%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT132^1 : 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 : n027.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 08:44:53 AM UTC 2026
% Result : Theorem 2.84s 1.83s
% Output : Refutation 2.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT132^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n027.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 06:08:37 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.38 thf(spec,logic,$$dhol).
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 % File : DAT132^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.38 % Domain : Data Structures
% 0.16/0.38 % Problem : Coinductive list 3961
% 0.16/0.38 % Version : [Bla16] axioms : Especial.
% 0.16/0.38 % English :
% 0.16/0.38
% 0.16/0.38 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.16/0.38 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.38 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.38 % Source : [Bla16]
% 0.16/0.38 % Names : coinductive_list__3961.p [Bla16]
% 0.16/0.38
% 0.16/0.38 % Status : Theorem
% 0.16/0.38 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.3.0, 0.00 v7.1.0
% 0.16/0.38 % Syntax : Number of formulae : 317 ( 165 unt; 58 typ; 0 def)
% 0.16/0.38 % Number of atoms : 615 ( 452 equ; 0 cnn)
% 0.16/0.38 % Maximal formula atoms : 11 ( 2 avg)
% 0.16/0.38 % Number of connectives : 3591 ( 112 ~; 34 |; 71 &;3158 @)
% 0.16/0.38 % ( 0 <=>; 216 =>; 0 <=; 0 <~>)
% 0.16/0.38 % Maximal formula depth : 22 ( 6 avg)
% 0.16/0.38 % Number of types : 2 ( 1 usr)
% 0.16/0.38 % Number of type conns : 198 ( 198 >; 0 *; 0 +; 0 <<)
% 0.16/0.38 % Number of symbols : 60 ( 57 usr; 11 con; 0-5 aty)
% 0.16/0.38 % Number of variables : 1005 ( 17 ^; 881 !; 58 ?;1005 :)
% 0.16/0.38 % ( 49 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.38 % SPC : TH1_THM_EQU_NAR
% 0.16/0.38
% 0.16/0.38 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.38 % 2016-07-13 15:04:06.870
% 0.16/0.38 %------------------------------------------------------------------------------
% 0.16/0.38 %----Could-be-implicit typings (5)
% 0.16/0.38 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.16/0.38 coindu1593790203_llist: $tType > $tType ).
% 0.16/0.38
% 0.16/0.38 thf(ty_t_List_Olist,type,
% 0.16/0.38 list: $tType > $tType ).
% 0.16/0.38
% 0.16/0.38 thf(ty_t_Set_Oset,type,
% 0.16/0.38 set: $tType > $tType ).
% 0.16/0.38
% 0.16/0.38 thf(ty_t_itself,type,
% 0.16/0.38 itself: $tType > $tType ).
% 0.16/0.38
% 0.16/0.38 thf(ty_tf_a,type,
% 0.16/0.38 a: $tType ).
% 0.16/0.38
% 0.16/0.38 %----Explicit typings (53)
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix,type,
% 0.16/0.38 coindu1571841457prefix:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.16/0.38 coindu268472904append:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.16/0.38 coindu1213758845finite:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of,type,
% 0.16/0.38 coindu1736001939ist_of:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of__aux,type,
% 0.16/0.38 coindu1542816657of_aux:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast,type,
% 0.16/0.38 coindu2000965700_llast:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 0.16/0.38 coindu300403952lexord:
% 0.16/0.38 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.16/0.38 coindu1121789889_LCons:
% 0.16/0.38 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.16/0.38 coindu1598213697e_LNil:
% 0.16/0.38 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.16/0.38 coindu1046438764le_lhd:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.16/0.38 coindu335574135_lnull:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 0.16/0.38 coindu1112613586e_lset:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist__of,type,
% 0.16/0.38 coindu1079202755ist_of:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.16/0.38 coindu567634248member:
% 0.16/0.38 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.16/0.38 coindu574146665prefix:
% 0.16/0.38 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_HOL_Oundefined,type,
% 0.16/0.38 undefined:
% 0.16/0.38 !>[A: $tType] : A ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_If,type,
% 0.16/0.38 if:
% 0.16/0.38 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Oappend,type,
% 0.16/0.38 append:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Obind,type,
% 0.16/0.38 bind:
% 0.16/0.38 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Obutlast,type,
% 0.16/0.38 butlast:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Oinsert,type,
% 0.16/0.38 insert:
% 0.16/0.38 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olast,type,
% 0.16/0.38 last:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist_OCons,type,
% 0.16/0.38 cons:
% 0.16/0.38 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist_ONil,type,
% 0.16/0.38 nil:
% 0.16/0.38 !>[A: $tType] : ( list @ A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist_Ocase__list,type,
% 0.16/0.38 case_list:
% 0.16/0.38 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist_Ohd,type,
% 0.16/0.38 hd:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist_Omap,type,
% 0.16/0.38 map:
% 0.16/0.38 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist_Otl,type,
% 0.16/0.38 tl:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Olist__ex1,type,
% 0.16/0.38 list_ex1:
% 0.16/0.38 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Omap__tailrec,type,
% 0.16/0.38 map_tailrec:
% 0.16/0.38 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Omap__tailrec__rev,type,
% 0.16/0.38 map_tailrec_rev:
% 0.16/0.38 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Omaps,type,
% 0.16/0.38 maps:
% 0.16/0.38 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Oproduct__lists,type,
% 0.16/0.38 product_lists:
% 0.16/0.38 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Oremdups__adj,type,
% 0.16/0.38 remdups_adj:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Orev,type,
% 0.16/0.38 rev:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Orotate1,type,
% 0.16/0.38 rotate1:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_List_Osublists,type,
% 0.16/0.38 sublists:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Pure_Otype,type,
% 0.16/0.38 type:
% 0.16/0.38 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Set_OCollect,type,
% 0.16/0.38 collect:
% 0.16/0.38 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Sublist_Oprefixes,type,
% 0.16/0.38 prefixes:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Sublist_Oprefixes__rel,type,
% 0.16/0.38 prefixes_rel:
% 0.16/0.38 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_Wellfounded_Oaccp,type,
% 0.16/0.38 accp:
% 0.16/0.38 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_c_member,type,
% 0.16/0.38 member:
% 0.16/0.38 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_XS_H____,type,
% 0.16/0.38 xs: list @ a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_r,type,
% 0.16/0.38 r: a > a > $o ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_thesis____,type,
% 0.16/0.38 thesis: $o ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_xs,type,
% 0.16/0.38 xs2: list @ a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_xs_H____,type,
% 0.16/0.38 xs3: coindu1593790203_llist @ a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_y____,type,
% 0.16/0.38 y: a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_ys,type,
% 0.16/0.38 ys: list @ a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_ys_H____,type,
% 0.16/0.38 ys2: coindu1593790203_llist @ a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_zs_H____,type,
% 0.16/0.38 zs: list @ a ).
% 0.16/0.38
% 0.16/0.38 thf(sy_v_zs____,type,
% 0.16/0.38 zs2: coindu1593790203_llist @ a ).
% 0.16/0.38
% 0.16/0.38 %----Relevant facts (254)
% 0.16/0.38 thf(fact_0_llist__of__inject,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.38 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 0.16/0.38 = ( coindu1079202755ist_of @ A @ Ys ) )
% 0.16/0.38 = ( Xs = Ys ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist_of_inject
% 0.16/0.38 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062zs_H_O_Azs_A_061_Allist__of_Azs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.16/0.38 ~ ! [Zs: list @ a] :
% 0.16/0.38 ( zs2
% 0.16/0.38 != ( coindu1079202755ist_of @ a @ Zs ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>\<And>thesis. (\<And>zs'. zs = llist_of zs' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.16/0.38 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.16/0.38 ~ ! [XS: list @ a] :
% 0.16/0.38 ( xs3
% 0.16/0.38 != ( coindu1079202755ist_of @ a @ XS ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>\<And>thesis. (\<And>XS'. xs' = llist_of XS' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.16/0.38 thf(fact_3__092_060open_062lfinite_Ays_H_092_060close_062,axiom,
% 0.16/0.38 coindu1213758845finite @ a @ ys2 ).
% 0.16/0.38
% 0.16/0.38 % \<open>lfinite ys'\<close>
% 0.16/0.38 thf(fact_4_list__of__llist__of,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A] :
% 0.16/0.38 ( ( coindu1736001939ist_of @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 0.16/0.38 = Xs ) ).
% 0.16/0.38
% 0.16/0.38 % list_of_llist_of
% 0.16/0.38 thf(fact_5__092_060open_062zs_A_061_Allist__of_Azs_H_092_060close_062,axiom,
% 0.16/0.38 ( zs2
% 0.16/0.38 = ( coindu1079202755ist_of @ a @ zs ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>zs = llist_of zs'\<close>
% 0.16/0.38 thf(fact_6__092_060open_062llist__of_Ays_A_061_Alappend_Azs_A_ILCons_Ay_Ays_H_J_092_060close_062,axiom,
% 0.16/0.38 ( ( coindu1079202755ist_of @ a @ ys )
% 0.16/0.38 = ( coindu268472904append @ a @ zs2 @ ( coindu1121789889_LCons @ a @ y @ ys2 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>llist_of ys = lappend zs (LCons y ys')\<close>
% 0.16/0.38 thf(fact_7__092_060open_062xs_H_A_061_Allist__of_AXS_H_092_060close_062,axiom,
% 0.16/0.38 ( xs3
% 0.16/0.38 = ( coindu1079202755ist_of @ a @ xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>xs' = llist_of XS'\<close>
% 0.16/0.38 thf(fact_8__092_060open_062lfinite_A_Illist__of_Ays_J_092_060close_062,axiom,
% 0.16/0.38 coindu1213758845finite @ a @ ( coindu1079202755ist_of @ a @ ys ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>lfinite (llist_of ys)\<close>
% 0.16/0.38 thf(fact_9__092_060open_062lfinite_A_Illist__of_Axs_J_092_060close_062,axiom,
% 0.16/0.38 coindu1213758845finite @ a @ ( coindu1079202755ist_of @ a @ xs2 ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>lfinite (llist_of xs)\<close>
% 0.16/0.38 thf(fact_10__092_060open_062llexord_Ar_A_Illist__of_Axs_J_A_Illist__of_Ays_J_092_060close_062,axiom,
% 0.16/0.38 coindu300403952lexord @ a @ r @ ( coindu1079202755ist_of @ a @ xs2 ) @ ( coindu1079202755ist_of @ a @ ys ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>llexord r (llist_of xs) (llist_of ys)\<close>
% 0.16/0.38 thf(fact_11_lfinite__llist__of,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A] : ( coindu1213758845finite @ A @ ( coindu1079202755ist_of @ A @ Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_llist_of
% 0.16/0.38 thf(fact_12_llast__llist__of,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A] :
% 0.16/0.38 ( ( coindu2000965700_llast @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 0.16/0.38 = ( last @ A @ Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % llast_llist_of
% 0.16/0.38 thf(fact_13__092_060open_062lfinite_Azs_092_060close_062,axiom,
% 0.16/0.38 coindu1213758845finite @ a @ zs2 ).
% 0.16/0.38
% 0.16/0.38 % \<open>lfinite zs\<close>
% 0.16/0.38 thf(fact_14__092_060open_062lfinite_Axs_H_092_060close_062,axiom,
% 0.16/0.38 coindu1213758845finite @ a @ xs3 ).
% 0.16/0.38
% 0.16/0.38 % \<open>lfinite xs'\<close>
% 0.16/0.38 thf(fact_15_llist_Oinject,axiom,
% 0.16/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.16/0.38 = ( ( X21 = Y21 )
% 0.16/0.38 & ( X22 = Y22 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.inject
% 0.16/0.38 thf(fact_16_llexord__refl,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ Xs ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_refl
% 0.16/0.38 thf(fact_17__092_060open_062llist__of_Axs_A_061_Alappend_Azs_Axs_H_092_060close_062,axiom,
% 0.16/0.38 ( ( coindu1079202755ist_of @ a @ xs2 )
% 0.16/0.38 = ( coindu268472904append @ a @ zs2 @ xs3 ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>llist_of xs = lappend zs xs'\<close>
% 0.16/0.38 thf(fact_18_lappend__code_I2_J,axiom,
% 0.16/0.38 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_code(2)
% 0.16/0.38 thf(fact_19_lfinite__code_I2_J,axiom,
% 0.16/0.38 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.16/0.38 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.16/0.38 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_code(2)
% 0.16/0.38 thf(fact_20_lfinite__LCons,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.38 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_LCons
% 0.16/0.38 thf(fact_21_lfinite__lappend,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.38 = ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_lappend
% 0.16/0.38 thf(fact_22_llexord__LCons__LCons,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.38 = ( ( ( X = Y )
% 0.16/0.38 & ( coindu300403952lexord @ A @ R @ Xs @ Ys ) )
% 0.16/0.38 | ( R @ X @ Y ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_LCons_LCons
% 0.16/0.38 thf(fact_23_llast__LCons2,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.16/0.38 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llast_LCons2
% 0.16/0.38 thf(fact_24_llist__of__list__of,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ( coindu1079202755ist_of @ A @ ( coindu1736001939ist_of @ A @ Xs ) )
% 0.16/0.38 = Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist_of_list_of
% 0.16/0.38 thf(fact_25_llast__lappend__LCons,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) )
% 0.16/0.38 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llast_lappend_LCons
% 0.16/0.38 thf(fact_26_llexord__code_I3_J,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.38 = ( ( R @ X @ Y )
% 0.16/0.38 | ( ( X = Y )
% 0.16/0.38 & ( coindu300403952lexord @ A @ R @ Xs @ Ys ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_code(3)
% 0.16/0.38 thf(fact_27_lappend__inf,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.38 = Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_inf
% 0.16/0.38 thf(fact_28_lappend__assoc,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs2 )
% 0.16/0.38 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs2 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_assoc
% 0.16/0.38 thf(fact_29_llexord__trans,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.38 => ( ( coindu300403952lexord @ A @ R @ Ys @ Zs2 )
% 0.16/0.38 => ( ! [A2: A,B2: A,C: A] :
% 0.16/0.38 ( ( R @ A2 @ B2 )
% 0.16/0.38 => ( ( R @ B2 @ C )
% 0.16/0.38 => ( R @ A2 @ C ) ) )
% 0.16/0.38 => ( coindu300403952lexord @ A @ R @ Xs @ Zs2 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_trans
% 0.16/0.38 thf(fact_30_llexord__linear,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ! [X2: A,Y2: A] :
% 0.16/0.38 ( ( R @ X2 @ Y2 )
% 0.16/0.38 | ( X2 = Y2 )
% 0.16/0.38 | ( R @ Y2 @ X2 ) )
% 0.16/0.38 => ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.38 | ( coindu300403952lexord @ A @ R @ Ys @ Xs ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_linear
% 0.16/0.38 thf(fact_31_llexord__antisym,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.38 => ( ( coindu300403952lexord @ A @ R @ Ys @ Xs )
% 0.16/0.38 => ( ! [A2: A,B2: A] :
% 0.16/0.38 ( ( R @ A2 @ B2 )
% 0.16/0.38 => ~ ( R @ B2 @ A2 ) )
% 0.16/0.38 => ( Xs = Ys ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_antisym
% 0.16/0.38 thf(fact_32_llexord__LCons__left,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.16/0.38 = ( ? [Y3: A,Ys2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Ys
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) )
% 0.16/0.38 & ( ( ( X = Y3 )
% 0.16/0.38 & ( coindu300403952lexord @ A @ R @ Xs @ Ys2 ) )
% 0.16/0.38 | ( R @ X @ Y3 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_LCons_left
% 0.16/0.38 thf(fact_33_llexord__append__right,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_append_right
% 0.16/0.38 thf(fact_34_llexord__lappend__leftI,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ Ys @ Zs2 )
% 0.16/0.38 => ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs2 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_lappend_leftI
% 0.16/0.38 thf(fact_35_lfinite__LConsI,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_LConsI
% 0.16/0.38 thf(fact_36_llexord__LCons__eq,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.38 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_LCons_eq
% 0.16/0.38 thf(fact_37_llexord__LCons__less,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( R @ X @ Y )
% 0.16/0.38 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_LCons_less
% 0.16/0.38 thf(fact_38__092_060open_062xs_A_061_Azs_H_A_064_AXS_H_092_060close_062,axiom,
% 0.16/0.38 ( xs2
% 0.16/0.38 = ( append @ a @ zs @ xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>xs = zs' @ XS'\<close>
% 0.16/0.38 thf(fact_39__092_060open_062xs_H_A_061_ALNil_A_092_060or_062_Ar_A_Ilhd_Axs_H_J_Ay_092_060close_062,axiom,
% 0.16/0.38 ( ( xs3
% 0.16/0.38 = ( coindu1598213697e_LNil @ a ) )
% 0.16/0.38 | ( r @ ( coindu1046438764le_lhd @ a @ xs3 ) @ y ) ) ).
% 0.16/0.38
% 0.16/0.38 % \<open>xs' = LNil \<or> r (lhd xs') y\<close>
% 0.16/0.38 thf(fact_40_list__of__LCons,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ( coindu1736001939ist_of @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.38 = ( cons @ A @ X @ ( coindu1736001939ist_of @ A @ Xs ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % list_of_LCons
% 0.16/0.38 thf(fact_41_lmember__code_I2_J,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.38 = ( ( X = Y )
% 0.16/0.38 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lmember_code(2)
% 0.16/0.38 thf(fact_42_list__of__lappend,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ( coindu1213758845finite @ A @ Ys )
% 0.16/0.38 => ( ( coindu1736001939ist_of @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.38 = ( append @ A @ ( coindu1736001939ist_of @ A @ Xs ) @ ( coindu1736001939ist_of @ A @ Ys ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % list_of_lappend
% 0.16/0.38 thf(fact_43_lfinite__rev__induct,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.16/0.38 => ( ( P @ Xs2 )
% 0.16/0.38 => ( P @ ( coindu268472904append @ A @ Xs2 @ ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 0.16/0.38 => ( P @ Xs ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_rev_induct
% 0.16/0.38 thf(fact_44_llexord__lappend__left,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,R: A > A > $o,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ! [X2: A] :
% 0.16/0.38 ( ( member @ A @ X2 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ~ ( R @ X2 @ X2 ) )
% 0.16/0.38 => ( ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs2 ) )
% 0.16/0.38 = ( coindu300403952lexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_lappend_left
% 0.16/0.38 thf(fact_45_mem__Collect__eq,axiom,
% 0.16/0.38 ! [A: $tType,A3: A,P: A > $o] :
% 0.16/0.38 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.16/0.38 = ( P @ A3 ) ) ).
% 0.16/0.38
% 0.16/0.38 % mem_Collect_eq
% 0.16/0.38 thf(fact_46_Collect__mem__eq,axiom,
% 0.16/0.38 ! [A: $tType,A4: set @ A] :
% 0.16/0.38 ( ( collect @ A
% 0.16/0.38 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.16/0.38 = A4 ) ).
% 0.16/0.38
% 0.16/0.38 % Collect_mem_eq
% 0.16/0.38 thf(fact_47_Collect__cong,axiom,
% 0.16/0.38 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.38 ( ! [X2: A] :
% 0.16/0.38 ( ( P @ X2 )
% 0.16/0.38 = ( Q @ X2 ) )
% 0.16/0.38 => ( ( collect @ A @ P )
% 0.16/0.38 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % Collect_cong
% 0.16/0.38 thf(fact_48_ext,axiom,
% 0.16/0.38 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.16/0.38 ( ! [X2: A] :
% 0.16/0.38 ( ( F @ X2 )
% 0.16/0.38 = ( G @ X2 ) )
% 0.16/0.38 => ( F = G ) ) ).
% 0.16/0.38
% 0.16/0.38 % ext
% 0.16/0.38 thf(fact_49_llexord__lappend__leftD,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs2 ) )
% 0.16/0.38 => ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 => ( ! [X2: A] :
% 0.16/0.38 ( ( member @ A @ X2 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ~ ( R @ X2 @ X2 ) )
% 0.16/0.38 => ( coindu300403952lexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_lappend_leftD
% 0.16/0.38 thf(fact_50_split__llist,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ? [Ys3: coindu1593790203_llist @ A,Zs3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Xs
% 0.16/0.38 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs3 ) ) )
% 0.16/0.38 & ( coindu1213758845finite @ A @ Ys3 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % split_llist
% 0.16/0.38 thf(fact_51_split__llist__first,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ? [Ys3: coindu1593790203_llist @ A,Zs3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Xs
% 0.16/0.38 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs3 ) ) )
% 0.16/0.38 & ( coindu1213758845finite @ A @ Ys3 )
% 0.16/0.38 & ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys3 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % split_llist_first
% 0.16/0.38 thf(fact_52_llast__singleton,axiom,
% 0.16/0.38 ! [A: $tType,X: A] :
% 0.16/0.38 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.38 = X ) ).
% 0.16/0.38
% 0.16/0.38 % llast_singleton
% 0.16/0.38 thf(fact_53_lappend__LNil2,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 = Xs ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_LNil2
% 0.16/0.38 thf(fact_54_lappend__code_I1_J,axiom,
% 0.16/0.38 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.16/0.38 = Ys ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_code(1)
% 0.16/0.38 thf(fact_55_lfinite__code_I1_J,axiom,
% 0.16/0.38 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_code(1)
% 0.16/0.38 thf(fact_56_llexord__code_I1_J,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_code(1)
% 0.16/0.38 thf(fact_57_lset__lmember,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 = ( coindu567634248member @ A @ X @ Xs ) ) ).
% 0.16/0.38
% 0.16/0.38 % lset_lmember
% 0.16/0.38 thf(fact_58_lmember__code_I1_J,axiom,
% 0.16/0.38 ! [A: $tType,X: A] :
% 0.16/0.38 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 % lmember_code(1)
% 0.16/0.38 thf(fact_59_lhd__LCons,axiom,
% 0.16/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.16/0.38 = X21 ) ).
