 1407
% 2.69/1.53 % (15680)Time elapsed: 0.003 s
% 2.69/1.53 % (15680)Instructions burned: 3 (million)
% 2.69/1.53 % (15680)------------------------------
% 2.69/1.53 % (15680)------------------------------
% 2.69/1.53 % (15681)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/7Mi)
% 2.69/1.53 % (15683)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/4Mi)
% 2.69/1.54 % (15681)Instruction limit reached!
% 2.69/1.54 % (15681)------------------------------
% 2.69/1.54 % (15681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (15681)Termination reason: Unknown
% 2.69/1.54 % (15681)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (15681)Memory used [KB]: 1535
% 2.69/1.54 % (15681)Time elapsed: 0.006 s
% 2.69/1.54 % (15681)Instructions burned: 8 (million)
% 2.69/1.54 % (15681)------------------------------
% 2.69/1.54 % (15681)------------------------------
% 2.69/1.54 % (15683)Instruction limit reached!
% 2.69/1.54 % (15683)------------------------------
% 2.69/1.54 % (15683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (15683)Termination reason: Unknown
% 2.69/1.54 % (15683)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (15683)Memory used [KB]: 1407
% 2.69/1.54 % (15683)Time elapsed: 0.003 s
% 2.69/1.54 % (15683)Instructions burned: 6 (million)
% 2.69/1.54 % (15683)------------------------------
% 2.69/1.54 % (15683)------------------------------
% 2.69/1.54 % (15682)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/3Mi)
% 2.69/1.54 % (15682)Instruction limit reached!
% 2.69/1.54 % (15682)------------------------------
% 2.69/1.54 % (15682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.54 % (15682)Termination reason: Unknown
% 2.69/1.54 % (15682)Termination phase: shuffling
% 2.69/1.54
% 2.69/1.54 % (15682)Memory used [KB]: 1407
% 2.69/1.54 % (15682)Time elapsed: 0.003 s
% 2.69/1.54 % (15682)Instructions burned: 4 (million)
% 2.69/1.54 % (15682)------------------------------
% 2.69/1.54 % (15682)------------------------------
% 2.69/1.54 % (15684)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/18Mi)
% 2.69/1.54 % (15686)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/6Mi)
% 2.69/1.55 % (15685)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/710Mi)
% 2.69/1.55 % (15686)Instruction limit reached!
% 2.69/1.55 % (15686)------------------------------
% 2.69/1.55 % (15686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (15686)Termination reason: Unknown
% 2.69/1.55 % (15686)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (15686)Memory used [KB]: 1407
% 2.69/1.55 % (15686)Time elapsed: 0.003 s
% 2.69/1.55 % (15686)Instructions burned: 6 (million)
% 2.69/1.55 % (15686)------------------------------
% 2.69/1.55 % (15686)------------------------------
% 2.69/1.55 % (15687)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/902Mi)
% 2.69/1.55 % (15684)Instruction limit reached!
% 2.69/1.55 % (15684)------------------------------
% 2.69/1.55 % (15684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.55 % (15684)Termination reason: Unknown
% 2.69/1.55 % (15684)Termination phase: shuffling
% 2.69/1.55
% 2.69/1.55 % (15684)Memory used [KB]: 1663
% 2.69/1.55 % (15684)Time elapsed: 0.011 s
% 2.69/1.55 % (15684)Instructions burned: 19 (million)
% 2.69/1.55 % (15684)------------------------------
% 2.69/1.55 % (15684)------------------------------
% 2.69/1.56 % (15688)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/21Mi)
% 2.69/1.56 % (15689)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/5Mi)
% 2.69/1.56 % (15689)Instruction limit reached!
% 2.69/1.56 % (15689)------------------------------
% 2.69/1.56 % (15689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.56 % (15689)Termination reason: Unknown
% 2.69/1.56 % (15689)Termination phase: shuffling
% 2.69/1.56
% 2.69/1.56 % (15689)Memory used [KB]: 1407
% 2.69/1.56 % (15689)Time elapsed: 0.005 s
% 2.69/1.56 % (15689)Instructions burned: 6 (million)
% 2.69/1.56 % (15689)------------------------------
% 2.69/1.56 % (15689)------------------------------
% 2.69/1.57 % (15688)Instruction limit reached!