% 0.16/0.38
% 0.16/0.38 % lhd_LCons
% 0.16/0.38 thf(fact_60_llist_Oset__induct,axiom,
% 0.16/0.38 ! [A: $tType,X: A,A3: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A3 ) )
% 0.16/0.38 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.16/0.38 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A,Xa2: A] :
% 0.16/0.38 ( ( member @ A @ Xa2 @ ( coindu1112613586e_lset @ A @ Z2 ) )
% 0.16/0.38 => ( ( P @ Xa2 @ Z2 )
% 0.16/0.38 => ( P @ Xa2 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) ) ) )
% 0.16/0.38 => ( P @ X @ A3 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.set_induct
% 0.16/0.38 thf(fact_61_llist_Oset__cases,axiom,
% 0.16/0.38 ! [A: $tType,E: A,A3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A3 ) )
% 0.16/0.38 => ( ! [Z2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( A3
% 0.16/0.38 != ( coindu1121789889_LCons @ A @ E @ Z2 ) )
% 0.16/0.38 => ~ ! [Z1: A,Z2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( A3
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 0.16/0.38 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z2 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.set_cases
% 0.16/0.38 thf(fact_62_lset__induct_H,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.16/0.38 => ( ! [X4: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.16/0.38 => ( ( P @ Xs2 )
% 0.16/0.38 => ( P @ ( coindu1121789889_LCons @ A @ X4 @ Xs2 ) ) ) )
% 0.16/0.38 => ( P @ Xs ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lset_induct'
% 0.16/0.38 thf(fact_63_lset__induct,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 0.16/0.38 => ( ! [X4: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 0.16/0.38 => ( ( X != X4 )
% 0.16/0.38 => ( ( P @ Xs2 )
% 0.16/0.38 => ( P @ ( coindu1121789889_LCons @ A @ X4 @ Xs2 ) ) ) ) )
% 0.16/0.38 => ( P @ Xs ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lset_induct
% 0.16/0.38 thf(fact_64_lset__cases,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ( ! [Xs3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( Xs
% 0.16/0.38 != ( coindu1121789889_LCons @ A @ X @ Xs3 ) )
% 0.16/0.38 => ~ ! [X4: A,Xs3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Xs
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X4 @ Xs3 ) )
% 0.16/0.38 => ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs3 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lset_cases
% 0.16/0.38 thf(fact_65_llist_Oset__intros_I1_J,axiom,
% 0.16/0.38 ! [A: $tType,A1: A,A22: coindu1593790203_llist @ A] : ( member @ A @ A1 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.set_intros(1)
% 0.16/0.38 thf(fact_66_llist_Oset__intros_I2_J,axiom,
% 0.16/0.38 ! [A: $tType,X: A,A22: coindu1593790203_llist @ A,A1: A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A22 ) )
% 0.16/0.38 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.set_intros(2)
% 0.16/0.38 thf(fact_67_lset__intros_I1_J,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lset_intros(1)
% 0.16/0.38 thf(fact_68_lset__intros_I2_J,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,X5: A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lset_intros(2)
% 0.16/0.38 thf(fact_69_neq__LNil__conv,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Xs
% 0.16/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 = ( ? [X3: A,Xs4: coindu1593790203_llist @ A] :
% 0.16/0.38 ( Xs
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % neq_LNil_conv
% 0.16/0.38 thf(fact_70_llist_Oexhaust,axiom,
% 0.16/0.38 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Y
% 0.16/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.16/0.38 ( Y
% 0.16/0.38 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.exhaust
% 0.16/0.38 thf(fact_71_llist_Odistinct_I1_J,axiom,
% 0.16/0.38 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1598213697e_LNil @ A )
% 0.16/0.38 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist.distinct(1)
% 0.16/0.38 thf(fact_72_lappend__eq__LNil__iff,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 = ( ( Xs
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 & ( Ys
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_eq_LNil_iff
% 0.16/0.38 thf(fact_73_LNil__eq__lappend__iff,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( ( coindu1598213697e_LNil @ A )
% 0.16/0.38 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.38 = ( ( Xs
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 & ( Ys
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % LNil_eq_lappend_iff
% 0.16/0.38 thf(fact_74_lappend__LNil__LNil,axiom,
% 0.16/0.38 ! [A: $tType] :
% 0.16/0.38 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_LNil_LNil
% 0.16/0.38 thf(fact_75_lfinite__LNil,axiom,
% 0.16/0.38 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite_LNil
% 0.16/0.38 thf(fact_76_llexord__LNil,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_LNil
% 0.16/0.38 thf(fact_77_llexord__conv,axiom,
% 0.16/0.38 ! [A: $tType] :
% 0.16/0.38 ( ( coindu300403952lexord @ A )
% 0.16/0.38 = ( ^ [R2: A > A > $o,Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( Xs5 = Ys4 )
% 0.16/0.38 | ? [Zs4: coindu1593790203_llist @ A,Xs4: coindu1593790203_llist @ A,Y3: A,Ys2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Zs4 )
% 0.16/0.38 & ( Xs5
% 0.16/0.38 = ( coindu268472904append @ A @ Zs4 @ Xs4 ) )
% 0.16/0.38 & ( Ys4
% 0.16/0.38 = ( coindu268472904append @ A @ Zs4 @ ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) ) )
% 0.16/0.38 & ( ( Xs4
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 | ( R2 @ ( coindu1046438764le_lhd @ A @ Xs4 ) @ Y3 ) ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_conv
% 0.16/0.38 thf(fact_78_in__lset__lappend__iff,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.16/0.38 = ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 0.16/0.38 | ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.38 & ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % in_lset_lappend_iff
% 0.16/0.38 thf(fact_79_lappend__snocL1__conv__LCons2,axiom,
% 0.16/0.38 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.16/0.38 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_snocL1_conv_LCons2
% 0.16/0.38 thf(fact_80_lfinite_Oinducts,axiom,
% 0.16/0.38 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ X )
% 0.16/0.38 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.16/0.38 => ( ( P @ Xs2 )
% 0.16/0.38 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.16/0.38 => ( P @ X ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite.inducts
% 0.16/0.38 thf(fact_81_lfinite_Osimps,axiom,
% 0.16/0.38 ! [A: $tType] :
% 0.16/0.38 ( ( coindu1213758845finite @ A )
% 0.16/0.38 = ( ^ [A5: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( A5
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 | ? [Xs5: coindu1593790203_llist @ A,X3: A] :
% 0.16/0.38 ( ( A5
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 0.16/0.38 & ( coindu1213758845finite @ A @ Xs5 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite.simps
% 0.16/0.38 thf(fact_82_lfinite_Ocases,axiom,
% 0.16/0.38 ! [A: $tType,A3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu1213758845finite @ A @ A3 )
% 0.16/0.38 => ( ( A3
% 0.16/0.38 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ? [X2: A] :
% 0.16/0.38 ( A3
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.38 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lfinite.cases
% 0.16/0.38 thf(fact_83_lappend__llist__of__llist__of,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.38 ( ( coindu268472904append @ A @ ( coindu1079202755ist_of @ A @ Xs ) @ ( coindu1079202755ist_of @ A @ Ys ) )
% 0.16/0.38 = ( coindu1079202755ist_of @ A @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % lappend_llist_of_llist_of
% 0.16/0.38 thf(fact_84_llist__of_Osimps_I2_J,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.38 ( ( coindu1079202755ist_of @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X @ ( coindu1079202755ist_of @ A @ Xs ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist_of.simps(2)
% 0.16/0.38 thf(fact_85_llist__of__eq__LCons__conv,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.38 = ( ? [Xs4: list @ A] :
% 0.16/0.38 ( ( Xs
% 0.16/0.38 = ( cons @ A @ Y @ Xs4 ) )
% 0.16/0.38 & ( Ys
% 0.16/0.38 = ( coindu1079202755ist_of @ A @ Xs4 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llist_of_eq_LCons_conv
% 0.16/0.38 thf(fact_86_llexord_Ocoinduct,axiom,
% 0.16/0.38 ! [A: $tType,X6: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R: A > A > $o] :
% 0.16/0.38 ( ( X6 @ X @ Xa )
% 0.16/0.38 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( X6 @ X2 @ Xa2 )
% 0.16/0.38 => ( ? [Xs6: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 0.16/0.38 ( ( X2
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Xb @ Xs6 ) )
% 0.16/0.38 & ( Xa2
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 0.16/0.38 & ( ( X6 @ Xs6 @ Ys5 )
% 0.16/0.38 | ( coindu300403952lexord @ A @ R @ Xs6 @ Ys5 ) ) )
% 0.16/0.38 | ? [Xb: A,Y4: A,Xs6: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( X2
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Xb @ Xs6 ) )
% 0.16/0.38 & ( Xa2
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Y4 @ Ys5 ) )
% 0.16/0.38 & ( R @ Xb @ Y4 ) )
% 0.16/0.38 | ? [Ys5: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( X2
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 & ( Xa2 = Ys5 ) ) ) )
% 0.16/0.38 => ( coindu300403952lexord @ A @ R @ X @ Xa ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord.coinduct
% 0.16/0.38 thf(fact_87_llexord_Osimps,axiom,
% 0.16/0.38 ! [A: $tType] :
% 0.16/0.38 ( ( coindu300403952lexord @ A )
% 0.16/0.38 = ( ^ [R2: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ? [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 0.16/0.38 ( ( A12
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 0.16/0.38 & ( A23
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 0.16/0.38 & ( coindu300403952lexord @ A @ R2 @ Xs5 @ Ys4 ) )
% 0.16/0.38 | ? [X3: A,Y3: A,Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( A12
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 0.16/0.38 & ( A23
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Y3 @ Ys4 ) )
% 0.16/0.38 & ( R2 @ X3 @ Y3 ) )
% 0.16/0.38 | ? [Ys4: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( A12
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 & ( A23 = Ys4 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord.simps
% 0.16/0.38 thf(fact_88_llexord_Ocases,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.16/0.38 ( ( coindu300403952lexord @ A @ R @ A1 @ A22 )
% 0.16/0.38 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 0.16/0.38 ( ( A1
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.38 => ( ( A22
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 0.16/0.38 => ~ ( coindu300403952lexord @ A @ R @ Xs2 @ Ys3 ) ) )
% 0.16/0.38 => ( ! [X2: A] :
% 0.16/0.38 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.38 ( A1
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.38 => ! [Y2: A] :
% 0.16/0.38 ( ? [Ys3: coindu1593790203_llist @ A] :
% 0.16/0.38 ( A22
% 0.16/0.38 = ( coindu1121789889_LCons @ A @ Y2 @ Ys3 ) )
% 0.16/0.38 => ~ ( R @ X2 @ Y2 ) ) )
% 0.16/0.38 => ~ ( ( A1
% 0.16/0.38 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.38 => ! [Ys3: coindu1593790203_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord.cases
% 0.16/0.38 thf(fact_89_llexord__code_I2_J,axiom,
% 0.16/0.38 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.38 ~ ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.38
% 0.16/0.38 % llexord_code(2)
% 0.16/0.38 thf(fact_90_same__append__eq,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.16/0.38 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.38 = ( append @ A @ Xs @ Zs2 ) )
% 0.16/0.38 = ( Ys = Zs2 ) ) ).
% 0.16/0.38
% 0.16/0.38 % same_append_eq
% 0.16/0.38 thf(fact_91_append__same__eq,axiom,
% 0.16/0.38 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.16/0.38 ( ( ( append @ A @ Ys @ Xs )
% 0.16/0.38 = ( append @ A @ Zs2 @ Xs ) )
% 0.16/0.38 = ( Ys = Zs2 ) ) ).
% 0.16/0.38
% 0.16/0.38 % append_same_eq
% 0.16/0.38 thf(fact_92_append__assoc,axiom,
% 0.16/0.38 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.16/0.38 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 0.16/0.38 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % append_assoc
% 0.16/0.38 thf(fact_93_list_Oinject,axiom,
% 0.16/0.38 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.16/0.38 ( ( ( cons @ A @ X21 @ X22 )
% 0.16/0.38 = ( cons @ A @ Y21 @ Y22 ) )
% 0.16/0.38 = ( ( X21 = Y21 )
% 0.16/0.38 & ( X22 = Y22 ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % list.inject
% 0.16/0.38 thf(fact_94_append__Cons,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.38 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.16/0.38 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.38
% 0.16/0.38 % append_Cons
% 0.16/0.38 thf(fact_95_Cons__eq__appendI,axiom,
% 0.16/0.38 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.16/0.38 ( ( ( cons @ A @ X @ Xs1 )
% 0.16/0.39 = Ys )
% 0.16/0.39 => ( ( Xs
% 0.16/0.39 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.16/0.39 => ( ( cons @ A @ X @ Xs )
% 0.16/0.39 = ( append @ A @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Cons_eq_appendI
% 0.16/0.39 thf(fact_96_lappend__llist__of__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1079202755ist_of @ A @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( coindu268472904append @ A @ ( coindu1079202755ist_of @ A @ ( append @ A @ Xs @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_llist_of_LCons
% 0.16/0.39 thf(fact_97_list__of__aux__code_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1542816657of_aux @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( coindu1542816657of_aux @ A @ ( cons @ A @ Y @ Xs ) @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_of_aux_code(2)
% 0.16/0.39 thf(fact_98_append__Nil2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % append_Nil2
% 0.16/0.39 thf(fact_99_append__self__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.39 = Xs )
% 0.16/0.39 = ( Ys
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_self_conv
% 0.16/0.39 thf(fact_100_self__append__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( Ys
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % self_append_conv
% 0.16/0.39 thf(fact_101_append__self__conv2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.39 = Ys )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_self_conv2
% 0.16/0.39 thf(fact_102_self__append__conv2,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % self_append_conv2
% 0.16/0.39 thf(fact_103_Nil__is__append__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( nil @ A )
% 0.16/0.39 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( nil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Nil_is_append_conv
% 0.16/0.39 thf(fact_104_append__is__Nil__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( nil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_is_Nil_conv
% 0.16/0.39 thf(fact_105_append1__eq__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.16/0.39 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.16/0.39 = ( ( Xs = Ys )
% 0.16/0.39 & ( X = Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append1_eq_conv
% 0.16/0.39 thf(fact_106_last__appendR,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( last @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_appendR
% 0.16/0.39 thf(fact_107_last__appendL,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( last @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_appendL
% 0.16/0.39 thf(fact_108_list__of__LNil,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1736001939ist_of @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_of_LNil
% 0.16/0.39 thf(fact_109_last__snoc,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.16/0.39 = X ) ).
% 0.16/0.39
% 0.16/0.39 % last_snoc
% 0.16/0.39 thf(fact_110_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.16/0.39 ( ! [F2: A > B,X1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 0.16/0.39 => ( ! [F2: A > B,A2: A,As: list @ A,Bs: list @ B] :
% 0.16/0.39 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A2 ) @ Bs ) )
% 0.16/0.39 => ( P @ F2 @ ( cons @ A @ A2 @ As ) @ Bs ) )
% 0.16/0.39 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_tailrec_rev.induct
% 0.16/0.39 thf(fact_111_list__nonempty__induct,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( Xs2
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 0.16/0.39 => ( P @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_nonempty_induct
% 0.16/0.39 thf(fact_112_remdups__adj_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.16/0.39 ( ( P @ ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.16/0.39 => ( ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( ( X2 = Y2 )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.16/0.39 => ( ( ( X2 != Y2 )
% 0.16/0.39 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.16/0.39 => ( P @ A0 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % remdups_adj.induct
% 0.16/0.39 thf(fact_113_remdups__adj_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,X: list @ A] :
% 0.16/0.39 ( ( X
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A] :
% 0.16/0.39 ( X
% 0.16/0.39 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.16/0.39 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.16/0.39 ( X
% 0.16/0.39 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % remdups_adj.cases
% 0.16/0.39 thf(fact_114_append__Nil,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A] :
% 0.16/0.39 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.16/0.39 = Ys ) ).
% 0.16/0.39
% 0.16/0.39 % append_Nil
% 0.16/0.39 thf(fact_115_transpose_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,X: list @ ( list @ A )] :
% 0.16/0.39 ( ( X
% 0.16/0.39 != ( nil @ ( list @ A ) ) )
% 0.16/0.39 => ( ! [Xss: list @ ( list @ A )] :
% 0.16/0.39 ( X
% 0.16/0.39 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.16/0.39 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.16/0.39 ( X
% 0.16/0.39 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % transpose.cases
% 0.16/0.39 thf(fact_116_eq__Nil__appendI,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( Xs = Ys )
% 0.16/0.39 => ( Xs
% 0.16/0.39 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_Nil_appendI
% 0.16/0.39 thf(fact_117_splice_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.39 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.16/0.39 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 0.16/0.39 ( ( P @ Xs2 @ Ys3 )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) )
% 0.16/0.39 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % splice.induct
% 0.16/0.39 thf(fact_118_list__induct2_H,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.16/0.39 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 0.16/0.39 => ( ! [Y2: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys3 ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A,Y2: B,Ys3: list @ B] :
% 0.16/0.39 ( ( P @ Xs2 @ Ys3 )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys3 ) ) )
% 0.16/0.39 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_induct2'
% 0.16/0.39 thf(fact_119_neq__Nil__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 = ( ? [Y3: A,Ys4: list @ A] :
% 0.16/0.39 ( Xs
% 0.16/0.39 = ( cons @ A @ Y3 @ Ys4 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % neq_Nil_conv
% 0.16/0.39 thf(fact_120_list_Oinducts,axiom,
% 0.16/0.39 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.16/0.39 ( ( P @ ( nil @ A ) )
% 0.16/0.39 => ( ! [X1: A,X23: list @ A] :
% 0.16/0.39 ( ( P @ X23 )
% 0.16/0.39 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.16/0.39 => ( P @ List ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.inducts
% 0.16/0.39 thf(fact_121_list_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,Y: list @ A] :
% 0.16/0.39 ( ( Y
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ~ ! [X212: A,X222: list @ A] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.exhaust
% 0.16/0.39 thf(fact_122_list_OdiscI,axiom,
% 0.16/0.39 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.16/0.39 ( ( List
% 0.16/0.39 = ( cons @ A @ X21 @ X22 ) )
% 0.16/0.39 => ( List
% 0.16/0.39 != ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.discI
% 0.16/0.39 thf(fact_123_list_Odistinct_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X21: A,X22: list @ A] :
% 0.16/0.39 ( ( nil @ A )
% 0.16/0.39 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.distinct(1)
% 0.16/0.39 thf(fact_124_list__of__code,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1736001939ist_of @ A )
% 0.16/0.39 = ( coindu1542816657of_aux @ A @ ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_of_code
% 0.16/0.39 thf(fact_125_rev__induct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.16/0.39 ( ( P @ ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 0.16/0.39 => ( P @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_induct
% 0.16/0.39 thf(fact_126_rev__exhaust,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ~ ! [Ys3: list @ A,Y2: A] :
% 0.16/0.39 ( Xs
% 0.16/0.39 != ( append @ A @ Ys3 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_exhaust
% 0.16/0.39 thf(fact_127_Cons__eq__append__conv,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.16/0.39 ( ( ( cons @ A @ X @ Xs )
% 0.16/0.39 = ( append @ A @ Ys @ Zs2 ) )
% 0.16/0.39 = ( ( ( Ys
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 & ( ( cons @ A @ X @ Xs )
% 0.16/0.39 = Zs2 ) )
% 0.16/0.39 | ? [Ys2: list @ A] :
% 0.16/0.39 ( ( ( cons @ A @ X @ Ys2 )
% 0.16/0.39 = Ys )
% 0.16/0.39 & ( Xs
% 0.16/0.39 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Cons_eq_append_conv
% 0.16/0.39 thf(fact_128_append__eq__Cons__conv,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Ys @ Zs2 )
% 0.16/0.39 = ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( ( ( Ys
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 & ( Zs2
% 0.16/0.39 = ( cons @ A @ X @ Xs ) ) )
% 0.16/0.39 | ? [Ys2: list @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( cons @ A @ X @ Ys2 ) )
% 0.16/0.39 & ( ( append @ A @ Ys2 @ Zs2 )
% 0.16/0.39 = Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_eq_Cons_conv
% 0.16/0.39 thf(fact_129_rev__nonempty__induct,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( Xs2
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 0.16/0.39 => ( P @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_nonempty_induct
% 0.16/0.39 thf(fact_130_last__ConsR,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( last @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_ConsR
% 0.16/0.39 thf(fact_131_last__ConsL,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = X ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_ConsL
% 0.16/0.39 thf(fact_132_last_Osimps,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = X ) )
% 0.16/0.39 & ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( last @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last.simps
% 0.16/0.39 thf(fact_133_longest__common__suffix,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ? [Ss: list @ A,Xs3: list @ A,Ys6: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( append @ A @ Xs3 @ Ss ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( append @ A @ Ys6 @ Ss ) )
% 0.16/0.39 & ( ( Xs3
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ( Ys6
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ( ( last @ A @ Xs3 )
% 0.16/0.39 != ( last @ A @ Ys6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % longest_common_suffix
% 0.16/0.39 thf(fact_134_last__append,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.39 ( ( ( Ys
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( last @ A @ Xs ) ) )
% 0.16/0.39 & ( ( Ys
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( last @ A @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_append
% 0.16/0.39 thf(fact_135_llist__of__eq__LNil__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist_of_eq_LNil_conv
% 0.16/0.39 thf(fact_136_llist__of_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1079202755ist_of @ A @ ( nil @ A ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist_of.simps(1)
% 0.16/0.39 thf(fact_137_not__Cons__self2,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( cons @ A @ X @ Xs )
% 0.16/0.39 != Xs ) ).
% 0.16/0.39
% 0.16/0.39 % not_Cons_self2
% 0.16/0.39 thf(fact_138_append__eq__appendI,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ Xs1 )
% 0.16/0.39 = Zs2 )
% 0.16/0.39 => ( ( Ys
% 0.16/0.39 = ( append @ A @ Xs1 @ Us ) )
% 0.16/0.39 => ( ( append @ A @ Xs @ Ys )
% 0.16/0.39 = ( append @ A @ Zs2 @ Us ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_eq_appendI
% 0.16/0.39 thf(fact_139_append__eq__append__conv2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.39 = ( append @ A @ Zs2 @ Ts ) )
% 0.16/0.39 = ( ? [Us2: list @ A] :
% 0.16/0.39 ( ( ( Xs
% 0.16/0.39 = ( append @ A @ Zs2 @ Us2 ) )
% 0.16/0.39 & ( ( append @ A @ Us2 @ Ys )
% 0.16/0.39 = Ts ) )
% 0.16/0.39 | ( ( ( append @ A @ Xs @ Us2 )
% 0.16/0.39 = Zs2 )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_eq_append_conv2
% 0.16/0.39 thf(fact_140_longest__common__prefix_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.39 ( ! [X2: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 0.16/0.39 ( ( ( X2 = Y2 )
% 0.16/0.39 => ( P @ Xs2 @ Ys3 ) )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) )
% 0.16/0.39 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.16/0.39 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 0.16/0.39 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % longest_common_prefix.induct
% 0.16/0.39 thf(fact_141_prefixes_Oinduct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.16/0.39 ( ( P @ ( nil @ A ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.16/0.39 => ( P @ A0 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes.induct
% 0.16/0.39 thf(fact_142_prefixes_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,X: list @ A] :
% 0.16/0.39 ( ( X
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ~ ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( X
% 0.16/0.39 != ( cons @ A @ X2 @ Xs2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes.cases
% 0.16/0.39 thf(fact_143_append__butlast__last__id,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.16/0.39 = Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % append_butlast_last_id
% 0.16/0.39 thf(fact_144_bind__simps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.16/0.39 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 0.16/0.39 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % bind_simps(2)
% 0.16/0.39 thf(fact_145_bind__simps_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.16/0.39 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % bind_simps(1)
% 0.16/0.39 thf(fact_146_butlast__snoc,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % butlast_snoc
% 0.16/0.39 thf(fact_147_butlast_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( butlast @ A @ ( nil @ A ) )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % butlast.simps(1)
% 0.16/0.39 thf(fact_148_butlast_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( nil @ A ) ) )
% 0.16/0.39 & ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % butlast.simps(2)
% 0.16/0.39 thf(fact_149_butlast__append,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.39 ( ( ( Ys
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( butlast @ A @ Xs ) ) )
% 0.16/0.39 & ( ( Ys
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % butlast_append
% 0.16/0.39 thf(fact_150_snoc__eq__iff__butlast,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A] :
% 0.16/0.39 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.16/0.39 = Ys )
% 0.16/0.39 = ( ( Ys
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 & ( ( butlast @ A @ Ys )
% 0.16/0.39 = Xs )
% 0.16/0.39 & ( ( last @ A @ Ys )
% 0.16/0.39 = X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % snoc_eq_iff_butlast
% 0.16/0.39 thf(fact_151_prefixes__snoc,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( prefixes @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.16/0.39 = ( append @ ( list @ A ) @ ( prefixes @ A @ Xs ) @ ( cons @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( nil @ ( list @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes_snoc
% 0.16/0.39 thf(fact_152_prefixes__eq__Snoc,axiom,
% 0.16/0.39 ! [A: $tType,Ys: list @ A,Xs: list @ ( list @ A ),X: list @ A] :
% 0.16/0.39 ( ( ( prefixes @ A @ Ys )
% 0.16/0.39 = ( append @ ( list @ A ) @ Xs @ ( cons @ ( list @ A ) @ X @ ( nil @ ( list @ A ) ) ) ) )
% 0.16/0.39 = ( ( ( ( Ys
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 & ( Xs
% 0.16/0.39 = ( nil @ ( list @ A ) ) ) )
% 0.16/0.39 | ? [Z: A,Zs4: list @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( append @ A @ Zs4 @ ( cons @ A @ Z @ ( nil @ A ) ) ) )
% 0.16/0.39 & ( Xs
% 0.16/0.39 = ( prefixes @ A @ Zs4 ) ) ) )
% 0.16/0.39 & ( X = Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes_eq_Snoc
% 0.16/0.39 thf(fact_153_sublists_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( sublists @ A @ ( nil @ A ) )
% 0.16/0.39 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % sublists.simps(1)
% 0.16/0.39 thf(fact_154_prefixes_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( prefixes @ A @ ( nil @ A ) )
% 0.16/0.39 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes.simps(1)
% 0.16/0.39 thf(fact_155_product__lists_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.16/0.39 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % product_lists.simps(1)
% 0.16/0.39 thf(fact_156_llimit__induct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.16/0.39 => ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.16/0.39 => ( ( ! [Ys5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Ys5 @ Xs )
% 0.16/0.39 => ( P @ Ys5 ) )
% 0.16/0.39 => ( P @ Xs ) )
% 0.16/0.39 => ( P @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llimit_induct
% 0.16/0.39 thf(fact_157_prefixes_Oelims,axiom,
% 0.16/0.39 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 0.16/0.39 ( ( ( prefixes @ A @ X )
% 0.16/0.39 = Y )
% 0.16/0.39 => ( ( ( X
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( Y
% 0.16/0.39 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.16/0.39 => ~ ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( X
% 0.16/0.39 = ( cons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ( Y
% 0.16/0.39 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes.elims
% 0.16/0.39 thf(fact_158_Nil__is__map__conv,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.16/0.39 ( ( ( nil @ A )
% 0.16/0.39 = ( map @ B @ A @ F @ Xs ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Nil_is_map_conv
% 0.16/0.39 thf(fact_159_map__is__Nil__conv,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.16/0.39 ( ( ( map @ B @ A @ F @ Xs )
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_is_Nil_conv
% 0.16/0.39 thf(fact_160_list_Omap__disc__iff,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: A > B,A3: list @ A] :
% 0.16/0.39 ( ( ( map @ A @ B @ F @ A3 )
% 0.16/0.39 = ( nil @ B ) )
% 0.16/0.39 = ( A3
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.map_disc_iff
% 0.16/0.39 thf(fact_161_map__append,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Ys: list @ B] :
% 0.16/0.39 ( ( map @ B @ A @ F @ ( append @ B @ Xs @ Ys ) )
% 0.16/0.39 = ( append @ A @ ( map @ B @ A @ F @ Xs ) @ ( map @ B @ A @ F @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_append
% 0.16/0.39 thf(fact_162_lstrict__prefix__code_I4_J,axiom,
% 0.16/0.39 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B,Y: B,Ys: coindu1593790203_llist @ B] :
% 0.16/0.39 ( ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 0.16/0.39 = ( ( X = Y )
% 0.16/0.39 & ( coindu574146665prefix @ B @ Xs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(4)
% 0.16/0.39 thf(fact_163_lstrict__prefix__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(1)
% 0.16/0.39 thf(fact_164_lstrict__prefix__code_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,Y: B,Ys: coindu1593790203_llist @ B] : ( coindu574146665prefix @ B @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(2)
% 0.16/0.39 thf(fact_165_lstrict__prefix__code_I3_J,axiom,
% 0.16/0.39 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.16/0.39 ~ ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(3)
% 0.16/0.39 thf(fact_166_llist__less__induct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ! [Ys5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Ys5 @ Xs2 )
% 0.16/0.39 => ( P @ Ys5 ) )
% 0.16/0.39 => ( P @ Xs2 ) )
% 0.16/0.39 => ( P @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist_less_induct
% 0.16/0.39 thf(fact_167_map__butlast,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.16/0.39 ( ( map @ B @ A @ F @ ( butlast @ B @ Xs ) )
% 0.16/0.39 = ( butlast @ A @ ( map @ B @ A @ F @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_butlast
% 0.16/0.39 thf(fact_168_list_Osimps_I8_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: A > B] :
% 0.16/0.39 ( ( map @ A @ B @ F @ ( nil @ A ) )
% 0.16/0.39 = ( nil @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.simps(8)
% 0.16/0.39 thf(fact_169_list_Osimps_I9_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: list @ A] :
% 0.16/0.39 ( ( map @ A @ B @ F @ ( cons @ A @ X21 @ X22 ) )
% 0.16/0.39 = ( cons @ B @ ( F @ X21 ) @ ( map @ A @ B @ F @ X22 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.simps(9)
% 0.16/0.39 thf(fact_170_Cons__eq__map__D,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 0.16/0.39 ( ( ( cons @ A @ X @ Xs )
% 0.16/0.39 = ( map @ B @ A @ F @ Ys ) )
% 0.16/0.39 => ? [Z3: B,Zs3: list @ B] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( cons @ B @ Z3 @ Zs3 ) )
% 0.16/0.39 & ( X
% 0.16/0.39 = ( F @ Z3 ) )
% 0.16/0.39 & ( Xs
% 0.16/0.39 = ( map @ B @ A @ F @ Zs3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Cons_eq_map_D
% 0.16/0.39 thf(fact_171_map__eq__Cons__D,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 0.16/0.39 ( ( ( map @ B @ A @ F @ Xs )
% 0.16/0.39 = ( cons @ A @ Y @ Ys ) )
% 0.16/0.39 => ? [Z3: B,Zs3: list @ B] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( cons @ B @ Z3 @ Zs3 ) )
% 0.16/0.39 & ( ( F @ Z3 )
% 0.16/0.39 = Y )
% 0.16/0.39 & ( ( map @ B @ A @ F @ Zs3 )
% 0.16/0.39 = Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_eq_Cons_D
% 0.16/0.39 thf(fact_172_Cons__eq__map__conv,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 0.16/0.39 ( ( ( cons @ A @ X @ Xs )
% 0.16/0.39 = ( map @ B @ A @ F @ Ys ) )
% 0.16/0.39 = ( ? [Z: B,Zs4: list @ B] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( cons @ B @ Z @ Zs4 ) )
% 0.16/0.39 & ( X
% 0.16/0.39 = ( F @ Z ) )
% 0.16/0.39 & ( Xs
% 0.16/0.39 = ( map @ B @ A @ F @ Zs4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Cons_eq_map_conv
% 0.16/0.39 thf(fact_173_map__eq__Cons__conv,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 0.16/0.39 ( ( ( map @ B @ A @ F @ Xs )
% 0.16/0.39 = ( cons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ? [Z: B,Zs4: list @ B] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( cons @ B @ Z @ Zs4 ) )
% 0.16/0.39 & ( ( F @ Z )
% 0.16/0.39 = Y )
% 0.16/0.39 & ( ( map @ B @ A @ F @ Zs4 )
% 0.16/0.39 = Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_eq_Cons_conv
% 0.16/0.39 thf(fact_174_lstrict__prefix__lfinite1,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_lfinite1
% 0.16/0.39 thf(fact_175_last__map,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( last @ B @ ( map @ A @ B @ F @ Xs ) )
% 0.16/0.39 = ( F @ ( last @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_map
% 0.16/0.39 thf(fact_176_prefixes_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( prefixes @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X ) @ ( prefixes @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes.simps(2)
% 0.16/0.39 thf(fact_177_prefixes_Opelims,axiom,
% 0.16/0.39 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 0.16/0.39 ( ( ( prefixes @ A @ X )
% 0.16/0.39 = Y )
% 0.16/0.39 => ( ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ X )
% 0.16/0.39 => ( ( ( X
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( Y
% 0.16/0.39 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.39 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( nil @ A ) ) ) )
% 0.16/0.39 => ~ ! [X2: A,Xs2: list @ A] :
% 0.16/0.39 ( ( X
% 0.16/0.39 = ( cons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ( ( Y
% 0.16/0.39 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) )
% 0.16/0.39 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( cons @ A @ X2 @ Xs2 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prefixes.pelims
% 0.16/0.39 thf(fact_178_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [Xs4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y @ Xs4 ) )
% 0.16/0.39 & ( coindu1571841457prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(3)
% 0.16/0.39 thf(fact_179_maps__simps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 0.16/0.39 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 0.16/0.39 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % maps_simps(1)
% 0.16/0.39 thf(fact_180_maps__simps_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.16/0.39 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % maps_simps(2)
% 0.16/0.39 thf(fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1571841457prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(2)
% 0.16/0.39 thf(fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(1)
% 0.16/0.39 thf(fact_183_insert__Nil,axiom,
% 0.16/0.39 ! [A: $tType,X: A] :
% 0.16/0.39 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.16/0.39 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % insert_Nil
% 0.16/0.39 thf(fact_184_rotate1_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rotate1.simps(2)
% 0.16/0.39 thf(fact_185_map__eq__map__tailrec,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( map @ A @ B )
% 0.16/0.39 = ( map_tailrec @ A @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_eq_map_tailrec
% 0.16/0.39 thf(fact_186_rotate1__is__Nil__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( rotate1 @ A @ Xs )
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rotate1_is_Nil_conv
% 0.16/0.39 thf(fact_187_rotate1_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % rotate1.simps(1)
% 0.16/0.39 thf(fact_188_hd__list__of,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( hd @ A @ ( coindu1736001939ist_of @ A @ Xs ) )
% 0.16/0.39 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_list_of
% 0.16/0.39 thf(fact_189_list__ex1__simps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o] :
% 0.16/0.39 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_ex1_simps(1)
% 0.16/0.39 thf(fact_190_list__of__LCons__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.16/0.39 ( ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu1736001939ist_of @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( cons @ A @ X @ ( coindu1736001939ist_of @ A @ Xs ) ) ) )
% 0.16/0.39 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu1736001939ist_of @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( undefined @ ( list @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_of_LCons_conv
% 0.16/0.39 thf(fact_191_hd__append2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( hd @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_append2
% 0.16/0.39 thf(fact_192_lhd__llist__of,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( coindu1046438764le_lhd @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 0.16/0.39 = ( hd @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lhd_llist_of
% 0.16/0.39 thf(fact_193_list_Osel_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X21: A,X22: list @ A] :
% 0.16/0.39 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.16/0.39 = X21 ) ).
% 0.16/0.39
% 0.16/0.39 % list.sel(1)
% 0.16/0.39 thf(fact_194_list_Omap__sel_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,A3: list @ A,F: A > B] :
% 0.16/0.39 ( ( A3
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( hd @ B @ ( map @ A @ B @ F @ A3 ) )
% 0.16/0.39 = ( F @ ( hd @ A @ A3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.map_sel(1)
% 0.16/0.39 thf(fact_195_hd__map,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( hd @ B @ ( map @ A @ B @ F @ Xs ) )
% 0.16/0.39 = ( F @ ( hd @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_map
% 0.16/0.39 thf(fact_196_longest__common__prefix,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ? [Ps: list @ A,Xs3: list @ A,Ys6: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( append @ A @ Ps @ Xs3 ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( append @ A @ Ps @ Ys6 ) )
% 0.16/0.39 & ( ( Xs3
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ( Ys6
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ( ( hd @ A @ Xs3 )
% 0.16/0.39 != ( hd @ A @ Ys6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % longest_common_prefix
% 0.16/0.39 thf(fact_197_hd__append,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( hd @ A @ Ys ) ) )
% 0.16/0.39 & ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( hd @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_append
% 0.16/0.39 thf(fact_198_llast__LNil,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu2000965700_llast @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( undefined @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_LNil
% 0.16/0.39 thf(fact_199_llast__linfinite,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ Xs )
% 0.16/0.39 = ( undefined @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_linfinite
% 0.16/0.39 thf(fact_200_list__of__aux__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1542816657of_aux @ A )
% 0.16/0.39 = ( ^ [Xs5: list @ A,Ys4: coindu1593790203_llist @ A] : ( if @ ( list @ A ) @ ( coindu1213758845finite @ A @ Ys4 ) @ ( append @ A @ ( rev @ A @ Xs5 ) @ ( coindu1736001939ist_of @ A @ Ys4 ) ) @ ( undefined @ ( list @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_of_aux_def
% 0.16/0.39 thf(fact_201_rotate1__hd__tl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( rotate1 @ A @ Xs )
% 0.16/0.39 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rotate1_hd_tl
% 0.16/0.39 thf(fact_202_rev__rev__ident,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % rev_rev_ident
% 0.16/0.39 thf(fact_203_rev__is__rev__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( rev @ A @ Xs )
% 0.16/0.39 = ( rev @ A @ Ys ) )
% 0.16/0.39 = ( Xs = Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_is_rev_conv
% 0.16/0.39 thf(fact_204_Nil__is__rev__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( nil @ A )
% 0.16/0.39 = ( rev @ A @ Xs ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Nil_is_rev_conv
% 0.16/0.39 thf(fact_205_rev__is__Nil__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( rev @ A @ Xs )
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_is_Nil_conv
% 0.16/0.39 thf(fact_206_rev__append,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( rev @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( append @ A @ ( rev @ A @ Ys ) @ ( rev @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_append
% 0.16/0.39 thf(fact_207_rev__singleton__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.39 ( ( ( rev @ A @ Xs )
% 0.16/0.39 = ( cons @ A @ X @ ( nil @ A ) ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_singleton_conv
% 0.16/0.39 thf(fact_208_singleton__rev__conv,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 0.16/0.39 = ( rev @ A @ Xs ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % singleton_rev_conv
% 0.16/0.39 thf(fact_209_tl__append2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % tl_append2
% 0.16/0.39 thf(fact_210_rev__eq__Cons__iff,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.16/0.39 ( ( ( rev @ A @ Xs )
% 0.16/0.39 = ( cons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( append @ A @ ( rev @ A @ Ys ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_eq_Cons_iff
% 0.16/0.39 thf(fact_211_list_Ocollapse,axiom,
% 0.16/0.39 ! [A: $tType,List: list @ A] :
% 0.16/0.39 ( ( List
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.16/0.39 = List ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.collapse
% 0.16/0.39 thf(fact_212_hd__Cons__tl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.16/0.39 = Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_Cons_tl
% 0.16/0.39 thf(fact_213_map__tl,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.16/0.39 ( ( map @ B @ A @ F @ ( tl @ B @ Xs ) )
% 0.16/0.39 = ( tl @ A @ ( map @ B @ A @ F @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_tl
% 0.16/0.39 thf(fact_214_rev__map,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.16/0.39 ( ( rev @ A @ ( map @ B @ A @ F @ Xs ) )
% 0.16/0.39 = ( map @ B @ A @ F @ ( rev @ B @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_map
% 0.16/0.39 thf(fact_215_rev__swap,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.39 ( ( ( rev @ A @ Xs )
% 0.16/0.39 = Ys )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( rev @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_swap
% 0.16/0.39 thf(fact_216_list_Osel_I2_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( tl @ A @ ( nil @ A ) )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.sel(2)
% 0.16/0.39 thf(fact_217_list_Osel_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,X21: A,X22: list @ A] :
% 0.16/0.39 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.16/0.39 = X22 ) ).
% 0.16/0.39
% 0.16/0.39 % list.sel(3)
% 0.16/0.39 thf(fact_218_butlast__tl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 0.16/0.39 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % butlast_tl
% 0.16/0.39 thf(fact_219_rev_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( rev @ A @ ( nil @ A ) )
% 0.16/0.39 = ( nil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev.simps(1)
% 0.16/0.39 thf(fact_220_list_Omap__sel_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,A3: list @ A,F: A > B] :
% 0.16/0.39 ( ( A3
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( tl @ B @ ( map @ A @ B @ F @ A3 ) )
% 0.16/0.39 = ( map @ A @ B @ F @ ( tl @ A @ A3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.map_sel(2)
% 0.16/0.39 thf(fact_221_tl__Nil,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( tl @ A @ Xs )
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ? [X3: A] :
% 0.16/0.39 ( Xs
% 0.16/0.39 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % tl_Nil
% 0.16/0.39 thf(fact_222_Nil__tl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( nil @ A )
% 0.16/0.39 = ( tl @ A @ Xs ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ? [X3: A] :
% 0.16/0.39 ( Xs
% 0.16/0.39 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Nil_tl
% 0.16/0.39 thf(fact_223_list_Oexpand,axiom,
% 0.16/0.39 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.16/0.39 ( ( ( List
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( List2
% 0.16/0.39 = ( nil @ A ) ) )
% 0.16/0.39 => ( ( ( List
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( List2
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( ( hd @ A @ List )
% 0.16/0.39 = ( hd @ A @ List2 ) )
% 0.16/0.39 & ( ( tl @ A @ List )
% 0.16/0.39 = ( tl @ A @ List2 ) ) ) ) )
% 0.16/0.39 => ( List = List2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.expand
% 0.16/0.39 thf(fact_224_last__tl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( Xs
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 | ( ( tl @ A @ Xs )
% 0.16/0.39 != ( nil @ A ) ) )
% 0.16/0.39 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 0.16/0.39 = ( last @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_tl
% 0.16/0.39 thf(fact_225_list__of__aux__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( coindu1542816657of_aux @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( rev @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % list_of_aux_code(1)
% 0.16/0.39 thf(fact_226_rev_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( rev @ A @ ( cons @ A @ X @ Xs ) )
% 0.16/0.39 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev.simps(2)
% 0.16/0.39 thf(fact_227_hd__rev,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 0.16/0.39 = ( last @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_rev
% 0.16/0.39 thf(fact_228_last__rev,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 0.16/0.39 = ( hd @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % last_rev
% 0.16/0.39 thf(fact_229_list_Oexhaust__sel,axiom,
% 0.16/0.39 ! [A: $tType,List: list @ A] :
% 0.16/0.39 ( ( List
% 0.16/0.39 != ( nil @ A ) )
% 0.16/0.39 => ( List
% 0.16/0.39 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.exhaust_sel
% 0.16/0.39 thf(fact_230_map__tailrec__def,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( map_tailrec @ A @ B )
% 0.16/0.39 = ( ^ [F3: A > B,As2: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F3 @ As2 @ ( nil @ B ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_tailrec_def
% 0.16/0.39 thf(fact_231_list_Osplit__sel__asm,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( list @ A ) > B,List: list @ A] :
% 0.16/0.39 ( ( P @ ( case_list @ B @ A @ F1 @ F22 @ List ) )
% 0.16/0.39 = ( ~ ( ( ( List
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 & ~ ( P @ F1 ) )
% 0.16/0.39 | ( ( List
% 0.16/0.39 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.16/0.39 & ~ ( P @ ( F22 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.split_sel_asm
% 0.16/0.39 thf(fact_232_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: A > B,Bs2: list @ B] :
% 0.16/0.39 ( ( map_tailrec_rev @ A @ B @ F @ ( nil @ A ) @ Bs2 )
% 0.16/0.39 = Bs2 ) ).
% 0.16/0.39
% 0.16/0.39 % map_tailrec_rev.simps(1)
% 0.16/0.39 thf(fact_233_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F: A > B,A3: A,As3: list @ A,Bs2: list @ B] :
% 0.16/0.39 ( ( map_tailrec_rev @ A @ B @ F @ ( cons @ A @ A3 @ As3 ) @ Bs2 )
% 0.16/0.39 = ( map_tailrec_rev @ A @ B @ F @ As3 @ ( cons @ B @ ( F @ A3 ) @ Bs2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_tailrec_rev.simps(2)
% 0.16/0.39 thf(fact_234_list_Osimps_I4_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,F1: B,F22: A > ( list @ A ) > B] :
% 0.16/0.39 ( ( case_list @ B @ A @ F1 @ F22 @ ( nil @ A ) )
% 0.16/0.39 = F1 ) ).
% 0.16/0.39
% 0.16/0.39 % list.simps(4)
% 0.16/0.39 thf(fact_235_list_Osimps_I5_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F1: B,F22: A > ( list @ A ) > B,X21: A,X22: list @ A] :
% 0.16/0.39 ( ( case_list @ B @ A @ F1 @ F22 @ ( cons @ A @ X21 @ X22 ) )
% 0.16/0.39 = ( F22 @ X21 @ X22 ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.simps(5)
% 0.16/0.39 thf(fact_236_map__tailrec__rev_Oelims,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X: A > B,Xa: list @ A,Xb2: list @ B,Y: list @ B] :
% 0.16/0.39 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa @ Xb2 )
% 0.16/0.39 = Y )
% 0.16/0.39 => ( ( ( Xa
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( Y != Xb2 ) )
% 0.16/0.39 => ~ ! [A2: A,As: list @ A] :
% 0.16/0.39 ( ( Xa
% 0.16/0.39 = ( cons @ A @ A2 @ As ) )
% 0.16/0.39 => ( Y
% 0.16/0.39 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A2 ) @ Xb2 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_tailrec_rev.elims
% 0.16/0.39 thf(fact_237_list_Ocase__eq__if,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType] :
% 0.16/0.39 ( ( case_list @ B @ A )
% 0.16/0.39 = ( ^ [F12: B,F23: A > ( list @ A ) > B,List3: list @ A] :
% 0.16/0.39 ( if @ B
% 0.16/0.39 @ ( List3
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 @ F12
% 0.16/0.39 @ ( F23 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.case_eq_if
% 0.16/0.39 thf(fact_238_map__tailrec__rev,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType] :
% 0.16/0.39 ( ( map_tailrec_rev @ B @ A )
% 0.16/0.39 = ( ^ [F3: B > A,As2: list @ B] : ( append @ A @ ( rev @ A @ ( map @ B @ A @ F3 @ As2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % map_tailrec_rev
% 0.16/0.39 thf(fact_239_list_Osplit__sel,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( list @ A ) > B,List: list @ A] :
% 0.16/0.39 ( ( P @ ( case_list @ B @ A @ F1 @ F22 @ List ) )
% 0.16/0.39 = ( ( ( List
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 => ( P @ F1 ) )
% 0.16/0.39 & ( ( List
% 0.16/0.39 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.16/0.39 => ( P @ ( F22 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % list.split_sel
% 0.16/0.39 thf(fact_240_remdups__adj__append,axiom,
% 0.16/0.39 ! [A: $tType,Xs_1: list @ A,X: A,Xs_2: list @ A] :
% 0.16/0.39 ( ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ Xs_2 ) ) )
% 0.16/0.39 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs_2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % remdups_adj_append
% 0.16/0.39 thf(fact_241_llast__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ Xs ) ) )
% 0.16/0.39 & ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ Ys ) ) )
% 0.16/0.39 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( undefined @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_lappend
% 0.16/0.39 thf(fact_242_lappend_Odisc__iff_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.16/0.39 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc_iff(2)
% 0.16/0.39 thf(fact_243_lnull__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_lappend
% 0.16/0.39 thf(fact_244_remdups__adj__Nil__iff,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( ( remdups_adj @ A @ Xs )
% 0.16/0.39 = ( nil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % remdups_adj_Nil_iff
% 0.16/0.39 thf(fact_245_llexord__LNil__right,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,R: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LNil_right
% 0.16/0.39 thf(fact_246_remdups__adj__rev,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( remdups_adj @ A @ ( rev @ A @ Xs ) )
% 0.16/0.39 = ( rev @ A @ ( remdups_adj @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % remdups_adj_rev
% 0.16/0.39 thf(fact_247_hd__remdups__adj,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( hd @ A @ ( remdups_adj @ A @ Xs ) )
% 0.16/0.39 = ( hd @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % hd_remdups_adj
% 0.16/0.39 thf(fact_248_lnull__llist__of,axiom,
% 0.16/0.39 ! [A: $tType,Xs: list @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( nil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_llist_of
% 0.16/0.39 thf(fact_249_lhd__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 0.16/0.39 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lhd_lappend
% 0.16/0.39 thf(fact_250_remdups__adj__Cons__alt,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.39 ( ( cons @ A @ X @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) )
% 0.16/0.39 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % remdups_adj_Cons_alt
% 0.16/0.39 thf(fact_251_llast__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = X ) )
% 0.16/0.39 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_LCons
% 0.16/0.39 thf(fact_252_lappend_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.16/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.exhaust
% 0.16/0.39 thf(fact_253_lzip_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.16/0.39 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.16/0.39 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lzip.exhaust
% 0.16/0.39
% 0.16/0.39 %----Helper facts (3)
% 0.16/0.39 thf(help_If_3_1_T,axiom,
% 0.16/0.39 ! [P: $o] :
% 0.16/0.39 ( ( P = $true )
% 0.16/0.39 | ( P = $false ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(help_If_2_1_T,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Y: A] :
% 0.16/0.39 ( ( if @ A @ $false @ X @ Y )
% 0.16/0.39 = Y ) ).
% 0.16/0.39
% 0.16/0.39 thf(help_If_1_1_T,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Y: A] :
% 0.16/0.39 ( ( if @ A @ $true @ X @ Y )
% 0.16/0.39 = X ) ).
% 0.16/0.39
% 0.16/0.39 %----Conjectures (2)
% 0.16/0.39 thf(conj_0,hypothesis,
% 0.16/0.39 ! [YS: list @ a] :
% 0.16/0.39 ( ( ys2
% 0.16/0.39 = ( coindu1079202755ist_of @ a @ YS ) )
% 0.16/0.39 => thesis ) ).
% 0.16/0.39
% 0.16/0.39 thf(conj_1,conjecture,
% 0.16/0.39 thesis ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.51/1.59 ---- Embedded in THF ---
% 2.51/1.59 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.51/1.59 %%% Generated on Tue Feb 24 06:08:38 EST 2026
% 2.51/1.59 %%% using '$$dhol' embedding, version 1.3.0.
% 2.51/1.59 %%% Logic specification used:
% 2.51/1.59 %%% thf(spec, logic, $$dhol).
% 2.51/1.59
% 2.51/1.59 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SSpVV69JSc/DTF2DTF1697.p
% 2.51/1.59 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 2.51/1.59 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.51/1.59 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.51/1.59 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.51/1.59 thf(ty_tf_a, type, a: $tType).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix, type, coindu1571841457prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of, type, coindu1736001939ist_of: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (list @ A))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of__aux, type, coindu1542816657of_aux: (!> [A:$tType]: (((list @ A) > ((coindu1593790203_llist @ A) > (list @ A)))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast, type, coindu2000965700_llast: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord, type, coindu300403952lexord: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd, type, coindu1046438764le_lhd: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset, type, coindu1112613586e_lset: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (set @ A))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist__of, type, coindu1079202755ist_of: (!> [A:$tType]: (((list @ A) > (coindu1593790203_llist @ A))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 2.51/1.59 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix, type, coindu574146665prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 2.51/1.59 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.51/1.59 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.51/1.59 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.51/1.59 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.51/1.59 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.51/1.59 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.51/1.59 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.51/1.59 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.51/1.59 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.51/1.59 thf(sy_c_List_Olist_Ocase__list, type, case_list: (!> [B:$tType,A:$tType]: ((B > ((A > ((list @ A) > B)) > ((list @ A) > B)))))).