% 2.69/1.57 % (15688)------------------------------
% 2.69/1.57 % (15688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (15688)Termination reason: Unknown
% 2.69/1.57 % (15688)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (15688)Memory used [KB]: 1791
% 2.69/1.57 % (15688)Time elapsed: 0.012 s
% 2.69/1.57 % (15688)Instructions burned: 21 (million)
% 2.69/1.57 % (15688)------------------------------
% 2.69/1.57 % (15688)------------------------------
% 2.69/1.57 % (15690)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_15555 for (2999ds/6Mi)
% 2.69/1.57 % (15690)Instruction limit reached!
% 2.69/1.57 % (15690)------------------------------
% 2.69/1.57 % (15690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.57 % (15690)Termination reason: Unknown
% 2.69/1.57 % (15690)Termination phase: shuffling
% 2.69/1.57
% 2.69/1.57 % (15690)Memory used [KB]: 1407
% 2.69/1.57 % (15690)Time elapsed: 0.005 s
% 2.69/1.57 % (15690)Instructions burned: 8 (million)
% 2.69/1.57 % (15690)------------------------------
% 2.69/1.57 % (15690)------------------------------
% 2.69/1.58 % (15691)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15555 for (2998ds/377Mi)
% 2.69/1.58 % (15692)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15555 for (2998ds/779Mi)
% 2.69/1.59 % (15693)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15555 for (2998ds/19Mi)
% 2.69/1.60 % (15693)Instruction limit reached!
% 2.69/1.60 % (15693)------------------------------
% 2.69/1.60 % (15693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.60 % (15693)Termination reason: Unknown
% 2.69/1.60 % (15693)Termination phase: shuffling
% 2.69/1.60
% 2.69/1.60 % (15693)Memory used [KB]: 1663
% 2.69/1.60 % (15693)Time elapsed: 0.011 s
% 2.69/1.60 % (15693)Instructions burned: 20 (million)
% 2.69/1.60 % (15693)------------------------------
% 2.69/1.60 % (15693)------------------------------
% 2.69/1.61 % (15694)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15555 for (2998ds/879Mi)
% 2.69/1.61 % (15676)First to succeed.
% 2.69/1.61 % (15670)Instruction limit reached!
% 2.69/1.61 % (15670)------------------------------
% 2.69/1.61 % (15670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.61 % (15670)Termination reason: Unknown
% 2.69/1.61 % (15670)Termination phase: Saturation
% 2.69/1.61
% 2.69/1.61 % (15670)Memory used [KB]: 6908
% 2.69/1.61 % (15670)Time elapsed: 0.137 s
% 2.69/1.61 % (15670)Instructions burned: 276 (million)
% 2.69/1.61 % (15670)------------------------------
% 2.69/1.61 % (15670)------------------------------
% 2.69/1.61 % (15676)Refutation found. Thanks to Tanya!
% 2.69/1.61 % SZS status Theorem for DTF2THF_15555
% 2.69/1.61 % SZS output start Proof for DTF2THF_15555
% 2.69/1.61 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.69/1.61 thf(type_def_7, type, coindu1593790203_llist: ($tType) > $tType).
% 2.69/1.61 thf(type_def_8, type, set: ($tType) > $tType).
% 2.69/1.61 thf(type_def_9, type, a: $tType).
% 2.69/1.61 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 2.69/1.61 thf(func_def_1, type, set: ($tType) > $tType).
% 2.69/1.61 thf(func_def_2, type, itself: ($tType) > $tType).
% 2.69/1.61 thf(func_def_3, type, a: $tType).
% 2.69/1.61 thf(func_def_4, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.69/1.61 thf(func_def_5, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.69/1.61 thf(func_def_6, type, semilattice_inf: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.69/1.61 thf(func_def_7, type, coindu1571841457prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_8, type, coindu526335360e_lSup: !>[X0: $tType]:(set @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.69/1.61 thf(func_def_9, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.69/1.61 thf(func_def_10, type, coindu6345450stinct: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_11, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_12, type, coindu2000965700_llast: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.69/1.61 thf(func_def_13, type, coindu300403952lexord: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_14, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.69/1.61 thf(func_def_15, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.69/1.61 thf(func_def_16, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0)).