% 2.51/1.59 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.51/1.59 thf(sy_c_List_Olist_Omap, type, map: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((list @ A) > (list @ Aa)))))).
% 2.51/1.59 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.51/1.59 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.51/1.59 thf(sy_c_List_Omap__tailrec, type, map_tailrec: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > (list @ B)))))).
% 2.51/1.59 thf(sy_c_List_Omap__tailrec__rev, type, map_tailrec_rev: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > ((list @ B) > (list @ B))))))).
% 2.51/1.59 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.51/1.59 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.51/1.59 thf(sy_c_List_Oremdups__adj, type, remdups_adj: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.51/1.59 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.51/1.59 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.51/1.59 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.51/1.59 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 2.51/1.59 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.51/1.59 thf(sy_c_Sublist_Oprefixes, type, prefixes: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.51/1.59 thf(sy_c_Sublist_Oprefixes__rel, type, prefixes_rel: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.51/1.59 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.51/1.59 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.51/1.59 thf(sy_v_XS_H____, type, xs: (list @ a)).
% 2.51/1.59 thf(sy_v_r, type, r: (a > (a > $o))).
% 2.51/1.59 thf(sy_v_thesis____, type, thesis: $o).
% 2.51/1.59 thf(sy_v_xs, type, xs2: (list @ a)).
% 2.51/1.59 thf(sy_v_xs_H____, type, xs3: (coindu1593790203_llist @ a)).
% 2.51/1.59 thf(sy_v_y____, type, y: a).
% 2.51/1.59 thf(sy_v_ys, type, ys: (list @ a)).
% 2.51/1.59 thf(sy_v_ys_H____, type, ys2: (coindu1593790203_llist @ a)).
% 2.51/1.59 thf(sy_v_zs_H____, type, zs: (list @ a)).
% 2.51/1.59 thf(sy_v_zs____, type, zs2: (coindu1593790203_llist @ a)).
% 2.51/1.59 thf(fact_0_llist__of__inject, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((coindu1079202755ist_of @ A) @ Xs) = ((coindu1079202755ist_of @ A) @ Ys)) = (Xs = Ys))))).
% 2.51/1.59 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062zs_H_O_Azs_A_061_Allist__of_Azs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Zs:(list @ a)]: ((zs2 != ((coindu1079202755ist_of @ a) @ Zs))))))).
% 2.51/1.59 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [XS:(list @ a)]: ((xs3 != ((coindu1079202755ist_of @ a) @ XS))))))).
% 2.51/1.59 thf(fact_3__092_060open_062lfinite_Ays_H_092_060close_062, axiom, ((coindu1213758845finite @ a) @ ys2)).
% 2.51/1.59 thf(fact_4_list__of__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coindu1736001939ist_of @ A) @ ((coindu1079202755ist_of @ A) @ Xs)) = Xs)))).
% 2.51/1.59 thf(fact_5__092_060open_062zs_A_061_Allist__of_Azs_H_092_060close_062, axiom, (zs2 = ((coindu1079202755ist_of @ a) @ zs))).
% 2.51/1.59 thf(fact_6__092_060open_062llist__of_Ays_A_061_Alappend_Azs_A_ILCons_Ay_Ays_H_J_092_060close_062, axiom, (((coindu1079202755ist_of @ a) @ ys) = (((coindu268472904append @ a) @ zs2) @ (((coindu1121789889_LCons @ a) @ y) @ ys2)))).
% 2.51/1.59 thf(fact_7__092_060open_062xs_H_A_061_Allist__of_AXS_H_092_060close_062, axiom, (xs3 = ((coindu1079202755ist_of @ a) @ xs))).
% 2.51/1.59 thf(fact_8__092_060open_062lfinite_A_Illist__of_Ays_J_092_060close_062, axiom, ((coindu1213758845finite @ a) @ ((coindu1079202755ist_of @ a) @ ys))).
% 2.51/1.59 thf(fact_9__092_060open_062lfinite_A_Illist__of_Axs_J_092_060close_062, axiom, ((coindu1213758845finite @ a) @ ((coindu1079202755ist_of @ a) @ xs2))).
% 2.51/1.59 thf(fact_10__092_060open_062llexord_Ar_A_Illist__of_Axs_J_A_Illist__of_Ays_J_092_060close_062, axiom, ((((coindu300403952lexord @ a) @ r) @ ((coindu1079202755ist_of @ a) @ xs2)) @ ((coindu1079202755ist_of @ a) @ ys))).
% 2.51/1.59 thf(fact_11_lfinite__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: (((coindu1213758845finite @ A) @ ((coindu1079202755ist_of @ A) @ Xs))))).
% 2.51/1.59 thf(fact_12_llast__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coindu2000965700_llast @ A) @ ((coindu1079202755ist_of @ A) @ Xs)) = ((last @ A) @ Xs))))).
% 2.51/1.59 thf(fact_13__092_060open_062lfinite_Azs_092_060close_062, axiom, ((coindu1213758845finite @ a) @ zs2)).
% 2.51/1.59 thf(fact_14__092_060open_062lfinite_Axs_H_092_060close_062, axiom, ((coindu1213758845finite @ a) @ xs3)).
% 2.51/1.59 thf(fact_15_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.51/1.59 thf(fact_16_llexord__refl, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ Xs) @ Xs)))).
% 2.51/1.59 thf(fact_17__092_060open_062llist__of_Axs_A_061_Alappend_Azs_Axs_H_092_060close_062, axiom, (((coindu1079202755ist_of @ a) @ xs2) = (((coindu268472904append @ a) @ zs2) @ xs3))).
% 2.51/1.59 thf(fact_18_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1121789889_LCons @ A) @ Xa) @ X)) @ Ys) = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu268472904append @ A) @ X) @ Ys)))))).
% 2.51/1.59 thf(fact_19_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 2.51/1.59 thf(fact_20_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 2.51/1.59 thf(fact_21_lfinite__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & ((coindu1213758845finite @ A) @ Ys)))))).
% 2.51/1.59 thf(fact_22_llexord__LCons__LCons, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (((X = Y) & ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys)) | ((R @ X) @ Y)))))).
% 2.51/1.59 thf(fact_23_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))) = ((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)))))).
% 2.51/1.59 thf(fact_24_llist__of__list__of, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (((coindu1079202755ist_of @ A) @ ((coindu1736001939ist_of @ A) @ Xs)) = Xs))))).
% 2.51/1.59 thf(fact_25_llast__lappend__LCons, axiom, (! [A:$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))))))).
% 2.51/1.59 thf(fact_26_llexord__code_I3_J, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (((R @ X) @ Y) | ((X = Y) & ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys))))))).
% 2.51/1.59 thf(fact_27_lappend__inf, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.51/1.59 thf(fact_28_lappend__assoc, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs2) = (((coindu268472904append @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs2)))))).
% 2.51/1.59 thf(fact_29_llexord__trans, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) => (((((coindu300403952lexord @ A) @ R) @ Ys) @ Zs2) => ((! [A2:A,B2:A,C:A]: ((((R @ A2) @ B2) => (((R @ B2) @ C) => ((R @ A2) @ C))))) => ((((coindu300403952lexord @ A) @ R) @ Xs) @ Zs2))))))).
% 2.51/1.59 thf(fact_30_llexord__linear, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((! [X2:A,Y2:A]: ((((R @ X2) @ Y2) | ((X2 = Y2) | ((R @ Y2) @ X2))))) => (((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) | ((((coindu300403952lexord @ A) @ R) @ Ys) @ Xs)))))).
% 2.51/1.59 thf(fact_31_llexord__antisym, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) => (((((coindu300403952lexord @ A) @ R) @ Ys) @ Xs) => ((! [A2:A,B2:A]: ((((R @ A2) @ B2) => (~ (((R @ B2) @ A2)))))) => (Xs = Ys))))))).
% 2.51/1.59 thf(fact_32_llexord__LCons__left, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Y3:A,Ys2:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ Y3) @ Ys2)) & (((X = Y3) & ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys2)) | ((R @ X) @ Y3))))))))).
% 2.51/1.59 thf(fact_33_llexord__append__right, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 2.51/1.59 thf(fact_34_llexord__lappend__leftI, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ Ys) @ Zs2) => ((((coindu300403952lexord @ A) @ R) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs2)))))).
% 2.51/1.59 thf(fact_35_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 2.51/1.59 thf(fact_36_llexord__LCons__eq, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: ((((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) => ((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 2.51/1.59 thf(fact_37_llexord__LCons__less, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Y:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((R @ X) @ Y) => ((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 2.51/1.59 thf(fact_38__092_060open_062xs_A_061_Azs_H_A_064_AXS_H_092_060close_062, axiom, (xs2 = (((append @ a) @ zs) @ xs))).
% 2.51/1.59 thf(fact_39__092_060open_062xs_H_A_061_ALNil_A_092_060or_062_Ar_A_Ilhd_Axs_H_J_Ay_092_060close_062, axiom, ((xs3 = (coindu1598213697e_LNil @ a)) | ((r @ ((coindu1046438764le_lhd @ a) @ xs3)) @ y))).
% 2.51/1.59 thf(fact_40_list__of__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => (((coindu1736001939ist_of @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((coindu1736001939ist_of @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_41_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 2.51/1.59 thf(fact_42_list__of__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (((coindu1213758845finite @ A) @ Ys) => (((coindu1736001939ist_of @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((coindu1736001939ist_of @ A) @ Xs)) @ ((coindu1736001939ist_of @ A) @ Ys)))))))).
% 2.51/1.59 thf(fact_43_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [X2:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu268472904append @ A) @ Xs2) @ (((coindu1121789889_LCons @ A) @ X2) @ (coindu1598213697e_LNil @ A)))))))) => (P @ Xs))))))).
% 2.51/1.59 thf(fact_44_llexord__lappend__left, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => ((! [X2:A]: (((((member @ A) @ X2) @ ((coindu1112613586e_lset @ A) @ Xs)) => (~ (((R @ X2) @ X2)))))) => (((((coindu300403952lexord @ A) @ R) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs2)) = ((((coindu300403952lexord @ A) @ R) @ Ys) @ Zs2))))))).
% 2.51/1.59 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.51/1.59 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) = A4)))).
% 2.51/1.59 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.51/1.59 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.51/1.59 thf(fact_49_llexord__lappend__leftD, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs2:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs2)) => (((coindu1213758845finite @ A) @ Xs) => ((! [X2:A]: (((((member @ A) @ X2) @ ((coindu1112613586e_lset @ A) @ Xs)) => (~ (((R @ X2) @ X2)))))) => ((((coindu300403952lexord @ A) @ R) @ Ys) @ Zs2))))))).
% 2.51/1.59 thf(fact_50_split__llist, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (? [Ys3:(coindu1593790203_llist @ A),Zs3:(coindu1593790203_llist @ A)]: (((Xs = (((coindu268472904append @ A) @ Ys3) @ (((coindu1121789889_LCons @ A) @ X) @ Zs3))) & ((coindu1213758845finite @ A) @ Ys3)))))))).
% 2.51/1.59 thf(fact_51_split__llist__first, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (? [Ys3:(coindu1593790203_llist @ A),Zs3:(coindu1593790203_llist @ A)]: (((Xs = (((coindu268472904append @ A) @ Ys3) @ (((coindu1121789889_LCons @ A) @ X) @ Zs3))) & (((coindu1213758845finite @ A) @ Ys3) & (~ ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Ys3)))))))))))).
% 2.51/1.59 thf(fact_52_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (coindu1598213697e_LNil @ A))) = X)))).
% 2.51/1.59 thf(fact_53_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 2.51/1.59 thf(fact_54_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 2.51/1.59 thf(fact_55_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.51/1.59 thf(fact_56_llexord__code_I1_J, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 2.51/1.59 thf(fact_57_lset__lmember, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) = (((coindu567634248member @ A) @ X) @ Xs))))).
% 2.51/1.59 thf(fact_58_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 2.51/1.59 thf(fact_59_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1046438764le_lhd @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X21)))).
% 2.51/1.59 thf(fact_60_llist_Oset__induct, axiom, (! [A:$tType,X:A,A3:(coindu1593790203_llist @ A),P:(A > ((coindu1593790203_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A3)) => ((! [Z1:A,Z2:(coindu1593790203_llist @ A)]: (((P @ Z1) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(coindu1593790203_llist @ A),Xa2:A]: (((((member @ A) @ Xa2) @ ((coindu1112613586e_lset @ A) @ Z2)) => (((P @ Xa2) @ Z2) => ((P @ Xa2) @ (((coindu1121789889_LCons @ A) @ Z1) @ Z2)))))) => ((P @ X) @ A3))))))).
% 2.51/1.59 thf(fact_61_llist_Oset__cases, axiom, (! [A:$tType,E:A,A3:(coindu1593790203_llist @ A)]: (((((member @ A) @ E) @ ((coindu1112613586e_lset @ A) @ A3)) => ((! [Z2:(coindu1593790203_llist @ A)]: ((A3 != (((coindu1121789889_LCons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(coindu1593790203_llist @ A)]: (((A3 = (((coindu1121789889_LCons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((coindu1112613586e_lset @ A) @ Z2)))))))))))))).
% 2.51/1.59 thf(fact_62_lset__induct_H, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X) @ Xs2)))) => ((! [X4:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X4) @ Xs2)))))) => (P @ Xs))))))).
% 2.51/1.59 thf(fact_63_lset__induct, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs2:(coindu1593790203_llist @ A)]: ((P @ (((coindu1121789889_LCons @ A) @ X) @ Xs2)))) => ((! [X4:A,Xs2:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs2)) => ((X != X4) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X4) @ Xs2))))))) => (P @ Xs))))))).
% 2.51/1.59 thf(fact_64_lset__cases, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => ((! [Xs3:(coindu1593790203_llist @ A)]: ((Xs != (((coindu1121789889_LCons @ A) @ X) @ Xs3)))) => (~ ((! [X4:A,Xs3:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ X4) @ Xs3)) => (~ ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs3)))))))))))))).
% 2.51/1.59 thf(fact_65_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coindu1593790203_llist @ A)]: ((((member @ A) @ A1) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A1) @ A22)))))).
% 2.51/1.59 thf(fact_66_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(coindu1593790203_llist @ A),A1:A]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ A22)) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ A1) @ A22))))))).
% 2.51/1.59 thf(fact_67_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 2.51/1.59 thf(fact_68_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),X5:A]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) => (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu1121789889_LCons @ A) @ X5) @ Xs))))))).
% 2.51/1.59 thf(fact_69_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X3:A,Xs4:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs4)))))))).
% 2.51/1.59 thf(fact_70_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 2.51/1.59 thf(fact_71_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 2.51/1.59 thf(fact_72_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.51/1.59 thf(fact_73_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.51/1.59 thf(fact_74_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.51/1.59 thf(fact_75_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.51/1.59 thf(fact_76_llexord__LNil, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 2.51/1.59 thf(fact_77_llexord__conv, axiom, (! [A:$tType]: (((coindu300403952lexord @ A) = (^ [R2:(A > (A > $o)),Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((Xs5 = Ys4) | (? [Zs4:(coindu1593790203_llist @ A),Xs4:(coindu1593790203_llist @ A),Y3:A,Ys2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Zs4) & ((Xs5 = (((coindu268472904append @ A) @ Zs4) @ Xs4)) & ((Ys4 = (((coindu268472904append @ A) @ Zs4) @ (((coindu1121789889_LCons @ A) @ Y3) @ Ys2))) & ((Xs4 = (coindu1598213697e_LNil @ A)) | ((R2 @ ((coindu1046438764le_lhd @ A) @ Xs4)) @ Y3)))))))))))))).
% 2.51/1.59 thf(fact_78_in__lset__lappend__iff, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))) = ((((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Xs)) | (((coindu1213758845finite @ A) @ Xs) & (((member @ A) @ X) @ ((coindu1112613586e_lset @ A) @ Ys)))))))).
% 2.51/1.59 thf(fact_79_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ (coindu1598213697e_LNil @ A)))) @ Ys) = (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 2.51/1.59 thf(fact_80_lfinite_Oinducts, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs2:(coindu1593790203_llist @ A),X2:A]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))) => (P @ X))))))).
% 2.51/1.59 thf(fact_81_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A5:(coindu1593790203_llist @ A)]: (((A5 = (coindu1598213697e_LNil @ A)) | (? [Xs5:(coindu1593790203_llist @ A),X3:A]: (((A5 = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)) & ((coindu1213758845finite @ A) @ Xs5))))))))))).
% 2.51/1.59 thf(fact_82_lfinite_Ocases, axiom, (! [A:$tType,A3:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ A3) => ((A3 != (coindu1598213697e_LNil @ A)) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X2:A]: ((A3 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (~ (((coindu1213758845finite @ A) @ Xs2))))))))))))).
% 2.51/1.59 thf(fact_83_lappend__llist__of__llist__of, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((coindu268472904append @ A) @ ((coindu1079202755ist_of @ A) @ Xs)) @ ((coindu1079202755ist_of @ A) @ Ys)) = ((coindu1079202755ist_of @ A) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.51/1.59 thf(fact_84_llist__of_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((coindu1079202755ist_of @ A) @ (((cons @ A) @ X) @ Xs)) = (((coindu1121789889_LCons @ A) @ X) @ ((coindu1079202755ist_of @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_85_llist__of__eq__LCons__conv, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1079202755ist_of @ A) @ Xs) = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (? [Xs4:(list @ A)]: (((Xs = (((cons @ A) @ Y) @ Xs4)) & (Ys = ((coindu1079202755ist_of @ A) @ Xs4))))))))).
% 2.51/1.59 thf(fact_86_llexord_Ocoinduct, axiom, (! [A:$tType,X6:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A),R:(A > (A > $o))]: ((((X6 @ X) @ Xa) => ((! [X2:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X6 @ X2) @ Xa2) => ((? [Xs6:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ A),Xb:A]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs6)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys5)) & (((X6 @ Xs6) @ Ys5) | ((((coindu300403952lexord @ A) @ R) @ Xs6) @ Ys5)))))) | ((? [Xb:A,Y4:A,Xs6:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ A)]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs6)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Y4) @ Ys5)) & ((R @ Xb) @ Y4))))) | (? [Ys5:(coindu1593790203_llist @ A)]: (((X2 = (coindu1598213697e_LNil @ A)) & (Xa2 = Ys5))))))))) => ((((coindu300403952lexord @ A) @ R) @ X) @ Xa)))))).
% 2.51/1.59 thf(fact_87_llexord_Osimps, axiom, (! [A:$tType]: (((coindu300403952lexord @ A) = (^ [R2:(A > (A > $o)),A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),X3:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)) & ((A23 = (((coindu1121789889_LCons @ A) @ X3) @ Ys4)) & ((((coindu300403952lexord @ A) @ R2) @ Xs5) @ Ys4))))) | ((? [X3:A,Y3:A,Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)) & ((A23 = (((coindu1121789889_LCons @ A) @ Y3) @ Ys4)) & ((R2 @ X3) @ Y3))))) | (? [Ys4:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Ys4)))))))))))).
% 2.51/1.59 thf(fact_88_llexord_Ocases, axiom, (! [A:$tType,R:(A > (A > $o)),A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ A1) @ A22) => ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X2:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) => ((A22 = (((coindu1121789889_LCons @ A) @ X2) @ Ys3)) => (~ (((((coindu300403952lexord @ A) @ R) @ Xs2) @ Ys3))))))) => ((! [X2:A]: (((? [Xs2:(coindu1593790203_llist @ A)]: ((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (! [Y2:A]: (((? [Ys3:(coindu1593790203_llist @ A)]: ((A22 = (((coindu1121789889_LCons @ A) @ Y2) @ Ys3)))) => (~ (((R @ X2) @ Y2))))))))) => (~ (((A1 = (coindu1598213697e_LNil @ A)) => (! [Ys3:(coindu1593790203_llist @ A)]: ((A22 != Ys3)))))))))))).
% 2.51/1.59 thf(fact_89_llexord__code_I2_J, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coindu1593790203_llist @ A)]: ((~ (((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 2.51/1.59 thf(fact_90_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs2)) = (Ys = Zs2))))).
% 2.51/1.59 thf(fact_91_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys = Zs2))))).
% 2.51/1.59 thf(fact_92_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs2)))))).
% 2.51/1.59 thf(fact_93_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.51/1.59 thf(fact_94_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.51/1.59 thf(fact_95_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs2)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs2))))))).
% 2.51/1.59 thf(fact_96_lappend__llist__of__LCons, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ ((coindu1079202755ist_of @ A) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (((coindu268472904append @ A) @ ((coindu1079202755ist_of @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ Y) @ (nil @ A))))) @ Ys))))).
% 2.51/1.59 thf(fact_97_list__of__aux__code_I2_J, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1542816657of_aux @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (((coindu1542816657of_aux @ A) @ (((cons @ A) @ Y) @ Xs)) @ Ys))))).
% 2.51/1.59 thf(fact_98_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.51/1.59 thf(fact_99_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.51/1.59 thf(fact_100_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.51/1.59 thf(fact_101_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_102_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_103_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.51/1.59 thf(fact_104_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.51/1.59 thf(fact_105_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.51/1.59 thf(fact_106_last__appendR, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys)))))).
% 2.51/1.59 thf(fact_107_last__appendL, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_108_list__of__LNil, axiom, (! [A:$tType]: ((((coindu1736001939ist_of @ A) @ (coindu1598213697e_LNil @ A)) = (nil @ A))))).
% 2.51/1.59 thf(fact_109_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.51/1.59 thf(fact_110_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X1))) => ((! [F2:(A > B),A2:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A2)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A2) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.51/1.59 thf(fact_111_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X2) @ Xs2)))))) => (P @ Xs))))))).
% 2.51/1.59 thf(fact_112_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((((X2 = Y2) => (P @ (((cons @ A) @ X2) @ Xs2))) => (((X2 != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 2.51/1.59 thf(fact_113_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X2:A]: ((X != (((cons @ A) @ X2) @ (nil @ A))))) => (~ ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 2.51/1.59 thf(fact_114_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.51/1.59 thf(fact_115_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X2:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X2) @ Xs2)) @ Xss))))))))))).
% 2.51/1.59 thf(fact_116_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.51/1.59 thf(fact_117_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [V:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V) @ Va)) @ (nil @ A)))) => ((! [X2:A,Xs2:(list @ A),Y2:A,Ys3:(list @ A)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys3))))) => ((P @ A0) @ A1))))))).
% 2.51/1.59 thf(fact_118_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X2) @ Xs2)) @ (nil @ B)))) => ((! [Y2:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y2) @ Ys3)))) => ((! [X2:A,Xs2:(list @ A),Y2:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys3))))) => ((P @ Xs) @ Ys)))))))).
% 2.51/1.59 thf(fact_119_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys4:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys4)))))))).
% 2.51/1.59 thf(fact_120_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 2.51/1.59 thf(fact_121_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.51/1.59 thf(fact_122_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.51/1.59 thf(fact_123_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.51/1.59 thf(fact_124_list__of__code, axiom, (! [A:$tType]: (((coindu1736001939ist_of @ A) = ((coindu1542816657of_aux @ A) @ (nil @ A)))))).
% 2.51/1.59 thf(fact_125_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.51/1.59 thf(fact_126_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y2:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y2) @ (nil @ A)))))))))))).
% 2.51/1.59 thf(fact_127_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs2)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs2)) | (? [Ys2:(list @ A)]: ((((((cons @ A) @ X) @ Ys2) = Ys) & (Xs = (((append @ A) @ Ys2) @ Zs2)))))))))).
% 2.51/1.59 thf(fact_128_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs2:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs2) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs2 = (((cons @ A) @ X) @ Xs))) | (? [Ys2:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys2)) & ((((append @ A) @ Ys2) @ Zs2) = Xs))))))))).
% 2.51/1.59 thf(fact_129_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.51/1.59 thf(fact_130_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_131_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X))))).
% 2.51/1.59 thf(fact_132_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_133_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ss:(list @ A),Xs3:(list @ A),Ys6:(list @ A)]: (((Xs = (((append @ A) @ Xs3) @ Ss)) & ((Ys = (((append @ A) @ Ys6) @ Ss)) & ((Xs3 = (nil @ A)) | ((Ys6 = (nil @ A)) | (((last @ A) @ Xs3) != ((last @ A) @ Ys6))))))))))).
% 2.51/1.59 thf(fact_134_last__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs))) & ((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys))))))).
% 2.51/1.59 thf(fact_135_llist__of__eq__LNil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((coindu1079202755ist_of @ A) @ Xs) = (coindu1598213697e_LNil @ A)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_136_llist__of_Osimps_I1_J, axiom, (! [A:$tType]: ((((coindu1079202755ist_of @ A) @ (nil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.51/1.59 thf(fact_137_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.51/1.59 thf(fact_138_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys:(list @ A),Us:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys = (((append @ A) @ Xs1) @ Us)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Us))))))).
% 2.51/1.59 thf(fact_139_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Ts)) = (? [Us2:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us2)) & ((((append @ A) @ Us2) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us2) = Zs2) & (Ys = (((append @ A) @ Us2) @ Ts)))))))))).
% 2.51/1.59 thf(fact_140_longest__common__prefix_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X2:A,Xs2:(list @ A),Y2:A,Ys3:(list @ A)]: ((((X2 = Y2) => ((P @ Xs2) @ Ys3)) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys3))))) => ((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [Uu:(list @ A)]: (((P @ Uu) @ (nil @ A)))) => ((P @ A0) @ A1))))))).
% 2.51/1.59 thf(fact_141_prefixes_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((cons @ A) @ X2) @ Xs2))))) => (P @ A0)))))).
% 2.51/1.59 thf(fact_142_prefixes_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ Xs2)))))))))).
% 2.51/1.59 thf(fact_143_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 2.51/1.59 thf(fact_144_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F) = (((append @ A) @ (F @ X)) @ ((((bind @ B) @ A) @ Xs) @ F)))))).
% 2.51/1.59 thf(fact_145_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F) = (nil @ A))))).
% 2.51/1.59 thf(fact_146_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = Xs)))).
% 2.51/1.59 thf(fact_147_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.51/1.59 thf(fact_148_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((butlast @ A) @ Xs)))))))).
% 2.51/1.59 thf(fact_149_butlast__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = ((butlast @ A) @ Xs))) & ((Ys != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys)))))))).
% 2.51/1.59 thf(fact_150_snoc__eq__iff__butlast, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A)]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = Ys) = ((Ys != (nil @ A)) & ((((butlast @ A) @ Ys) = Xs) & (((last @ A) @ Ys) = X))))))).
% 2.51/1.59 thf(fact_151_prefixes__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((prefixes @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = (((append @ (list @ A)) @ ((prefixes @ A) @ Xs)) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (nil @ (list @ A)))))))).
% 2.51/1.59 thf(fact_152_prefixes__eq__Snoc, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ (list @ A)),X:(list @ A)]: (((((prefixes @ A) @ Ys) = (((append @ (list @ A)) @ Xs) @ (((cons @ (list @ A)) @ X) @ (nil @ (list @ A))))) = ((((Ys = (nil @ A)) & (Xs = (nil @ (list @ A)))) | (? [Z:A,Zs4:(list @ A)]: (((Ys = (((append @ A) @ Zs4) @ (((cons @ A) @ Z) @ (nil @ A)))) & (Xs = ((prefixes @ A) @ Zs4)))))) & (X = Ys)))))).
% 2.51/1.59 thf(fact_153_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.51/1.59 thf(fact_154_prefixes_Osimps_I1_J, axiom, (! [A:$tType]: ((((prefixes @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.51/1.59 thf(fact_155_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.51/1.59 thf(fact_156_llimit__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((P @ (coindu1598213697e_LNil @ A)) => ((! [X2:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))) => (((! [Ys5:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys5) @ Xs) => (P @ Ys5)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.51/1.59 thf(fact_157_prefixes_Oelims, axiom, (! [A:$tType,X:(list @ A),Y:(list @ (list @ A))]: (((((prefixes @ A) @ X) = Y) => (((X = (nil @ A)) => (Y != (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) => (~ ((! [X2:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X2) @ Xs2)) => (Y != (((cons @ (list @ A)) @ (nil @ A)) @ ((((map @ (list @ A)) @ (list @ A)) @ ((cons @ A) @ X2)) @ ((prefixes @ A) @ Xs2)))))))))))))).
% 2.51/1.59 thf(fact_158_Nil__is__map__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((nil @ A) = ((((map @ B) @ A) @ F) @ Xs)) = (Xs = (nil @ B)))))).
% 2.51/1.59 thf(fact_159_map__is__Nil__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: (((((((map @ B) @ A) @ F) @ Xs) = (nil @ A)) = (Xs = (nil @ B)))))).
% 2.51/1.59 thf(fact_160_list_Omap__disc__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A3:(list @ A)]: (((((((map @ A) @ B) @ F) @ A3) = (nil @ B)) = (A3 = (nil @ A)))))).
% 2.51/1.59 thf(fact_161_map__append, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B),Ys:(list @ B)]: ((((((map @ B) @ A) @ F) @ (((append @ B) @ Xs) @ Ys)) = (((append @ A) @ ((((map @ B) @ A) @ F) @ Xs)) @ ((((map @ B) @ A) @ F) @ Ys)))))).
% 2.51/1.59 thf(fact_162_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B),Y:B,Ys:(coindu1593790203_llist @ B)]: (((((coindu574146665prefix @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu574146665prefix @ B) @ Xs) @ Ys)))))).
% 2.51/1.59 thf(fact_163_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu574146665prefix @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A))))))).
% 2.51/1.59 thf(fact_164_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coindu1593790203_llist @ B)]: ((((coindu574146665prefix @ B) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys))))).
% 2.51/1.59 thf(fact_165_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((~ ((((coindu574146665prefix @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) @ (coindu1598213697e_LNil @ B))))))).
% 2.51/1.59 thf(fact_166_llist__less__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((! [Xs2:(coindu1593790203_llist @ A)]: (((! [Ys5:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys5) @ Xs2) => (P @ Ys5)))) => (P @ Xs2)))) => (P @ Xs))))).
% 2.51/1.59 thf(fact_167_map__butlast, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((((map @ B) @ A) @ F) @ ((butlast @ B) @ Xs)) = ((butlast @ A) @ ((((map @ B) @ A) @ F) @ Xs)))))).
% 2.51/1.59 thf(fact_168_list_Osimps_I8_J, axiom, (! [A:$tType,B:$tType,F:(A > B)]: ((((((map @ A) @ B) @ F) @ (nil @ A)) = (nil @ B))))).
% 2.51/1.59 thf(fact_169_list_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:A,X22:(list @ A)]: ((((((map @ A) @ B) @ F) @ (((cons @ A) @ X21) @ X22)) = (((cons @ B) @ (F @ X21)) @ ((((map @ A) @ B) @ F) @ X22)))))).
% 2.51/1.59 thf(fact_170_Cons__eq__map__D, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F:(B > A),Ys:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F) @ Ys)) => (? [Z3:B,Zs3:(list @ B)]: (((Ys = (((cons @ B) @ Z3) @ Zs3)) & ((X = (F @ Z3)) & (Xs = ((((map @ B) @ A) @ F) @ Zs3)))))))))).
% 2.51/1.59 thf(fact_171_map__eq__Cons__D, axiom, (! [B:$tType,A:$tType,F:(B > A),Xs:(list @ B),Y:A,Ys:(list @ A)]: (((((((map @ B) @ A) @ F) @ Xs) = (((cons @ A) @ Y) @ Ys)) => (? [Z3:B,Zs3:(list @ B)]: (((Xs = (((cons @ B) @ Z3) @ Zs3)) & (((F @ Z3) = Y) & (((((map @ B) @ A) @ F) @ Zs3) = Ys))))))))).
% 2.51/1.59 thf(fact_172_Cons__eq__map__conv, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F:(B > A),Ys:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F) @ Ys)) = (? [Z:B,Zs4:(list @ B)]: (((Ys = (((cons @ B) @ Z) @ Zs4)) & ((X = (F @ Z)) & (Xs = ((((map @ B) @ A) @ F) @ Zs4)))))))))).
% 2.51/1.59 thf(fact_173_map__eq__Cons__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B),Y:A,Ys:(list @ A)]: (((((((map @ B) @ A) @ F) @ Xs) = (((cons @ A) @ Y) @ Ys)) = (? [Z:B,Zs4:(list @ B)]: (((Xs = (((cons @ B) @ Z) @ Zs4)) & (((F @ Z) = Y) & (((((map @ B) @ A) @ F) @ Zs4) = Ys))))))))).
% 2.51/1.59 thf(fact_174_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Xs) @ Ys) => ((coindu1213758845finite @ A) @ Xs))))).
% 2.51/1.59 thf(fact_175_last__map, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F:(A > B)]: (((Xs != (nil @ A)) => (((last @ B) @ ((((map @ A) @ B) @ F) @ Xs)) = (F @ ((last @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_176_prefixes_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((prefixes @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ (list @ A)) @ (nil @ A)) @ ((((map @ (list @ A)) @ (list @ A)) @ ((cons @ A) @ X)) @ ((prefixes @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_177_prefixes_Opelims, axiom, (! [A:$tType,X:(list @ A),Y:(list @ (list @ A))]: (((((prefixes @ A) @ X) = Y) => ((((accp @ (list @ A)) @ (prefixes_rel @ A)) @ X) => (((X = (nil @ A)) => ((Y = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A)))) => (~ ((((accp @ (list @ A)) @ (prefixes_rel @ A)) @ (nil @ A)))))) => (~ ((! [X2:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X2) @ Xs2)) => ((Y = (((cons @ (list @ A)) @ (nil @ A)) @ ((((map @ (list @ A)) @ (list @ A)) @ ((cons @ A) @ X2)) @ ((prefixes @ A) @ Xs2)))) => (~ ((((accp @ (list @ A)) @ (prefixes_rel @ A)) @ (((cons @ A) @ X2) @ Xs2)))))))))))))))).
% 2.51/1.59 thf(fact_178_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1571841457prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs4:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs4)) & (((coindu1571841457prefix @ A) @ Xs4) @ Ys))))))))).
% 2.51/1.59 thf(fact_179_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F:(B > (list @ A)),X:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F) @ (((cons @ B) @ X) @ Xs)) = (((append @ A) @ (F @ X)) @ ((((maps @ B) @ A) @ F) @ Xs)))))).
% 2.51/1.59 thf(fact_180_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((maps @ B) @ A) @ F) @ (nil @ B)) = (nil @ A))))).
% 2.51/1.59 thf(fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1571841457prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 2.51/1.59 thf(fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1571841457prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = (Xs = (coindu1598213697e_LNil @ A)))))).
% 2.51/1.59 thf(fact_183_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.51/1.59 thf(fact_184_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.51/1.59 thf(fact_185_map__eq__map__tailrec, axiom, (! [B:$tType,A:$tType]: ((((map @ A) @ B) = ((map_tailrec @ A) @ B))))).
% 2.51/1.59 thf(fact_186_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_187_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 2.51/1.59 thf(fact_188_hd__list__of, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (((hd @ A) @ ((coindu1736001939ist_of @ A) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_189_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 2.51/1.59 thf(fact_190_list__of__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: (((((coindu1213758845finite @ A) @ Xs) => (((coindu1736001939ist_of @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((coindu1736001939ist_of @ A) @ Xs)))) & ((~ (((coindu1213758845finite @ A) @ Xs))) => (((coindu1736001939ist_of @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = (undefined @ (list @ A)))))))).
% 2.51/1.59 thf(fact_191_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_192_lhd__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coindu1046438764le_lhd @ A) @ ((coindu1079202755ist_of @ A) @ Xs)) = ((hd @ A) @ Xs))))).
% 2.51/1.59 thf(fact_193_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X22)) = X21)))).
% 2.51/1.59 thf(fact_194_list_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,A3:(list @ A),F:(A > B)]: (((A3 != (nil @ A)) => (((hd @ B) @ ((((map @ A) @ B) @ F) @ A3)) = (F @ ((hd @ A) @ A3))))))).
% 2.51/1.59 thf(fact_195_hd__map, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F:(A > B)]: (((Xs != (nil @ A)) => (((hd @ B) @ ((((map @ A) @ B) @ F) @ Xs)) = (F @ ((hd @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_196_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ps:(list @ A),Xs3:(list @ A),Ys6:(list @ A)]: (((Xs = (((append @ A) @ Ps) @ Xs3)) & ((Ys = (((append @ A) @ Ps) @ Ys6)) & ((Xs3 = (nil @ A)) | ((Ys6 = (nil @ A)) | (((hd @ A) @ Xs3) != ((hd @ A) @ Ys6))))))))))).
% 2.51/1.59 thf(fact_197_hd__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((Xs = (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Ys))) & ((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys)) = ((hd @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_198_llast__LNil, axiom, (! [A:$tType]: ((((coindu2000965700_llast @ A) @ (coindu1598213697e_LNil @ A)) = (undefined @ A))))).
% 2.51/1.59 thf(fact_199_llast__linfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ Xs) = (undefined @ A)))))).
% 2.51/1.59 thf(fact_200_list__of__aux__def, axiom, (! [A:$tType]: (((coindu1542816657of_aux @ A) = (^ [Xs5:(list @ A),Ys4:(coindu1593790203_llist @ A)]: (((((if @ (list @ A)) @ ((coindu1213758845finite @ A) @ Ys4)) @ (((append @ A) @ ((rev @ A) @ Xs5)) @ ((coindu1736001939ist_of @ A) @ Ys4))) @ (undefined @ (list @ A))))))))).
% 2.51/1.59 thf(fact_201_rotate1__hd__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((rotate1 @ A) @ Xs) = (((append @ A) @ ((tl @ A) @ Xs)) @ (((cons @ A) @ ((hd @ A) @ Xs)) @ (nil @ A)))))))).
% 2.51/1.59 thf(fact_202_rev__rev__ident, axiom, (! [A:$tType,Xs:(list @ A)]: ((((rev @ A) @ ((rev @ A) @ Xs)) = Xs)))).
% 2.51/1.59 thf(fact_203_rev__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((rev @ A) @ Xs) = ((rev @ A) @ Ys)) = (Xs = Ys))))).
% 2.51/1.59 thf(fact_204_Nil__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((rev @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_205_rev__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rev @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_206_rev__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((rev @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((rev @ A) @ Ys)) @ ((rev @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_207_rev__singleton__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((((rev @ A) @ Xs) = (((cons @ A) @ X) @ (nil @ A))) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.51/1.59 thf(fact_208_singleton__rev__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((((cons @ A) @ X) @ (nil @ A)) = ((rev @ A) @ Xs)) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.51/1.59 thf(fact_209_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys)))))).
% 2.51/1.59 thf(fact_210_rev__eq__Cons__iff, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((rev @ A) @ Xs) = (((cons @ A) @ Y) @ Ys)) = (Xs = (((append @ A) @ ((rev @ A) @ Ys)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.51/1.59 thf(fact_211_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.51/1.59 thf(fact_212_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.51/1.59 thf(fact_213_map__tl, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((((map @ B) @ A) @ F) @ ((tl @ B) @ Xs)) = ((tl @ A) @ ((((map @ B) @ A) @ F) @ Xs)))))).
% 2.51/1.59 thf(fact_214_rev__map, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((rev @ A) @ ((((map @ B) @ A) @ F) @ Xs)) = ((((map @ B) @ A) @ F) @ ((rev @ B) @ Xs)))))).
% 2.51/1.59 thf(fact_215_rev__swap, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((rev @ A) @ Xs) = Ys) = (Xs = ((rev @ A) @ Ys)))))).
% 2.51/1.59 thf(fact_216_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.51/1.59 thf(fact_217_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X22)) = X22)))).
% 2.51/1.59 thf(fact_218_butlast__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((tl @ A) @ Xs)) = ((tl @ A) @ ((butlast @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_219_rev_Osimps_I1_J, axiom, (! [A:$tType]: ((((rev @ A) @ (nil @ A)) = (nil @ A))))).
% 2.51/1.59 thf(fact_220_list_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,A3:(list @ A),F:(A > B)]: (((A3 != (nil @ A)) => (((tl @ B) @ ((((map @ A) @ B) @ F) @ A3)) = ((((map @ A) @ B) @ F) @ ((tl @ A) @ A3))))))).
% 2.51/1.59 thf(fact_221_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.51/1.59 thf(fact_222_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X3:A]: ((Xs = (((cons @ A) @ X3) @ (nil @ A)))))))))).
% 2.51/1.59 thf(fact_223_list_Oexpand, axiom, (! [A:$tType,List:(list @ A),List2:(list @ A)]: ((((List = (nil @ A)) = (List2 = (nil @ A))) => (((List != (nil @ A)) => ((List2 != (nil @ A)) => ((((hd @ A) @ List) = ((hd @ A) @ List2)) & (((tl @ A) @ List) = ((tl @ A) @ List2))))) => (List = List2)))))).
% 2.51/1.59 thf(fact_224_last__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((Xs = (nil @ A)) | (((tl @ A) @ Xs) != (nil @ A))) => (((last @ A) @ ((tl @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_225_list__of__aux__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((coindu1542816657of_aux @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((rev @ A) @ Xs))))).
% 2.51/1.59 thf(fact_226_rev_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rev @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ ((rev @ A) @ Xs)) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.51/1.59 thf(fact_227_hd__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ ((rev @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_228_last__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ ((rev @ A) @ Xs)) = ((hd @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_229_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.51/1.59 thf(fact_230_map__tailrec__def, axiom, (! [B:$tType,A:$tType]: ((((map_tailrec @ A) @ B) = (^ [F3:(A > B),As2:(list @ A)]: (((rev @ B) @ (((((map_tailrec_rev @ A) @ B) @ F3) @ As2) @ (nil @ B))))))))).
% 2.51/1.59 thf(fact_231_list_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > ((list @ A) > B)),List:(list @ A)]: (((P @ (((((case_list @ B) @ A) @ F1) @ F22) @ List)) = (~ ((((List = (nil @ A)) & (~ ((P @ F1)))) | ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) & (~ ((P @ ((F22 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))))))).
% 2.51/1.59 thf(fact_232_map__tailrec__rev_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,F:(A > B),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F) @ (nil @ A)) @ Bs2) = Bs2)))).
% 2.51/1.59 thf(fact_233_map__tailrec__rev_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,F:(A > B),A3:A,As3:(list @ A),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F) @ (((cons @ A) @ A3) @ As3)) @ Bs2) = (((((map_tailrec_rev @ A) @ B) @ F) @ As3) @ (((cons @ B) @ (F @ A3)) @ Bs2)))))).
% 2.51/1.59 thf(fact_234_list_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F22:(A > ((list @ A) > B))]: (((((((case_list @ B) @ A) @ F1) @ F22) @ (nil @ A)) = F1)))).
% 2.51/1.59 thf(fact_235_list_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > ((list @ A) > B)),X21:A,X22:(list @ A)]: (((((((case_list @ B) @ A) @ F1) @ F22) @ (((cons @ A) @ X21) @ X22)) = ((F22 @ X21) @ X22))))).
% 2.51/1.59 thf(fact_236_map__tailrec__rev_Oelims, axiom, (! [A:$tType,B:$tType,X:(A > B),Xa:(list @ A),Xb2:(list @ B),Y:(list @ B)]: ((((((((map_tailrec_rev @ A) @ B) @ X) @ Xa) @ Xb2) = Y) => (((Xa = (nil @ A)) => (Y != Xb2)) => (~ ((! [A2:A,As:(list @ A)]: (((Xa = (((cons @ A) @ A2) @ As)) => (Y != (((((map_tailrec_rev @ A) @ B) @ X) @ As) @ (((cons @ B) @ (X @ A2)) @ Xb2))))))))))))).
% 2.51/1.59 thf(fact_237_list_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_list @ B) @ A) = (^ [F12:B,F23:(A > ((list @ A) > B)),List3:(list @ A)]: (((((if @ B) @ (List3 = (nil @ A))) @ F12) @ ((F23 @ ((hd @ A) @ List3)) @ ((tl @ A) @ List3))))))))).
% 2.51/1.59 thf(fact_238_map__tailrec__rev, axiom, (! [A:$tType,B:$tType]: ((((map_tailrec_rev @ B) @ A) = (^ [F3:(B > A),As2:(list @ B)]: (((append @ A) @ ((rev @ A) @ ((((map @ B) @ A) @ F3) @ As2))))))))).
% 2.51/1.59 thf(fact_239_list_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F22:(A > ((list @ A) > B)),List:(list @ A)]: (((P @ (((((case_list @ B) @ A) @ F1) @ F22) @ List)) = (((List = (nil @ A)) => (P @ F1)) & ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) => (P @ ((F22 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))).
% 2.51/1.59 thf(fact_240_remdups__adj__append, axiom, (! [A:$tType,Xs_1:(list @ A),X:A,Xs_2:(list @ A)]: ((((remdups_adj @ A) @ (((append @ A) @ Xs_1) @ (((cons @ A) @ X) @ Xs_2))) = (((append @ A) @ ((remdups_adj @ A) @ (((append @ A) @ Xs_1) @ (((cons @ A) @ X) @ (nil @ A))))) @ ((tl @ A) @ ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs_2)))))))).
% 2.51/1.59 thf(fact_241_llast__lappend, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Ys) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu2000965700_llast @ A) @ Xs))) & ((~ (((coindu335574135_lnull @ A) @ Ys))) => ((((coindu1213758845finite @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu2000965700_llast @ A) @ Ys))) & ((~ (((coindu1213758845finite @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 2.51/1.59 thf(fact_242_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.51/1.59 thf(fact_243_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 2.51/1.59 thf(fact_244_remdups__adj__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A)]: (((((remdups_adj @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_245_llexord__LNil__right, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => (((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_246_remdups__adj__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((remdups_adj @ A) @ ((rev @ A) @ Xs)) = ((rev @ A) @ ((remdups_adj @ A) @ Xs)))))).
% 2.51/1.59 thf(fact_247_hd__remdups__adj, axiom, (! [A:$tType,Xs:(list @ A)]: ((((hd @ A) @ ((remdups_adj @ A) @ Xs)) = ((hd @ A) @ Xs))))).
% 2.51/1.59 thf(fact_248_lnull__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coindu335574135_lnull @ A) @ ((coindu1079202755ist_of @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.51/1.59 thf(fact_249_lhd__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu1046438764le_lhd @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1046438764le_lhd @ A) @ Ys))) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_250_remdups__adj__Cons__alt, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ ((tl @ A) @ ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs)))) = ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs)))))).
% 2.51/1.59 thf(fact_251_llast__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = X)) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu2000965700_llast @ A) @ Xs))))))).
% 2.51/1.59 thf(fact_252_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.51/1.59 thf(fact_253_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)))))))).
% 2.51/1.59 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.51/1.59 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.51/1.59 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.51/1.59 thf(conj_0, hypothesis, (! [YS:(list @ a)]: (((ys2 = ((coindu1079202755ist_of @ a) @ YS)) => thesis)))).
% 2.51/1.59 thf(conj_1, conjecture, thesis).
% 2.51/1.59 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.SSpVV69JSc/DTF2DTF1697.p
% 2.51/1.59 ------------------------
% 2.79/1.63 ---- Cleaned THF ---
% 2.79/1.63 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 2.79/1.63 coindu1593790203_llist: $tType > $tType ).
% 2.79/1.63
% 2.79/1.63 thf(ty_t_List_Olist,type,
% 2.79/1.63 list: $tType > $tType ).
% 2.79/1.63
% 2.79/1.63 thf(ty_t_Set_Oset,type,
% 2.79/1.63 set: $tType > $tType ).
% 2.79/1.63
% 2.79/1.63 thf(ty_t_itself,type,
% 2.79/1.63 itself: $tType > $tType ).