% 2.69/1.61 thf(func_def_17, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.69/1.61 thf(func_def_18, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_19, type, coindu1112613586e_lset: !>[X0: $tType]:(coindu1593790203_llist @ X0 > set @ X0)).
% 2.69/1.61 thf(func_def_20, type, coindu1047225960le_ltl: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.69/1.61 thf(func_def_21, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_22, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_23, type, coindu721411036eWhile: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.69/1.61 thf(func_def_24, type, coindu543932918sorted: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > $o)).
% 2.69/1.61 thf(func_def_25, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 2.69/1.61 thf(func_def_26, type, comple2143767107ompact: !>[X0: $tType]:((set @ X0 > X0) > (X0 > X0 > $o) > X0 > $o)).
% 2.69/1.61 thf(func_def_27, type, comple1412571634l_cont: !>[X0: $tType, X1: $tType]:((set @ X0 > X0) > (X0 > X0 > $o) > (set @ X1 > X1) > (X1 > X1 > $o) > (X0 > X1) > $o)).
% 2.69/1.61 thf(func_def_28, type, comple1986059218ssible: !>[X0: $tType]:((set @ X0 > X0) > (X0 > X0 > $o) > (X0 > $o) > $o)).
% 2.69/1.61 thf(func_def_29, type, comple1193779247_chain: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > $o)).
% 2.69/1.61 thf(func_def_30, type, finite_finite: !>[X0: $tType]:(set @ X0 > $o)).
% 2.69/1.61 thf(func_def_31, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.69/1.61 thf(func_def_32, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.69/1.61 thf(func_def_33, type, max: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 2.69/1.61 thf(func_def_34, type, min: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > X0)).
% 2.69/1.61 thf(func_def_35, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.69/1.61 thf(func_def_36, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.69/1.61 thf(func_def_37, type, set_atLeast: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.69/1.61 thf(func_def_38, type, set_atLeastAtMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > set @ X0)).
% 2.69/1.61 thf(func_def_39, type, set_atMost: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.69/1.61 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.69/1.61 thf(func_def_41, type, ya: set @ coindu1593790203_llist @ a).
% 2.69/1.61 thf(func_def_42, type, less_eq: a > a > $o).
% 2.69/1.61 thf(func_def_43, type, xs: coindu1593790203_llist @ a).
% 2.69/1.61 thf(f1328,plain,(
% 2.69/1.61 $false),
% 2.69/1.61 inference(trivial_inequality_removal,[status(thm)],[f1327])).
% 2.69/1.61 thf(f1327,plain,(
% 2.69/1.61 ($false = $true)),
% 2.69/1.61 inference(boolean_simplification,[status(thm)],[f1326])).
% 2.69/1.61 thf(f1326,plain,(
% 2.69/1.61 ($true = (~ $true))),
% 2.69/1.61 inference(forward_demodulation,[status(thm)],[f1325,f1191])).
% 2.69/1.61 thf(f1191,plain,(
% 2.69/1.61 ((less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs))) = $true)),
% 2.69/1.61 inference(cnf_transformation,[status(thm)],[f447])).
% 2.69/1.61 thf(f447,plain,(
% 2.69/1.61 ((less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs))) = $true)),
% 2.69/1.61 inference(fool_elimination,[status(thm)],[f446])).
% 2.69/1.61 thf(f446,plain,(
% 2.69/1.61 (less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))),
% 2.69/1.61 inference(rectify,[status(thm)],[f2])).
% 2.69/1.61 thf(f2,axiom,(
% 2.69/1.61 (less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))),
% 2.69/1.61 file('/export/starexec/sandbox/tmp/tmp.hgRkZ6IOB8/DTF2THF_15555.p',fact_1__092_060open_062lhd_Axs_A_092_060le_062_Alhd_A_Iltl_Axs_J_092_060close_062)).