% 2.79/1.63
% 2.79/1.63 thf(ty_tf_a,type,
% 2.79/1.63 a: $tType ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix,type,
% 2.79/1.63 coindu1571841457prefix:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 2.79/1.63 coindu268472904append:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 2.79/1.63 coindu1213758845finite:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of,type,
% 2.79/1.63 coindu1736001939ist_of:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olist__of__aux,type,
% 2.79/1.63 coindu1542816657of_aux:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast,type,
% 2.79/1.63 coindu2000965700_llast:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 2.79/1.63 coindu300403952lexord:
% 2.79/1.63 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 2.79/1.63 coindu1121789889_LCons:
% 2.79/1.63 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 2.79/1.63 coindu1598213697e_LNil:
% 2.79/1.63 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 2.79/1.63 coindu1046438764le_lhd:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 2.79/1.63 coindu335574135_lnull:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olset,type,
% 2.79/1.63 coindu1112613586e_lset:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist__of,type,
% 2.79/1.63 coindu1079202755ist_of:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 2.79/1.63 coindu567634248member:
% 2.79/1.63 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 2.79/1.63 coindu574146665prefix:
% 2.79/1.63 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_HOL_Oundefined,type,
% 2.79/1.63 undefined:
% 2.79/1.63 !>[A: $tType] : A ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_If,type,
% 2.79/1.63 if:
% 2.79/1.63 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Oappend,type,
% 2.79/1.63 append:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Obind,type,
% 2.79/1.63 bind:
% 2.79/1.63 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Obutlast,type,
% 2.79/1.63 butlast:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Oinsert,type,
% 2.79/1.63 insert:
% 2.79/1.63 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olast,type,
% 2.79/1.63 last:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist_OCons,type,
% 2.79/1.63 cons:
% 2.79/1.63 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist_ONil,type,
% 2.79/1.63 nil:
% 2.79/1.63 !>[A: $tType] : ( list @ A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist_Ocase__list,type,
% 2.79/1.63 case_list:
% 2.79/1.63 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist_Ohd,type,
% 2.79/1.63 hd:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist_Omap,type,
% 2.79/1.63 map:
% 2.79/1.63 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist_Otl,type,
% 2.79/1.63 tl:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Olist__ex1,type,
% 2.79/1.63 list_ex1:
% 2.79/1.63 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Omap__tailrec,type,
% 2.79/1.63 map_tailrec:
% 2.79/1.63 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Omap__tailrec__rev,type,
% 2.79/1.63 map_tailrec_rev:
% 2.79/1.63 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Omaps,type,
% 2.79/1.63 maps:
% 2.79/1.63 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Oproduct__lists,type,
% 2.79/1.63 product_lists:
% 2.79/1.63 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Oremdups__adj,type,
% 2.79/1.63 remdups_adj:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Orev,type,
% 2.79/1.63 rev:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Orotate1,type,
% 2.79/1.63 rotate1:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_List_Osublists,type,
% 2.79/1.63 sublists:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Pure_Otype,type,
% 2.79/1.63 type:
% 2.79/1.63 !>[A: $tType] : ( itself @ A ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Set_OCollect,type,
% 2.79/1.63 collect:
% 2.79/1.63 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Sublist_Oprefixes,type,
% 2.79/1.63 prefixes:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Sublist_Oprefixes__rel,type,
% 2.79/1.63 prefixes_rel:
% 2.79/1.63 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_Wellfounded_Oaccp,type,
% 2.79/1.63 accp:
% 2.79/1.63 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_c_member,type,
% 2.79/1.63 member:
% 2.79/1.63 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_XS_H____,type,
% 2.79/1.63 xs: list @ a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_r,type,
% 2.79/1.63 r: a > a > $o ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_thesis____,type,
% 2.79/1.63 thesis: $o ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_xs,type,
% 2.79/1.63 xs2: list @ a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_xs_H____,type,
% 2.79/1.63 xs3: coindu1593790203_llist @ a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_y____,type,
% 2.79/1.63 y: a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_ys,type,
% 2.79/1.63 ys: list @ a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_ys_H____,type,
% 2.79/1.63 ys2: coindu1593790203_llist @ a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_zs_H____,type,
% 2.79/1.63 zs: list @ a ).
% 2.79/1.63
% 2.79/1.63 thf(sy_v_zs____,type,
% 2.79/1.63 zs2: coindu1593790203_llist @ a ).
% 2.79/1.63
% 2.79/1.63 thf(fact_0_llist__of__inject,axiom,
% 2.79/1.63 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.63 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 2.79/1.63 = ( coindu1079202755ist_of @ A @ Ys ) )
% 2.79/1.63 = ( Xs = Ys ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062zs_H_O_Azs_A_061_Allist__of_Azs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.79/1.63 ~ ! [Zs: list @ a] :
% 2.79/1.63 ( zs2
% 2.79/1.63 != ( coindu1079202755ist_of @ a @ Zs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.79/1.63 ~ ! [XS: list @ a] :
% 2.79/1.63 ( xs3
% 2.79/1.63 != ( coindu1079202755ist_of @ a @ XS ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_3__092_060open_062lfinite_Ays_H_092_060close_062,axiom,
% 2.79/1.63 coindu1213758845finite @ a @ ys2 ).
% 2.79/1.63
% 2.79/1.63 thf(fact_4_list__of__llist__of,axiom,
% 2.79/1.63 ! [A: $tType,Xs: list @ A] :
% 2.79/1.63 ( ( coindu1736001939ist_of @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 2.79/1.63 = Xs ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_5__092_060open_062zs_A_061_Allist__of_Azs_H_092_060close_062,axiom,
% 2.79/1.63 ( zs2
% 2.79/1.63 = ( coindu1079202755ist_of @ a @ zs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_6__092_060open_062llist__of_Ays_A_061_Alappend_Azs_A_ILCons_Ay_Ays_H_J_092_060close_062,axiom,
% 2.79/1.63 ( ( coindu1079202755ist_of @ a @ ys )
% 2.79/1.63 = ( coindu268472904append @ a @ zs2 @ ( coindu1121789889_LCons @ a @ y @ ys2 ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_7__092_060open_062xs_H_A_061_Allist__of_AXS_H_092_060close_062,axiom,
% 2.79/1.63 ( xs3
% 2.79/1.63 = ( coindu1079202755ist_of @ a @ xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_8__092_060open_062lfinite_A_Illist__of_Ays_J_092_060close_062,axiom,
% 2.79/1.63 coindu1213758845finite @ a @ ( coindu1079202755ist_of @ a @ ys ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_9__092_060open_062lfinite_A_Illist__of_Axs_J_092_060close_062,axiom,
% 2.79/1.63 coindu1213758845finite @ a @ ( coindu1079202755ist_of @ a @ xs2 ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_10__092_060open_062llexord_Ar_A_Illist__of_Axs_J_A_Illist__of_Ays_J_092_060close_062,axiom,
% 2.79/1.63 coindu300403952lexord @ a @ r @ ( coindu1079202755ist_of @ a @ xs2 ) @ ( coindu1079202755ist_of @ a @ ys ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_11_lfinite__llist__of,axiom,
% 2.79/1.63 ! [A: $tType,Xs: list @ A] : ( coindu1213758845finite @ A @ ( coindu1079202755ist_of @ A @ Xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_12_llast__llist__of,axiom,
% 2.79/1.63 ! [A: $tType,Xs: list @ A] :
% 2.79/1.63 ( ( coindu2000965700_llast @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 2.79/1.63 = ( last @ A @ Xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_13__092_060open_062lfinite_Azs_092_060close_062,axiom,
% 2.79/1.63 coindu1213758845finite @ a @ zs2 ).
% 2.79/1.63
% 2.79/1.63 thf(fact_14__092_060open_062lfinite_Axs_H_092_060close_062,axiom,
% 2.79/1.63 coindu1213758845finite @ a @ xs3 ).
% 2.79/1.63
% 2.79/1.63 thf(fact_15_llist_Oinject,axiom,
% 2.79/1.63 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 2.79/1.63 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 2.79/1.63 = ( ( X21 = Y21 )
% 2.79/1.63 & ( X22 = Y22 ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_16_llexord__refl,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ Xs ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_17__092_060open_062llist__of_Axs_A_061_Alappend_Azs_Axs_H_092_060close_062,axiom,
% 2.79/1.63 ( ( coindu1079202755ist_of @ a @ xs2 )
% 2.79/1.63 = ( coindu268472904append @ a @ zs2 @ xs3 ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_18_lappend__code_I2_J,axiom,
% 2.79/1.63 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 2.79/1.63 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_19_lfinite__code_I2_J,axiom,
% 2.79/1.63 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 2.79/1.63 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 2.79/1.63 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_20_lfinite__LCons,axiom,
% 2.79/1.63 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.79/1.63 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_21_lfinite__lappend,axiom,
% 2.79/1.63 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.63 = ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.63 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_22_llexord__LCons__LCons,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.63 = ( ( ( X = Y )
% 2.79/1.63 & ( coindu300403952lexord @ A @ R @ Xs @ Ys ) )
% 2.79/1.63 | ( R @ X @ Y ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_23_llast__LCons2,axiom,
% 2.79/1.63 ! [A: $tType,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 2.79/1.63 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_24_llist__of__list__of,axiom,
% 2.79/1.63 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.63 => ( ( coindu1079202755ist_of @ A @ ( coindu1736001939ist_of @ A @ Xs ) )
% 2.79/1.63 = Xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_25_llast__lappend__LCons,axiom,
% 2.79/1.63 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.63 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) )
% 2.79/1.63 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_26_llexord__code_I3_J,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.63 = ( ( R @ X @ Y )
% 2.79/1.63 | ( ( X = Y )
% 2.79/1.63 & ( coindu300403952lexord @ A @ R @ Xs @ Ys ) ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_27_lappend__inf,axiom,
% 2.79/1.63 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.79/1.63 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.79/1.63 = Xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_28_lappend__assoc,axiom,
% 2.79/1.63 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs2 )
% 2.79/1.63 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs2 ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_29_llexord__trans,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.79/1.63 => ( ( coindu300403952lexord @ A @ R @ Ys @ Zs2 )
% 2.79/1.63 => ( ! [A2: A,B2: A,C: A] :
% 2.79/1.63 ( ( R @ A2 @ B2 )
% 2.79/1.63 => ( ( R @ B2 @ C )
% 2.79/1.63 => ( R @ A2 @ C ) ) )
% 2.79/1.63 => ( coindu300403952lexord @ A @ R @ Xs @ Zs2 ) ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_30_llexord__linear,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ! [X2: A,Y2: A] :
% 2.79/1.63 ( ( R @ X2 @ Y2 )
% 2.79/1.63 | ( X2 = Y2 )
% 2.79/1.63 | ( R @ Y2 @ X2 ) )
% 2.79/1.63 => ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.79/1.63 | ( coindu300403952lexord @ A @ R @ Ys @ Xs ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_31_llexord__antisym,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.79/1.63 => ( ( coindu300403952lexord @ A @ R @ Ys @ Xs )
% 2.79/1.63 => ( ! [A2: A,B2: A] :
% 2.79/1.63 ( ( R @ A2 @ B2 )
% 2.79/1.63 => ~ ( R @ B2 @ A2 ) )
% 2.79/1.63 => ( Xs = Ys ) ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_32_llexord__LCons__left,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 2.79/1.63 = ( ? [Y3: A,Ys2: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( Ys
% 2.79/1.63 = ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) )
% 2.79/1.63 & ( ( ( X = Y3 )
% 2.79/1.63 & ( coindu300403952lexord @ A @ R @ Xs @ Ys2 ) )
% 2.79/1.63 | ( R @ X @ Y3 ) ) ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_33_llexord__append__right,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_34_llexord__lappend__leftI,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ Ys @ Zs2 )
% 2.79/1.63 => ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs2 ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_35_lfinite__LConsI,axiom,
% 2.79/1.63 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.79/1.63 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.63 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_36_llexord__LCons__eq,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 2.79/1.63 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.79/1.63 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_37_llexord__LCons__less,axiom,
% 2.79/1.63 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.63 ( ( R @ X @ Y )
% 2.79/1.63 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_38__092_060open_062xs_A_061_Azs_H_A_064_AXS_H_092_060close_062,axiom,
% 2.79/1.63 ( xs2
% 2.79/1.63 = ( append @ a @ zs @ xs ) ) ).
% 2.79/1.63
% 2.79/1.63 thf(fact_39__092_060open_062xs_H_A_061_ALNil_A_092_060or_062_Ar_A_Ilhd_Axs_H_J_Ay_092_060close_062,axiom,
% 2.79/1.63 ( ( xs3
% 2.79/1.63 = ( coindu1598213697e_LNil @ a ) )
% 2.79/1.64 | ( r @ ( coindu1046438764le_lhd @ a @ xs3 ) @ y ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_40_list__of__LCons,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu1736001939ist_of @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.79/1.64 = ( cons @ A @ X @ ( coindu1736001939ist_of @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_41_lmember__code_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( ( X = Y )
% 2.79/1.64 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_42_list__of__lappend,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu1213758845finite @ A @ Ys )
% 2.79/1.64 => ( ( coindu1736001939ist_of @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( append @ A @ ( coindu1736001939ist_of @ A @ Xs ) @ ( coindu1736001939ist_of @ A @ Ys ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_43_lfinite__rev__induct,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( coindu268472904append @ A @ Xs2 @ ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_44_llexord__lappend__left,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,R: A > A > $o,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ! [X2: A] :
% 2.79/1.64 ( ( member @ A @ X2 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ~ ( R @ X2 @ X2 ) )
% 2.79/1.64 => ( ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs2 ) )
% 2.79/1.64 = ( coindu300403952lexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_45_mem__Collect__eq,axiom,
% 2.79/1.64 ! [A: $tType,A3: A,P: A > $o] :
% 2.79/1.64 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.79/1.64 = ( P @ A3 ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_46_Collect__mem__eq,axiom,
% 2.79/1.64 ! [A: $tType,A4: set @ A] :
% 2.79/1.64 ( ( collect @ A
% 2.79/1.64 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 2.79/1.64 = A4 ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_47_Collect__cong,axiom,
% 2.79/1.64 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.79/1.64 ( ! [X2: A] :
% 2.79/1.64 ( ( P @ X2 )
% 2.79/1.64 = ( Q @ X2 ) )
% 2.79/1.64 => ( ( collect @ A @ P )
% 2.79/1.64 = ( collect @ A @ Q ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_48_ext,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.79/1.64 ( ! [X2: A] :
% 2.79/1.64 ( ( F @ X2 )
% 2.79/1.64 = ( G @ X2 ) )
% 2.79/1.64 => ( F = G ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_49_llexord__lappend__leftD,axiom,
% 2.79/1.64 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs2 ) )
% 2.79/1.64 => ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ! [X2: A] :
% 2.79/1.64 ( ( member @ A @ X2 @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ~ ( R @ X2 @ X2 ) )
% 2.79/1.64 => ( coindu300403952lexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_50_split__llist,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ? [Ys3: coindu1593790203_llist @ A,Zs3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs3 ) ) )
% 2.79/1.64 & ( coindu1213758845finite @ A @ Ys3 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_51_split__llist__first,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ? [Ys3: coindu1593790203_llist @ A,Zs3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( coindu268472904append @ A @ Ys3 @ ( coindu1121789889_LCons @ A @ X @ Zs3 ) ) )
% 2.79/1.64 & ( coindu1213758845finite @ A @ Ys3 )
% 2.79/1.64 & ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys3 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_52_llast__singleton,axiom,
% 2.79/1.64 ! [A: $tType,X: A] :
% 2.79/1.64 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) )
% 2.79/1.64 = X ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_53_lappend__LNil2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = Xs ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_54_lappend__code_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 2.79/1.64 = Ys ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_55_lfinite__code_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_56_llexord__code_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_57_lset__lmember,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 = ( coindu567634248member @ A @ X @ Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_58_lmember__code_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A] :
% 2.79/1.64 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_59_lhd__LCons,axiom,
% 2.79/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.79/1.64 = X21 ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_60_llist_Oset__induct,axiom,
% 2.79/1.64 ! [A: $tType,X: A,A3: coindu1593790203_llist @ A,P: A > ( coindu1593790203_llist @ A ) > $o] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A3 ) )
% 2.79/1.64 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A] : ( P @ Z1 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 2.79/1.64 => ( ! [Z1: A,Z2: coindu1593790203_llist @ A,Xa2: A] :
% 2.79/1.64 ( ( member @ A @ Xa2 @ ( coindu1112613586e_lset @ A @ Z2 ) )
% 2.79/1.64 => ( ( P @ Xa2 @ Z2 )
% 2.79/1.64 => ( P @ Xa2 @ ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) ) ) )
% 2.79/1.64 => ( P @ X @ A3 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_61_llist_Oset__cases,axiom,
% 2.79/1.64 ! [A: $tType,E: A,A3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ E @ ( coindu1112613586e_lset @ A @ A3 ) )
% 2.79/1.64 => ( ! [Z2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( A3
% 2.79/1.64 != ( coindu1121789889_LCons @ A @ E @ Z2 ) )
% 2.79/1.64 => ~ ! [Z1: A,Z2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( A3
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Z1 @ Z2 ) )
% 2.79/1.64 => ~ ( member @ A @ E @ ( coindu1112613586e_lset @ A @ Z2 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_62_lset__induct_H,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 2.79/1.64 => ( ! [X4: A,Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X4 @ Xs2 ) ) ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_63_lset__induct,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ( ! [Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X @ Xs2 ) )
% 2.79/1.64 => ( ! [X4: A,Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs2 ) )
% 2.79/1.64 => ( ( X != X4 )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X4 @ Xs2 ) ) ) ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_64_lset__cases,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ( ! [Xs3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( Xs
% 2.79/1.64 != ( coindu1121789889_LCons @ A @ X @ Xs3 ) )
% 2.79/1.64 => ~ ! [X4: A,Xs3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X4 @ Xs3 ) )
% 2.79/1.64 => ~ ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs3 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_65_llist_Oset__intros_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,A1: A,A22: coindu1593790203_llist @ A] : ( member @ A @ A1 @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_66_llist_Oset__intros_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,A22: coindu1593790203_llist @ A,A1: A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ A22 ) )
% 2.79/1.64 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_67_lset__intros_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_68_lset__intros_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,X5: A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 => ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_69_neq__LNil__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( ? [X3: A,Xs4: coindu1593790203_llist @ A] :
% 2.79/1.64 ( Xs
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_70_llist_Oexhaust,axiom,
% 2.79/1.64 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Y
% 2.79/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 2.79/1.64 ( Y
% 2.79/1.64 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_71_llist_Odistinct_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1598213697e_LNil @ A )
% 2.79/1.64 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_72_lappend__eq__LNil__iff,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_73_LNil__eq__lappend__iff,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ( coindu1598213697e_LNil @ A )
% 2.79/1.64 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_74_lappend__LNil__LNil,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_75_lfinite__LNil,axiom,
% 2.79/1.64 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_76_llexord__LNil,axiom,
% 2.79/1.64 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_77_llexord__conv,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu300403952lexord @ A )
% 2.79/1.64 = ( ^ [R2: A > A > $o,Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Xs5 = Ys4 )
% 2.79/1.64 | ? [Zs4: coindu1593790203_llist @ A,Xs4: coindu1593790203_llist @ A,Y3: A,Ys2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Zs4 )
% 2.79/1.64 & ( Xs5
% 2.79/1.64 = ( coindu268472904append @ A @ Zs4 @ Xs4 ) )
% 2.79/1.64 & ( Ys4
% 2.79/1.64 = ( coindu268472904append @ A @ Zs4 @ ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) ) )
% 2.79/1.64 & ( ( Xs4
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 | ( R2 @ ( coindu1046438764le_lhd @ A @ Xs4 ) @ Y3 ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_78_in__lset__lappend__iff,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 2.79/1.64 = ( ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Xs ) )
% 2.79/1.64 | ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 & ( member @ A @ X @ ( coindu1112613586e_lset @ A @ Ys ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_79_lappend__snocL1__conv__LCons2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 2.79/1.64 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_80_lfinite_Oinducts,axiom,
% 2.79/1.64 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ X )
% 2.79/1.64 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.79/1.64 => ( P @ X ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_81_lfinite_Osimps,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu1213758845finite @ A )
% 2.79/1.64 = ( ^ [A5: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( A5
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 | ? [Xs5: coindu1593790203_llist @ A,X3: A] :
% 2.79/1.64 ( ( A5
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 2.79/1.64 & ( coindu1213758845finite @ A @ Xs5 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_82_lfinite_Ocases,axiom,
% 2.79/1.64 ! [A: $tType,A3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ A3 )
% 2.79/1.64 => ( ( A3
% 2.79/1.64 != ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ? [X2: A] :
% 2.79/1.64 ( A3
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.79/1.64 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_83_lappend__llist__of__llist__of,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( coindu268472904append @ A @ ( coindu1079202755ist_of @ A @ Xs ) @ ( coindu1079202755ist_of @ A @ Ys ) )
% 2.79/1.64 = ( coindu1079202755ist_of @ A @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_84_llist__of_Osimps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( coindu1079202755ist_of @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X @ ( coindu1079202755ist_of @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_85_llist__of__eq__LCons__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( ? [Xs4: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( cons @ A @ Y @ Xs4 ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( coindu1079202755ist_of @ A @ Xs4 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_86_llexord_Ocoinduct,axiom,
% 2.79/1.64 ! [A: $tType,X6: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R: A > A > $o] :
% 2.79/1.64 ( ( X6 @ X @ Xa )
% 2.79/1.64 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( X6 @ X2 @ Xa2 )
% 2.79/1.64 => ( ? [Xs6: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 2.79/1.64 ( ( X2
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Xb @ Xs6 ) )
% 2.79/1.64 & ( Xa2
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 2.79/1.64 & ( ( X6 @ Xs6 @ Ys5 )
% 2.79/1.64 | ( coindu300403952lexord @ A @ R @ Xs6 @ Ys5 ) ) )
% 2.79/1.64 | ? [Xb: A,Y4: A,Xs6: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( X2
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Xb @ Xs6 ) )
% 2.79/1.64 & ( Xa2
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Y4 @ Ys5 ) )
% 2.79/1.64 & ( R @ Xb @ Y4 ) )
% 2.79/1.64 | ? [Ys5: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( X2
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 & ( Xa2 = Ys5 ) ) ) )
% 2.79/1.64 => ( coindu300403952lexord @ A @ R @ X @ Xa ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_87_llexord_Osimps,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu300403952lexord @ A )
% 2.79/1.64 = ( ^ [R2: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ? [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 2.79/1.64 ( ( A12
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 2.79/1.64 & ( A23
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 2.79/1.64 & ( coindu300403952lexord @ A @ R2 @ Xs5 @ Ys4 ) )
% 2.79/1.64 | ? [X3: A,Y3: A,Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( A12
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 2.79/1.64 & ( A23
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Y3 @ Ys4 ) )
% 2.79/1.64 & ( R2 @ X3 @ Y3 ) )
% 2.79/1.64 | ? [Ys4: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( A12
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 & ( A23 = Ys4 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_88_llexord_Ocases,axiom,
% 2.79/1.64 ! [A: $tType,R: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu300403952lexord @ A @ R @ A1 @ A22 )
% 2.79/1.64 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 2.79/1.64 ( ( A1
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.79/1.64 => ( ( A22
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 2.79/1.64 => ~ ( coindu300403952lexord @ A @ R @ Xs2 @ Ys3 ) ) )
% 2.79/1.64 => ( ! [X2: A] :
% 2.79/1.64 ( ? [Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( A1
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.79/1.64 => ! [Y2: A] :
% 2.79/1.64 ( ? [Ys3: coindu1593790203_llist @ A] :
% 2.79/1.64 ( A22
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Y2 @ Ys3 ) )
% 2.79/1.64 => ~ ( R @ X2 @ Y2 ) ) )
% 2.79/1.64 => ~ ( ( A1
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 => ! [Ys3: coindu1593790203_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_89_llexord__code_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ~ ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_90_same__append__eq,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ Ys )
% 2.79/1.64 = ( append @ A @ Xs @ Zs2 ) )
% 2.79/1.64 = ( Ys = Zs2 ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_91_append__same__eq,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Ys @ Xs )
% 2.79/1.64 = ( append @ A @ Zs2 @ Xs ) )
% 2.79/1.64 = ( Ys = Zs2 ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_92_append__assoc,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.79/1.64 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 2.79/1.64 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_93_list_Oinject,axiom,
% 2.79/1.64 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.79/1.64 ( ( ( cons @ A @ X21 @ X22 )
% 2.79/1.64 = ( cons @ A @ Y21 @ Y22 ) )
% 2.79/1.64 = ( ( X21 = Y21 )
% 2.79/1.64 & ( X22 = Y22 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_94_append__Cons,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.79/1.64 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_95_Cons__eq__appendI,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.79/1.64 ( ( ( cons @ A @ X @ Xs1 )
% 2.79/1.64 = Ys )
% 2.79/1.64 => ( ( Xs
% 2.79/1.64 = ( append @ A @ Xs1 @ Zs2 ) )
% 2.79/1.64 => ( ( cons @ A @ X @ Xs )
% 2.79/1.64 = ( append @ A @ Ys @ Zs2 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_96_lappend__llist__of__LCons,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu268472904append @ A @ ( coindu1079202755ist_of @ A @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( coindu268472904append @ A @ ( coindu1079202755ist_of @ A @ ( append @ A @ Xs @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ Ys ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_97_list__of__aux__code_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1542816657of_aux @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( coindu1542816657of_aux @ A @ ( cons @ A @ Y @ Xs ) @ Ys ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_98_append__Nil2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.79/1.64 = Xs ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_99_append__self__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ Ys )
% 2.79/1.64 = Xs )
% 2.79/1.64 = ( Ys
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_100_self__append__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( Ys
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_101_append__self__conv2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ Ys )
% 2.79/1.64 = Ys )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_102_self__append__conv2,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 = ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_103_Nil__is__append__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( nil @ A )
% 2.79/1.64 = ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( nil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_104_append__is__Nil__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ Ys )
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( nil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_105_append1__eq__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.79/1.64 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.79/1.64 = ( ( Xs = Ys )
% 2.79/1.64 & ( X = Y ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_106_last__appendR,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( last @ A @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_107_last__appendL,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( last @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_108_list__of__LNil,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu1736001939ist_of @ A @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_109_last__snoc,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.79/1.64 = X ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_110_map__tailrec__rev_Oinduct,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.79/1.64 ( ! [F2: A > B,X1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 2.79/1.64 => ( ! [F2: A > B,A2: A,As: list @ A,Bs: list @ B] :
% 2.79/1.64 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A2 ) @ Bs ) )
% 2.79/1.64 => ( P @ F2 @ ( cons @ A @ A2 @ As ) @ Bs ) )
% 2.79/1.64 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_111_list__nonempty__induct,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( Xs2
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_112_remdups__adj_Oinduct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.79/1.64 ( ( P @ ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.79/1.64 => ( ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( ( X2 = Y2 )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.79/1.64 => ( ( ( X2 != Y2 )
% 2.79/1.64 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.79/1.64 => ( P @ A0 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_113_remdups__adj_Ocases,axiom,
% 2.79/1.64 ! [A: $tType,X: list @ A] :
% 2.79/1.64 ( ( X
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A] :
% 2.79/1.64 ( X
% 2.79/1.64 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.79/1.64 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.79/1.64 ( X
% 2.79/1.64 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_114_append__Nil,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A] :
% 2.79/1.64 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.79/1.64 = Ys ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_115_transpose_Ocases,axiom,
% 2.79/1.64 ! [A: $tType,X: list @ ( list @ A )] :
% 2.79/1.64 ( ( X
% 2.79/1.64 != ( nil @ ( list @ A ) ) )
% 2.79/1.64 => ( ! [Xss: list @ ( list @ A )] :
% 2.79/1.64 ( X
% 2.79/1.64 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.79/1.64 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.79/1.64 ( X
% 2.79/1.64 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_116_eq__Nil__appendI,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( Xs = Ys )
% 2.79/1.64 => ( Xs
% 2.79/1.64 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_117_splice_Oinduct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.79/1.64 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.79/1.64 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 2.79/1.64 ( ( P @ Xs2 @ Ys3 )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) )
% 2.79/1.64 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_118_list__induct2_H,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.79/1.64 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 2.79/1.64 => ( ! [Y2: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys3 ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A,Y2: B,Ys3: list @ B] :
% 2.79/1.64 ( ( P @ Xs2 @ Ys3 )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys3 ) ) )
% 2.79/1.64 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_119_neq__Nil__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 = ( ? [Y3: A,Ys4: list @ A] :
% 2.79/1.64 ( Xs
% 2.79/1.64 = ( cons @ A @ Y3 @ Ys4 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_120_list_Oinducts,axiom,
% 2.79/1.64 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.79/1.64 ( ( P @ ( nil @ A ) )
% 2.79/1.64 => ( ! [X1: A,X23: list @ A] :
% 2.79/1.64 ( ( P @ X23 )
% 2.79/1.64 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 2.79/1.64 => ( P @ List ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_121_list_Oexhaust,axiom,
% 2.79/1.64 ! [A: $tType,Y: list @ A] :
% 2.79/1.64 ( ( Y
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ~ ! [X212: A,X222: list @ A] :
% 2.79/1.64 ( Y
% 2.79/1.64 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_122_list_OdiscI,axiom,
% 2.79/1.64 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.79/1.64 ( ( List
% 2.79/1.64 = ( cons @ A @ X21 @ X22 ) )
% 2.79/1.64 => ( List
% 2.79/1.64 != ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_123_list_Odistinct_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,X21: A,X22: list @ A] :
% 2.79/1.64 ( ( nil @ A )
% 2.79/1.64 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_124_list__of__code,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu1736001939ist_of @ A )
% 2.79/1.64 = ( coindu1542816657of_aux @ A @ ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_125_rev__induct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.79/1.64 ( ( P @ ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_126_rev__exhaust,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ~ ! [Ys3: list @ A,Y2: A] :
% 2.79/1.64 ( Xs
% 2.79/1.64 != ( append @ A @ Ys3 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_127_Cons__eq__append__conv,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.79/1.64 ( ( ( cons @ A @ X @ Xs )
% 2.79/1.64 = ( append @ A @ Ys @ Zs2 ) )
% 2.79/1.64 = ( ( ( Ys
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 & ( ( cons @ A @ X @ Xs )
% 2.79/1.64 = Zs2 ) )
% 2.79/1.64 | ? [Ys2: list @ A] :
% 2.79/1.64 ( ( ( cons @ A @ X @ Ys2 )
% 2.79/1.64 = Ys )
% 2.79/1.64 & ( Xs
% 2.79/1.64 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_128_append__eq__Cons__conv,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Ys @ Zs2 )
% 2.79/1.64 = ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( ( ( Ys
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 & ( Zs2
% 2.79/1.64 = ( cons @ A @ X @ Xs ) ) )
% 2.79/1.64 | ? [Ys2: list @ A] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 = ( cons @ A @ X @ Ys2 ) )
% 2.79/1.64 & ( ( append @ A @ Ys2 @ Zs2 )
% 2.79/1.64 = Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_129_rev__nonempty__induct,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( Xs2
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_130_last__ConsR,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( last @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_131_last__ConsL,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = X ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_132_last_Osimps,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = X ) )
% 2.79/1.64 & ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( last @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_133_longest__common__suffix,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ? [Ss: list @ A,Xs3: list @ A,Ys6: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( append @ A @ Xs3 @ Ss ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( append @ A @ Ys6 @ Ss ) )
% 2.79/1.64 & ( ( Xs3
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ( Ys6
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ( ( last @ A @ Xs3 )
% 2.79/1.64 != ( last @ A @ Ys6 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_134_last__append,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.79/1.64 ( ( ( Ys
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( last @ A @ Xs ) ) )
% 2.79/1.64 & ( ( Ys
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( last @ A @ Ys ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_135_llist__of__eq__LNil__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( coindu1079202755ist_of @ A @ Xs )
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_136_llist__of_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu1079202755ist_of @ A @ ( nil @ A ) )
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_137_not__Cons__self2,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( cons @ A @ X @ Xs )
% 2.79/1.64 != Xs ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_138_append__eq__appendI,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ Xs1 )
% 2.79/1.64 = Zs2 )
% 2.79/1.64 => ( ( Ys
% 2.79/1.64 = ( append @ A @ Xs1 @ Us ) )
% 2.79/1.64 => ( ( append @ A @ Xs @ Ys )
% 2.79/1.64 = ( append @ A @ Zs2 @ Us ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_139_append__eq__append__conv2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ Ys )
% 2.79/1.64 = ( append @ A @ Zs2 @ Ts ) )
% 2.79/1.64 = ( ? [Us2: list @ A] :
% 2.79/1.64 ( ( ( Xs
% 2.79/1.64 = ( append @ A @ Zs2 @ Us2 ) )
% 2.79/1.64 & ( ( append @ A @ Us2 @ Ys )
% 2.79/1.64 = Ts ) )
% 2.79/1.64 | ( ( ( append @ A @ Xs @ Us2 )
% 2.79/1.64 = Zs2 )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_140_longest__common__prefix_Oinduct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.79/1.64 ( ! [X2: A,Xs2: list @ A,Y2: A,Ys3: list @ A] :
% 2.79/1.64 ( ( ( X2 = Y2 )
% 2.79/1.64 => ( P @ Xs2 @ Ys3 ) )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys3 ) ) )
% 2.79/1.64 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.79/1.64 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 2.79/1.64 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_141_prefixes_Oinduct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.79/1.64 ( ( P @ ( nil @ A ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.79/1.64 => ( P @ A0 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_142_prefixes_Ocases,axiom,
% 2.79/1.64 ! [A: $tType,X: list @ A] :
% 2.79/1.64 ( ( X
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ~ ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( X
% 2.79/1.64 != ( cons @ A @ X2 @ Xs2 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_143_append__butlast__last__id,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 2.79/1.64 = Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_144_bind__simps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 2.79/1.64 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 2.79/1.64 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_145_bind__simps_I1_J,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.79/1.64 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_146_butlast__snoc,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.79/1.64 = Xs ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_147_butlast_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( butlast @ A @ ( nil @ A ) )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_148_butlast_Osimps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( nil @ A ) ) )
% 2.79/1.64 & ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_149_butlast__append,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.79/1.64 ( ( ( Ys
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( butlast @ A @ Xs ) ) )
% 2.79/1.64 & ( ( Ys
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_150_snoc__eq__iff__butlast,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A] :
% 2.79/1.64 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.79/1.64 = Ys )
% 2.79/1.64 = ( ( Ys
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 & ( ( butlast @ A @ Ys )
% 2.79/1.64 = Xs )
% 2.79/1.64 & ( ( last @ A @ Ys )
% 2.79/1.64 = X ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_151_prefixes__snoc,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( prefixes @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.79/1.64 = ( append @ ( list @ A ) @ ( prefixes @ A @ Xs ) @ ( cons @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( nil @ ( list @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_152_prefixes__eq__Snoc,axiom,
% 2.79/1.64 ! [A: $tType,Ys: list @ A,Xs: list @ ( list @ A ),X: list @ A] :
% 2.79/1.64 ( ( ( prefixes @ A @ Ys )
% 2.79/1.64 = ( append @ ( list @ A ) @ Xs @ ( cons @ ( list @ A ) @ X @ ( nil @ ( list @ A ) ) ) ) )
% 2.79/1.64 = ( ( ( ( Ys
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 & ( Xs
% 2.79/1.64 = ( nil @ ( list @ A ) ) ) )
% 2.79/1.64 | ? [Z: A,Zs4: list @ A] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 = ( append @ A @ Zs4 @ ( cons @ A @ Z @ ( nil @ A ) ) ) )
% 2.79/1.64 & ( Xs
% 2.79/1.64 = ( prefixes @ A @ Zs4 ) ) ) )
% 2.79/1.64 & ( X = Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_153_sublists_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( sublists @ A @ ( nil @ A ) )
% 2.79/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_154_prefixes_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( prefixes @ A @ ( nil @ A ) )
% 2.79/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_155_product__lists_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.79/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_156_llimit__induct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.79/1.64 => ( ( P @ Xs2 )
% 2.79/1.64 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.79/1.64 => ( ( ! [Ys5: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu574146665prefix @ A @ Ys5 @ Xs )
% 2.79/1.64 => ( P @ Ys5 ) )
% 2.79/1.64 => ( P @ Xs ) )
% 2.79/1.64 => ( P @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_157_prefixes_Oelims,axiom,
% 2.79/1.64 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 2.79/1.64 ( ( ( prefixes @ A @ X )
% 2.79/1.64 = Y )
% 2.79/1.64 => ( ( ( X
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( Y
% 2.79/1.64 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 2.79/1.64 => ~ ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( X
% 2.79/1.64 = ( cons @ A @ X2 @ Xs2 ) )
% 2.79/1.64 => ( Y
% 2.79/1.64 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_158_Nil__is__map__conv,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.79/1.64 ( ( ( nil @ A )
% 2.79/1.64 = ( map @ B @ A @ F @ Xs ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ B ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_159_map__is__Nil__conv,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.79/1.64 ( ( ( map @ B @ A @ F @ Xs )
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ B ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_160_list_Omap__disc__iff,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F: A > B,A3: list @ A] :
% 2.79/1.64 ( ( ( map @ A @ B @ F @ A3 )
% 2.79/1.64 = ( nil @ B ) )
% 2.79/1.64 = ( A3
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_161_map__append,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Ys: list @ B] :
% 2.79/1.64 ( ( map @ B @ A @ F @ ( append @ B @ Xs @ Ys ) )
% 2.79/1.64 = ( append @ A @ ( map @ B @ A @ F @ Xs ) @ ( map @ B @ A @ F @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_162_lstrict__prefix__code_I4_J,axiom,
% 2.79/1.64 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B,Y: B,Ys: coindu1593790203_llist @ B] :
% 2.79/1.64 ( ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 2.79/1.64 = ( ( X = Y )
% 2.79/1.64 & ( coindu574146665prefix @ B @ Xs @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_163_lstrict__prefix__code_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_164_lstrict__prefix__code_I2_J,axiom,
% 2.79/1.64 ! [B: $tType,Y: B,Ys: coindu1593790203_llist @ B] : ( coindu574146665prefix @ B @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_165_lstrict__prefix__code_I3_J,axiom,
% 2.79/1.64 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 2.79/1.64 ~ ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_166_llist__less__induct,axiom,
% 2.79/1.64 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ! [Xs2: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ! [Ys5: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu574146665prefix @ A @ Ys5 @ Xs2 )
% 2.79/1.64 => ( P @ Ys5 ) )
% 2.79/1.64 => ( P @ Xs2 ) )
% 2.79/1.64 => ( P @ Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_167_map__butlast,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.79/1.64 ( ( map @ B @ A @ F @ ( butlast @ B @ Xs ) )
% 2.79/1.64 = ( butlast @ A @ ( map @ B @ A @ F @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_168_list_Osimps_I8_J,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: A > B] :
% 2.79/1.64 ( ( map @ A @ B @ F @ ( nil @ A ) )
% 2.79/1.64 = ( nil @ B ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_169_list_Osimps_I9_J,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: list @ A] :
% 2.79/1.64 ( ( map @ A @ B @ F @ ( cons @ A @ X21 @ X22 ) )
% 2.79/1.64 = ( cons @ B @ ( F @ X21 ) @ ( map @ A @ B @ F @ X22 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_170_Cons__eq__map__D,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 2.79/1.64 ( ( ( cons @ A @ X @ Xs )
% 2.79/1.64 = ( map @ B @ A @ F @ Ys ) )
% 2.79/1.64 => ? [Z3: B,Zs3: list @ B] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 = ( cons @ B @ Z3 @ Zs3 ) )
% 2.79/1.64 & ( X
% 2.79/1.64 = ( F @ Z3 ) )
% 2.79/1.64 & ( Xs
% 2.79/1.64 = ( map @ B @ A @ F @ Zs3 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_171_map__eq__Cons__D,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 2.79/1.64 ( ( ( map @ B @ A @ F @ Xs )
% 2.79/1.64 = ( cons @ A @ Y @ Ys ) )
% 2.79/1.64 => ? [Z3: B,Zs3: list @ B] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( cons @ B @ Z3 @ Zs3 ) )
% 2.79/1.64 & ( ( F @ Z3 )
% 2.79/1.64 = Y )
% 2.79/1.64 & ( ( map @ B @ A @ F @ Zs3 )
% 2.79/1.64 = Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_172_Cons__eq__map__conv,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 2.79/1.64 ( ( ( cons @ A @ X @ Xs )
% 2.79/1.64 = ( map @ B @ A @ F @ Ys ) )
% 2.79/1.64 = ( ? [Z: B,Zs4: list @ B] :
% 2.79/1.64 ( ( Ys
% 2.79/1.64 = ( cons @ B @ Z @ Zs4 ) )
% 2.79/1.64 & ( X
% 2.79/1.64 = ( F @ Z ) )
% 2.79/1.64 & ( Xs
% 2.79/1.64 = ( map @ B @ A @ F @ Zs4 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_173_map__eq__Cons__conv,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 2.79/1.64 ( ( ( map @ B @ A @ F @ Xs )
% 2.79/1.64 = ( cons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( ? [Z: B,Zs4: list @ B] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( cons @ B @ Z @ Zs4 ) )
% 2.79/1.64 & ( ( F @ Z )
% 2.79/1.64 = Y )
% 2.79/1.64 & ( ( map @ B @ A @ F @ Zs4 )
% 2.79/1.64 = Ys ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_174_lstrict__prefix__lfinite1,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 2.79/1.64 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_175_last__map,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( last @ B @ ( map @ A @ B @ F @ Xs ) )
% 2.79/1.64 = ( F @ ( last @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_176_prefixes_Osimps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( prefixes @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X ) @ ( prefixes @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_177_prefixes_Opelims,axiom,
% 2.79/1.64 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 2.79/1.64 ( ( ( prefixes @ A @ X )
% 2.79/1.64 = Y )
% 2.79/1.64 => ( ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ X )
% 2.79/1.64 => ( ( ( X
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( Y
% 2.79/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) )
% 2.79/1.64 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( nil @ A ) ) ) )
% 2.79/1.64 => ~ ! [X2: A,Xs2: list @ A] :
% 2.79/1.64 ( ( X
% 2.79/1.64 = ( cons @ A @ X2 @ Xs2 ) )
% 2.79/1.64 => ( ( Y
% 2.79/1.64 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) )
% 2.79/1.64 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( cons @ A @ X2 @ Xs2 ) ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_178_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 | ? [Xs4: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( coindu1121789889_LCons @ A @ Y @ Xs4 ) )
% 2.79/1.64 & ( coindu1571841457prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_179_maps__simps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 2.79/1.64 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 2.79/1.64 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_180_maps__simps_I2_J,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.79/1.64 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_181_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1571841457prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_182_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_183_insert__Nil,axiom,
% 2.79/1.64 ! [A: $tType,X: A] :
% 2.79/1.64 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.79/1.64 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_184_rotate1_Osimps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_185_map__eq__map__tailrec,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType] :
% 2.79/1.64 ( ( map @ A @ B )
% 2.79/1.64 = ( map_tailrec @ A @ B ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_186_rotate1__is__Nil__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( rotate1 @ A @ Xs )
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_187_rotate1_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( rotate1 @ A @ ( nil @ A ) )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_188_hd__list__of,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( hd @ A @ ( coindu1736001939ist_of @ A @ Xs ) )
% 2.79/1.64 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_189_list__ex1__simps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,P: A > $o] :
% 2.79/1.64 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_190_list__of__LCons__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.79/1.64 ( ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu1736001939ist_of @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.79/1.64 = ( cons @ A @ X @ ( coindu1736001939ist_of @ A @ Xs ) ) ) )
% 2.79/1.64 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu1736001939ist_of @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.79/1.64 = ( undefined @ ( list @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_191_hd__append2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( hd @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_192_lhd__llist__of,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( coindu1046438764le_lhd @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 2.79/1.64 = ( hd @ A @ Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_193_list_Osel_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,X21: A,X22: list @ A] :
% 2.79/1.64 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.79/1.64 = X21 ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_194_list_Omap__sel_I1_J,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,A3: list @ A,F: A > B] :
% 2.79/1.64 ( ( A3
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( hd @ B @ ( map @ A @ B @ F @ A3 ) )
% 2.79/1.64 = ( F @ ( hd @ A @ A3 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_195_hd__map,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( hd @ B @ ( map @ A @ B @ F @ Xs ) )
% 2.79/1.64 = ( F @ ( hd @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_196_longest__common__prefix,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ? [Ps: list @ A,Xs3: list @ A,Ys6: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 = ( append @ A @ Ps @ Xs3 ) )
% 2.79/1.64 & ( Ys
% 2.79/1.64 = ( append @ A @ Ps @ Ys6 ) )
% 2.79/1.64 & ( ( Xs3
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ( Ys6
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ( ( hd @ A @ Xs3 )
% 2.79/1.64 != ( hd @ A @ Ys6 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_197_hd__append,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( hd @ A @ Ys ) ) )
% 2.79/1.64 & ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( hd @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( hd @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_198_llast__LNil,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu2000965700_llast @ A @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( undefined @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_199_llast__linfinite,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu2000965700_llast @ A @ Xs )
% 2.79/1.64 = ( undefined @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_200_list__of__aux__def,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( coindu1542816657of_aux @ A )
% 2.79/1.64 = ( ^ [Xs5: list @ A,Ys4: coindu1593790203_llist @ A] : ( if @ ( list @ A ) @ ( coindu1213758845finite @ A @ Ys4 ) @ ( append @ A @ ( rev @ A @ Xs5 ) @ ( coindu1736001939ist_of @ A @ Ys4 ) ) @ ( undefined @ ( list @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_201_rotate1__hd__tl,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( rotate1 @ A @ Xs )
% 2.79/1.64 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_202_rev__rev__ident,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 2.79/1.64 = Xs ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_203_rev__is__rev__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( rev @ A @ Xs )
% 2.79/1.64 = ( rev @ A @ Ys ) )
% 2.79/1.64 = ( Xs = Ys ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_204_Nil__is__rev__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( nil @ A )
% 2.79/1.64 = ( rev @ A @ Xs ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_205_rev__is__Nil__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( rev @ A @ Xs )
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_206_rev__append,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( rev @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( append @ A @ ( rev @ A @ Ys ) @ ( rev @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_207_rev__singleton__conv,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,X: A] :
% 2.79/1.64 ( ( ( rev @ A @ Xs )
% 2.79/1.64 = ( cons @ A @ X @ ( nil @ A ) ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_208_singleton__rev__conv,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 2.79/1.64 = ( rev @ A @ Xs ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_209_tl__append2,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( tl @ A @ ( append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( append @ A @ ( tl @ A @ Xs ) @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_210_rev__eq__Cons__iff,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.79/1.64 ( ( ( rev @ A @ Xs )
% 2.79/1.64 = ( cons @ A @ Y @ Ys ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( append @ A @ ( rev @ A @ Ys ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_211_list_Ocollapse,axiom,
% 2.79/1.64 ! [A: $tType,List: list @ A] :
% 2.79/1.64 ( ( List
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 2.79/1.64 = List ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_212_hd__Cons__tl,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 2.79/1.64 = Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_213_map__tl,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.79/1.64 ( ( map @ B @ A @ F @ ( tl @ B @ Xs ) )
% 2.79/1.64 = ( tl @ A @ ( map @ B @ A @ F @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_214_rev__map,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.79/1.64 ( ( rev @ A @ ( map @ B @ A @ F @ Xs ) )
% 2.79/1.64 = ( map @ B @ A @ F @ ( rev @ B @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_215_rev__swap,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.79/1.64 ( ( ( rev @ A @ Xs )
% 2.79/1.64 = Ys )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( rev @ A @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_216_list_Osel_I2_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( tl @ A @ ( nil @ A ) )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_217_list_Osel_I3_J,axiom,
% 2.79/1.64 ! [A: $tType,X21: A,X22: list @ A] :
% 2.79/1.64 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 2.79/1.64 = X22 ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_218_butlast__tl,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 2.79/1.64 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_219_rev_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType] :
% 2.79/1.64 ( ( rev @ A @ ( nil @ A ) )
% 2.79/1.64 = ( nil @ A ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_220_list_Omap__sel_I2_J,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,A3: list @ A,F: A > B] :
% 2.79/1.64 ( ( A3
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( tl @ B @ ( map @ A @ B @ F @ A3 ) )
% 2.79/1.64 = ( map @ A @ B @ F @ ( tl @ A @ A3 ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_221_tl__Nil,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( tl @ A @ Xs )
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ? [X3: A] :
% 2.79/1.64 ( Xs
% 2.79/1.64 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_222_Nil__tl,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( nil @ A )
% 2.79/1.64 = ( tl @ A @ Xs ) )
% 2.79/1.64 = ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ? [X3: A] :
% 2.79/1.64 ( Xs
% 2.79/1.64 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_223_list_Oexpand,axiom,
% 2.79/1.64 ! [A: $tType,List: list @ A,List2: list @ A] :
% 2.79/1.64 ( ( ( List
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( List2
% 2.79/1.64 = ( nil @ A ) ) )
% 2.79/1.64 => ( ( ( List
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( List2
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( ( hd @ A @ List )
% 2.79/1.64 = ( hd @ A @ List2 ) )
% 2.79/1.64 & ( ( tl @ A @ List )
% 2.79/1.64 = ( tl @ A @ List2 ) ) ) ) )
% 2.79/1.64 => ( List = List2 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_224_last__tl,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( Xs
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 | ( ( tl @ A @ Xs )
% 2.79/1.64 != ( nil @ A ) ) )
% 2.79/1.64 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 2.79/1.64 = ( last @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_225_list__of__aux__code_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( coindu1542816657of_aux @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.79/1.64 = ( rev @ A @ Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_226_rev_Osimps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( rev @ A @ ( cons @ A @ X @ Xs ) )
% 2.79/1.64 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_227_hd__rev,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 2.79/1.64 = ( last @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_228_last__rev,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( Xs
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 2.79/1.64 = ( hd @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_229_list_Oexhaust__sel,axiom,
% 2.79/1.64 ! [A: $tType,List: list @ A] :
% 2.79/1.64 ( ( List
% 2.79/1.64 != ( nil @ A ) )
% 2.79/1.64 => ( List
% 2.79/1.64 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_230_map__tailrec__def,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType] :
% 2.79/1.64 ( ( map_tailrec @ A @ B )
% 2.79/1.64 = ( ^ [F3: A > B,As2: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F3 @ As2 @ ( nil @ B ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_231_list_Osplit__sel__asm,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( list @ A ) > B,List: list @ A] :
% 2.79/1.64 ( ( P @ ( case_list @ B @ A @ F1 @ F22 @ List ) )
% 2.79/1.64 = ( ~ ( ( ( List
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 & ~ ( P @ F1 ) )
% 2.79/1.64 | ( ( List
% 2.79/1.64 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 2.79/1.64 & ~ ( P @ ( F22 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_232_map__tailrec__rev_Osimps_I1_J,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: A > B,Bs2: list @ B] :
% 2.79/1.64 ( ( map_tailrec_rev @ A @ B @ F @ ( nil @ A ) @ Bs2 )
% 2.79/1.64 = Bs2 ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_233_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F: A > B,A3: A,As3: list @ A,Bs2: list @ B] :
% 2.79/1.64 ( ( map_tailrec_rev @ A @ B @ F @ ( cons @ A @ A3 @ As3 ) @ Bs2 )
% 2.79/1.64 = ( map_tailrec_rev @ A @ B @ F @ As3 @ ( cons @ B @ ( F @ A3 ) @ Bs2 ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_234_list_Osimps_I4_J,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,F1: B,F22: A > ( list @ A ) > B] :
% 2.79/1.64 ( ( case_list @ B @ A @ F1 @ F22 @ ( nil @ A ) )
% 2.79/1.64 = F1 ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_235_list_Osimps_I5_J,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,F1: B,F22: A > ( list @ A ) > B,X21: A,X22: list @ A] :
% 2.79/1.64 ( ( case_list @ B @ A @ F1 @ F22 @ ( cons @ A @ X21 @ X22 ) )
% 2.79/1.64 = ( F22 @ X21 @ X22 ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_236_map__tailrec__rev_Oelims,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,X: A > B,Xa: list @ A,Xb2: list @ B,Y: list @ B] :
% 2.79/1.64 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa @ Xb2 )
% 2.79/1.64 = Y )
% 2.79/1.64 => ( ( ( Xa
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( Y != Xb2 ) )
% 2.79/1.64 => ~ ! [A2: A,As: list @ A] :
% 2.79/1.64 ( ( Xa
% 2.79/1.64 = ( cons @ A @ A2 @ As ) )
% 2.79/1.64 => ( Y
% 2.79/1.64 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A2 ) @ Xb2 ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_237_list_Ocase__eq__if,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType] :
% 2.79/1.64 ( ( case_list @ B @ A )
% 2.79/1.64 = ( ^ [F12: B,F23: A > ( list @ A ) > B,List3: list @ A] :
% 2.79/1.64 ( if @ B
% 2.79/1.64 @ ( List3
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 @ F12
% 2.79/1.64 @ ( F23 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_238_map__tailrec__rev,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType] :
% 2.79/1.64 ( ( map_tailrec_rev @ B @ A )
% 2.79/1.64 = ( ^ [F3: B > A,As2: list @ B] : ( append @ A @ ( rev @ A @ ( map @ B @ A @ F3 @ As2 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_239_list_Osplit__sel,axiom,
% 2.79/1.64 ! [B: $tType,A: $tType,P: B > $o,F1: B,F22: A > ( list @ A ) > B,List: list @ A] :
% 2.79/1.64 ( ( P @ ( case_list @ B @ A @ F1 @ F22 @ List ) )
% 2.79/1.64 = ( ( ( List
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 => ( P @ F1 ) )
% 2.79/1.64 & ( ( List
% 2.79/1.64 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 2.79/1.64 => ( P @ ( F22 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_240_remdups__adj__append,axiom,
% 2.79/1.64 ! [A: $tType,Xs_1: list @ A,X: A,Xs_2: list @ A] :
% 2.79/1.64 ( ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ Xs_2 ) ) )
% 2.79/1.64 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs_2 ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_241_llast__lappend,axiom,
% 2.79/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ( coindu335574135_lnull @ A @ Ys )
% 2.79/1.64 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( coindu2000965700_llast @ A @ Xs ) ) )
% 2.79/1.64 & ( ~ ( coindu335574135_lnull @ A @ Ys )
% 2.79/1.64 => ( ( ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( coindu2000965700_llast @ A @ Ys ) ) )
% 2.79/1.64 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.79/1.64 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( undefined @ A ) ) ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_242_lappend_Odisc__iff_I2_J,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 2.79/1.64 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_243_lnull__lappend,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_244_remdups__adj__Nil__iff,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( ( remdups_adj @ A @ Xs )
% 2.79/1.64 = ( nil @ A ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_245_llexord__LNil__right,axiom,
% 2.79/1.64 ! [A: $tType,Ys: coindu1593790203_llist @ A,R: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( coindu335574135_lnull @ A @ Ys )
% 2.79/1.64 => ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.79/1.64 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_246_remdups__adj__rev,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( remdups_adj @ A @ ( rev @ A @ Xs ) )
% 2.79/1.64 = ( rev @ A @ ( remdups_adj @ A @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_247_hd__remdups__adj,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( hd @ A @ ( remdups_adj @ A @ Xs ) )
% 2.79/1.64 = ( hd @ A @ Xs ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_248_lnull__llist__of,axiom,
% 2.79/1.64 ! [A: $tType,Xs: list @ A] :
% 2.79/1.64 ( ( coindu335574135_lnull @ A @ ( coindu1079202755ist_of @ A @ Xs ) )
% 2.79/1.64 = ( Xs
% 2.79/1.64 = ( nil @ A ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_249_lhd__lappend,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 2.79/1.64 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.79/1.64 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_250_remdups__adj__Cons__alt,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Xs: list @ A] :
% 2.79/1.64 ( ( cons @ A @ X @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) )
% 2.79/1.64 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_251_llast__LCons,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.79/1.64 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.79/1.64 = X ) )
% 2.79/1.64 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.79/1.64 = ( coindu2000965700_llast @ A @ Xs ) ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_252_lappend_Oexhaust,axiom,
% 2.79/1.64 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.79/1.64 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.79/1.64 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(fact_253_lzip_Oexhaust,axiom,
% 2.79/1.64 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.79/1.64 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 | ( coindu335574135_lnull @ B @ Ys ) )
% 2.79/1.64 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.79/1.64 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(help_If_3_1_T,axiom,
% 2.79/1.64 ! [P: $o] :
% 2.79/1.64 ( ( P = $true )
% 2.79/1.64 | ( P = $false ) ) ).