% 2.69/1.61 thf(f1325,plain,(
% 2.69/1.61 ((~ (less_eq @ (coindu1046438764le_lhd @ a @ xs) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))) = $true)),
% 2.69/1.61 inference(backward_demodulation,[status(thm)],[f1324,f1094])).
% 2.69/1.61 thf(f1094,plain,(
% 2.69/1.61 ((coindu1046438764le_lhd @ a @ xs) = (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)))),
% 2.69/1.61 inference(cnf_transformation,[status(thm)],[f421])).
% 2.69/1.61 thf(f421,plain,(
% 2.69/1.61 ((coindu1046438764le_lhd @ a @ xs) = (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)))),
% 2.69/1.61 inference(fool_elimination,[status(thm)],[f5])).
% 2.69/1.61 thf(f5,axiom,(
% 2.69/1.61 ((coindu1046438764le_lhd @ a @ xs) = (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)))),
% 2.69/1.61 file('/export/starexec/sandbox/tmp/tmp.hgRkZ6IOB8/DTF2THF_15555.p',fact_4__092_060open_062lhd_A_IlSup_AY_J_A_061_Alhd_Axs_092_060close_062)).
% 2.69/1.61 thf(f1324,plain,(
% 2.69/1.61 ((~ (less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)))) = $true)),
% 2.69/1.61 inference(backward_demodulation,[status(thm)],[f1176,f1223])).
% 2.69/1.61 thf(f1223,plain,(
% 2.69/1.61 ((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)) = (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 2.69/1.61 inference(cnf_transformation,[status(thm)],[f452])).
% 2.69/1.61 thf(f452,plain,(
% 2.69/1.61 ((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)) = (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 2.69/1.61 inference(fool_elimination,[status(thm)],[f6])).
% 2.69/1.61 thf(f6,axiom,(
% 2.69/1.61 ((coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ xs)) = (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 2.69/1.61 file('/export/starexec/sandbox/tmp/tmp.hgRkZ6IOB8/DTF2THF_15555.p',fact_5__092_060open_062lhd_A_Iltl_A_IlSup_AY_J_J_A_061_Alhd_A_Iltl_Axs_J_092_060close_062)).
% 2.69/1.61 thf(f1176,plain,(
% 2.69/1.61 ((~ (less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))) = $true)),
% 2.69/1.61 inference(cnf_transformation,[status(thm)],[f634])).
% 2.69/1.61 thf(f634,plain,(
% 2.69/1.61 ((~ (less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))) = $true)),
% 2.69/1.61 inference(fool_elimination,[status(thm)],[f633])).
% 2.69/1.61 thf(f633,plain,(
% 2.69/1.61 ~(less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 2.69/1.61 inference(rectify,[status(thm)],[f265])).
% 2.69/1.61 thf(f265,negated_conjecture,(
% 2.69/1.61 ~(less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 2.69/1.61 inference(negated_conjecture,[status(cth)],[f264])).
% 2.69/1.61 thf(f264,conjecture,(
% 2.69/1.61 (less_eq @ (coindu1046438764le_lhd @ a @ (coindu526335360e_lSup @ a @ ya)) @ (coindu1046438764le_lhd @ a @ (coindu1047225960le_ltl @ a @ (coindu526335360e_lSup @ a @ ya))))),
% 2.69/1.61 file('/export/starexec/sandbox/tmp/tmp.hgRkZ6IOB8/DTF2THF_15555.p',conj_0)).
% 2.69/1.61 % SZS output end Proof for DTF2THF_15555
% 2.69/1.61 % (15676)------------------------------
% 2.69/1.61 % (15676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.61 % (15676)Termination reason: Refutation
% 2.69/1.61
% 2.69/1.61 % (15676)Memory used [KB]: 7419
% 2.69/1.61 % (15676)Time elapsed: 0.105 s
% 2.69/1.61 % (15676)Instructions burned: 224 (million)
% 2.69/1.61 % (15676)------------------------------
% 2.69/1.61 % (15676)------------------------------
% 2.69/1.61 % (15664)Success in time 0.15 s
%------------------------------------------------------------------------------