% 2.79/1.64
% 2.79/1.64 thf(help_If_2_1_T,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Y: A] :
% 2.79/1.64 ( ( if @ A @ $false @ X @ Y )
% 2.79/1.64 = Y ) ).
% 2.79/1.64
% 2.79/1.64 thf(help_If_1_1_T,axiom,
% 2.79/1.64 ! [A: $tType,X: A,Y: A] :
% 2.79/1.64 ( ( if @ A @ $true @ X @ Y )
% 2.79/1.64 = X ) ).
% 2.79/1.64
% 2.79/1.64 thf(conj_0,hypothesis,
% 2.79/1.64 ! [YS: list @ a] :
% 2.79/1.64 ( ( ys2
% 2.79/1.64 = ( coindu1079202755ist_of @ a @ YS ) )
% 2.79/1.64 => thesis ) ).
% 2.79/1.64
% 2.79/1.64 thf(conj_1,conjecture,
% 2.79/1.64 thesis ).
% 2.79/1.64 ------------------------
% 2.79/1.67 % (1807)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/18Mi)
% 2.79/1.67 % (1803)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_1697 for (2999ds/27Mi)
% 2.79/1.67 % (1801)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/183Mi)
% 2.79/1.67 % (1806)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_1697 for (2999ds/275Mi)
% 2.79/1.67 % (1805)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_1697 for (2999ds/2Mi)
% 2.79/1.67 % (1802)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_1697 for (2999ds/4Mi)
% 2.79/1.67 % (1804)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/2Mi)
% 2.79/1.67 % (1804)Instruction limit reached!
% 2.79/1.67 % (1804)------------------------------
% 2.79/1.67 % (1804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.67 % (1804)Termination reason: Unknown
% 2.79/1.67 % (1804)Termination phase: shuffling
% 2.79/1.67
% 2.79/1.67 % (1804)Memory used [KB]: 1279
% 2.79/1.67 % (1804)Time elapsed: 0.003 s
% 2.79/1.67 % (1804)Instructions burned: 2 (million)
% 2.79/1.67 % (1804)------------------------------
% 2.79/1.67 % (1804)------------------------------
% 2.79/1.67 % (1805)Instruction limit reached!
% 2.79/1.67 % (1805)------------------------------
% 2.79/1.67 % (1805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.67 % (1805)Termination reason: Unknown
% 2.79/1.67 % (1805)Termination phase: shuffling
% 2.79/1.67
% 2.79/1.67 % (1805)Memory used [KB]: 1279
% 2.79/1.67 % (1805)Time elapsed: 0.003 s
% 2.79/1.67 % (1805)Instructions burned: 2 (million)
% 2.79/1.67 % (1805)------------------------------
% 2.79/1.67 % (1805)------------------------------
% 2.79/1.67 % (1802)Instruction limit reached!
% 2.79/1.67 % (1802)------------------------------
% 2.79/1.67 % (1802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.67 % (1802)Termination reason: Unknown
% 2.79/1.67 % (1802)Termination phase: shuffling
% 2.79/1.67
% 2.79/1.67 % (1802)Memory used [KB]: 1407
% 2.79/1.67 % (1802)Time elapsed: 0.004 s
% 2.79/1.67 % (1802)Instructions burned: 4 (million)
% 2.79/1.67 % (1802)------------------------------
% 2.79/1.67 % (1802)------------------------------
% 2.79/1.68 % (1807)Instruction limit reached!
% 2.79/1.68 % (1807)------------------------------
% 2.79/1.68 % (1807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.68 % (1807)Termination reason: Unknown
% 2.79/1.68 % (1807)Termination phase: Property scanning
% 2.79/1.68
% 2.79/1.68 % (1807)Memory used [KB]: 1663
% 2.79/1.68 % (1807)Time elapsed: 0.011 s
% 2.79/1.68 % (1807)Instructions burned: 19 (million)
% 2.79/1.68 % (1807)------------------------------
% 2.79/1.68 % (1807)------------------------------
% 2.79/1.68 % (1803)Instruction limit reached!
% 2.79/1.68 % (1803)------------------------------
% 2.79/1.68 % (1803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.68 % (1803)Termination reason: Unknown
% 2.79/1.68 % (1803)Termination phase: Property scanning
% 2.79/1.68
% 2.79/1.68 % (1803)Memory used [KB]: 1663
% 2.79/1.68 % (1803)Time elapsed: 0.015 s
% 2.79/1.68 % (1803)Instructions burned: 27 (million)
% 2.79/1.68 % (1803)------------------------------
% 2.79/1.68 % (1803)------------------------------
% 2.79/1.69 % (1809)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_1697 for (2999ds/37Mi)
% 2.79/1.69 % (1808)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/3Mi)
% 2.79/1.69 % (1810)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_1697 for (2999ds/15Mi)
% 2.79/1.69 % (1808)Instruction limit reached!
% 2.79/1.69 % (1808)------------------------------
% 2.79/1.69 % (1808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.79/1.69 % (1808)Termination reason: Unknown
% 2.79/1.69 % (1808)Termination phase: shuffling
% 2.79/1.69
% 2.79/1.69 % (1808)Memory used [KB]: 1407
% 2.79/1.69 % (1808)Time elapsed: 0.003 s
% 2.79/1.69 % (1808)Instructions burned: 3 (million)
% 2.79/1.69 % (1808)------------------------------
% 2.79/1.69 % (1808)------------------------------
% 2.84/1.70 % (1810)Instruction limit reached!
% 2.84/1.70 % (1810)------------------------------
% 2.84/1.70 % (1810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.70 % (1810)Termination reason: Unknown
% 2.84/1.70 % (1810)Termination phase: shuffling
% 2.84/1.70
% 2.84/1.70 % (1810)Memory used [KB]: 1535
% 2.84/1.70 % (1810)Time elapsed: 0.009 s
% 2.84/1.70 % (1810)Instructions burned: 15 (million)
% 2.84/1.70 % (1810)------------------------------
% 2.84/1.70 % (1810)------------------------------
% 2.84/1.70 % (1811)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_1697 for (2999ds/3Mi)
% 2.84/1.70 % (1811)Instruction limit reached!
% 2.84/1.70 % (1811)------------------------------
% 2.84/1.70 % (1811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.70 % (1811)Termination reason: Unknown
% 2.84/1.70 % (1811)Termination phase: shuffling
% 2.84/1.70
% 2.84/1.70 % (1811)Memory used [KB]: 1407
% 2.84/1.70 % (1811)Time elapsed: 0.003 s
% 2.84/1.70 % (1811)Instructions burned: 3 (million)
% 2.84/1.70 % (1811)------------------------------
% 2.84/1.70 % (1811)------------------------------
% 2.84/1.70 % (1812)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_1697 for (2999ds/1041Mi)
% 2.84/1.71 % (1813)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/7Mi)
% 2.84/1.71 % (1809)Instruction limit reached!
% 2.84/1.71 % (1809)------------------------------
% 2.84/1.71 % (1809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.71 % (1809)Termination reason: Unknown
% 2.84/1.71 % (1809)Termination phase: shuffling
% 2.84/1.71
% 2.84/1.71 % (1809)Memory used [KB]: 2046
% 2.84/1.71 % (1809)Time elapsed: 0.019 s
% 2.84/1.71 % (1809)Instructions burned: 38 (million)
% 2.84/1.71 % (1809)------------------------------
% 2.84/1.71 % (1809)------------------------------
% 2.84/1.71 % (1813)Instruction limit reached!
% 2.84/1.71 % (1813)------------------------------
% 2.84/1.71 % (1813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.71 % (1813)Termination reason: Unknown
% 2.84/1.71 % (1813)Termination phase: shuffling
% 2.84/1.71
% 2.84/1.71 % (1813)Memory used [KB]: 1407
% 2.84/1.71 % (1813)Time elapsed: 0.005 s
% 2.84/1.71 % (1813)Instructions burned: 7 (million)
% 2.84/1.71 % (1813)------------------------------
% 2.84/1.71 % (1813)------------------------------
% 2.84/1.71 % (1814)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/16Mi)
% 2.84/1.71 % (1815)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_1697 for (2999ds/3Mi)
% 2.84/1.72 % (1815)Instruction limit reached!
% 2.84/1.72 % (1815)------------------------------
% 2.84/1.72 % (1815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.72 % (1815)Termination reason: Unknown
% 2.84/1.72 % (1815)Termination phase: shuffling
% 2.84/1.72
% 2.84/1.72 % (1815)Memory used [KB]: 1407
% 2.84/1.72 % (1815)Time elapsed: 0.003 s
% 2.84/1.72 % (1815)Instructions burned: 3 (million)
% 2.84/1.72 % (1815)------------------------------
% 2.84/1.72 % (1815)------------------------------
% 2.84/1.72 % (1814)Instruction limit reached!
% 2.84/1.72 % (1814)------------------------------
% 2.84/1.72 % (1814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.72 % (1814)Termination reason: Unknown
% 2.84/1.72 % (1814)Termination phase: Property scanning
% 2.84/1.72
% 2.84/1.72 % (1814)Memory used [KB]: 1663
% 2.84/1.72 % (1814)Time elapsed: 0.010 s
% 2.84/1.72 % (1814)Instructions burned: 17 (million)
% 2.84/1.72 % (1814)------------------------------
% 2.84/1.72 % (1814)------------------------------
% 2.84/1.72 % (1816)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_1697 for (2999ds/3Mi)
% 2.84/1.72 % (1816)Instruction limit reached!
% 2.84/1.72 % (1816)------------------------------
% 2.84/1.72 % (1816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.72 % (1816)Termination reason: Unknown
% 2.84/1.72 % (1816)Termination phase: shuffling
% 2.84/1.72
% 2.84/1.72 % (1816)Memory used [KB]: 1407
% 2.84/1.72 % (1816)Time elapsed: 0.003 s
% 2.84/1.72 % (1816)Instructions burned: 3 (million)
% 2.84/1.72 % (1816)------------------------------
% 2.84/1.72 % (1816)------------------------------
% 2.84/1.73 % (1817)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/7Mi)
% 2.84/1.73 % (1817)Instruction limit reached!
% 2.84/1.73 % (1817)------------------------------
% 2.84/1.73 % (1817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.73 % (1817)Termination reason: Unknown
% 2.84/1.73 % (1817)Termination phase: shuffling
% 2.84/1.73
% 2.84/1.73 % (1817)Memory used [KB]: 1407
% 2.84/1.73 % (1817)Time elapsed: 0.005 s
% 2.84/1.73 % (1817)Instructions burned: 7 (million)
% 2.84/1.73 % (1817)------------------------------
% 2.84/1.73 % (1817)------------------------------
% 2.84/1.73 % (1818)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/3Mi)
% 2.84/1.73 % (1818)Instruction limit reached!
% 2.84/1.73 % (1818)------------------------------
% 2.84/1.73 % (1818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.73 % (1818)Termination reason: Unknown
% 2.84/1.73 % (1818)Termination phase: shuffling
% 2.84/1.73
% 2.84/1.73 % (1818)Memory used [KB]: 1407
% 2.84/1.73 % (1818)Time elapsed: 0.003 s
% 2.84/1.73 % (1818)Instructions burned: 3 (million)
% 2.84/1.73 % (1818)------------------------------
% 2.84/1.73 % (1818)------------------------------
% 2.84/1.74 % (1819)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/4Mi)
% 2.84/1.74 % (1819)Instruction limit reached!
% 2.84/1.74 % (1819)------------------------------
% 2.84/1.74 % (1819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.74 % (1819)Termination reason: Unknown
% 2.84/1.74 % (1819)Termination phase: shuffling
% 2.84/1.74
% 2.84/1.74 % (1819)Memory used [KB]: 1407
% 2.84/1.74 % (1819)Time elapsed: 0.004 s
% 2.84/1.74 % (1819)Instructions burned: 5 (million)
% 2.84/1.74 % (1819)------------------------------
% 2.84/1.74 % (1819)------------------------------
% 2.84/1.74 % (1820)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/18Mi)
% 2.84/1.75 % (1821)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/710Mi)
% 2.84/1.75 % (1822)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1697 for (2999ds/6Mi)
% 2.84/1.75 % (1820)Instruction limit reached!
% 2.84/1.75 % (1820)------------------------------
% 2.84/1.75 % (1820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.75 % (1820)Termination reason: Unknown
% 2.84/1.75 % (1820)Termination phase: Property scanning
% 2.84/1.75
% 2.84/1.75 % (1820)Memory used [KB]: 1663
% 2.84/1.75 % (1820)Time elapsed: 0.011 s
% 2.84/1.75 % (1820)Instructions burned: 19 (million)
% 2.84/1.75 % (1820)------------------------------
% 2.84/1.75 % (1820)------------------------------
% 2.84/1.75 % (1822)Instruction limit reached!
% 2.84/1.75 % (1822)------------------------------
% 2.84/1.75 % (1822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.75 % (1822)Termination reason: Unknown
% 2.84/1.75 % (1822)Termination phase: shuffling
% 2.84/1.75
% 2.84/1.75 % (1822)Memory used [KB]: 1407
% 2.84/1.75 % (1822)Time elapsed: 0.005 s
% 2.84/1.75 % (1822)Instructions burned: 7 (million)
% 2.84/1.75 % (1822)------------------------------
% 2.84/1.75 % (1822)------------------------------
% 2.84/1.76 % (1801)Instruction limit reached!
% 2.84/1.76 % (1801)------------------------------
% 2.84/1.76 % (1801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.76 % (1801)Termination reason: Unknown
% 2.84/1.76 % (1801)Termination phase: Saturation
% 2.84/1.76
% 2.84/1.76 % (1801)Memory used [KB]: 7036
% 2.84/1.76 % (1801)Time elapsed: 0.086 s
% 2.84/1.76 % (1801)Instructions burned: 184 (million)
% 2.84/1.76 % (1801)------------------------------
% 2.84/1.76 % (1801)------------------------------
% 2.84/1.76 % (1823)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_1697 for (2999ds/902Mi)
% 2.84/1.77 % (1824)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_1697 for (2999ds/21Mi)
% 2.84/1.77 % (1825)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1697 for (2998ds/5Mi)
% 2.84/1.77 % (1825)Instruction limit reached!
% 2.84/1.77 % (1825)------------------------------
% 2.84/1.77 % (1825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.77 % (1825)Termination reason: Unknown
% 2.84/1.77 % (1825)Termination phase: shuffling
% 2.84/1.77
% 2.84/1.77 % (1825)Memory used [KB]: 1407
% 2.84/1.77 % (1825)Time elapsed: 0.004 s
% 2.84/1.77 % (1825)Instructions burned: 6 (million)
% 2.84/1.77 % (1825)------------------------------
% 2.84/1.77 % (1825)------------------------------
% 2.84/1.77 % (1826)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_1697 for (2998ds/6Mi)
% 2.84/1.78 % (1826)Instruction limit reached!
% 2.84/1.78 % (1826)------------------------------
% 2.84/1.78 % (1826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.78 % (1826)Termination reason: Unknown
% 2.84/1.78 % (1826)Termination phase: shuffling
% 2.84/1.78
% 2.84/1.78 % (1826)Memory used [KB]: 1407
% 2.84/1.78 % (1826)Time elapsed: 0.005 s
% 2.84/1.78 % (1826)Instructions burned: 8 (million)
% 2.84/1.78 % (1826)------------------------------
% 2.84/1.78 % (1826)------------------------------
% 2.84/1.78 % (1824)Instruction limit reached!
% 2.84/1.78 % (1824)------------------------------
% 2.84/1.78 % (1824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.78 % (1824)Termination reason: Unknown
% 2.84/1.78 % (1824)Termination phase: shuffling
% 2.84/1.78
% 2.84/1.78 % (1824)Memory used [KB]: 1791
% 2.84/1.78 % (1824)Time elapsed: 0.012 s
% 2.84/1.78 % (1824)Instructions burned: 21 (million)
% 2.84/1.78 % (1824)------------------------------
% 2.84/1.78 % (1824)------------------------------
% 2.84/1.79 % (1827)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1697 for (2998ds/377Mi)
% 2.84/1.79 % (1828)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_1697 for (2998ds/779Mi)
% 2.84/1.79 % (1829)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_1697 for (2998ds/19Mi)
% 2.84/1.80 % (1829)Instruction limit reached!
% 2.84/1.80 % (1829)------------------------------
% 2.84/1.80 % (1829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.80 % (1829)Termination reason: Unknown
% 2.84/1.80 % (1829)Termination phase: shuffling
% 2.84/1.80
% 2.84/1.80 % (1829)Memory used [KB]: 1663
% 2.84/1.80 % (1829)Time elapsed: 0.011 s
% 2.84/1.80 % (1829)Instructions burned: 21 (million)
% 2.84/1.80 % (1829)------------------------------
% 2.84/1.80 % (1829)------------------------------
% 2.84/1.81 % (1806)Instruction limit reached!
% 2.84/1.81 % (1806)------------------------------
% 2.84/1.81 % (1806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.81 % (1806)Termination reason: Unknown
% 2.84/1.81 % (1806)Termination phase: Saturation
% 2.84/1.81
% 2.84/1.81 % (1806)Memory used [KB]: 6908
% 2.84/1.81 % (1806)Time elapsed: 0.136 s
% 2.84/1.81 % (1806)Instructions burned: 275 (million)
% 2.84/1.81 % (1806)------------------------------
% 2.84/1.81 % (1806)------------------------------
% 2.84/1.82 % (1831)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1697 for (2998ds/879Mi)
% 2.84/1.82 % (1833)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1697 for (2998ds/17Mi)
% 2.84/1.83 % (1823)First to succeed.
% 2.84/1.83 % (1823)Refutation found. Thanks to Tanya!
% 2.84/1.83 % SZS status Theorem for DTF2THF_1697
% 2.84/1.83 % SZS output start Proof for DTF2THF_1697
% 2.84/1.83 thf(type_def_5, type, coindu1593790203_llist: ($tType) > $tType).
% 2.84/1.83 thf(type_def_7, type, list: ($tType) > $tType).
% 2.84/1.83 thf(type_def_8, type, set: ($tType) > $tType).
% 2.84/1.83 thf(type_def_9, type, itself: ($tType) > $tType).
% 2.84/1.83 thf(type_def_10, type, a: $tType).
% 2.84/1.83 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 2.84/1.83 thf(func_def_1, type, list: ($tType) > $tType).
% 2.84/1.83 thf(func_def_2, type, set: ($tType) > $tType).
% 2.84/1.83 thf(func_def_3, type, itself: ($tType) > $tType).
% 2.84/1.83 thf(func_def_4, type, a: $tType).
% 2.84/1.83 thf(func_def_5, type, coindu1571841457prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.84/1.83 thf(func_def_6, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_7, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.84/1.83 thf(func_def_8, type, coindu1736001939ist_of: !>[X0: $tType]:(coindu1593790203_llist @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_9, type, coindu1542816657of_aux: !>[X0: $tType]:(list @ X0 > coindu1593790203_llist @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_10, type, coindu2000965700_llast: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.84/1.83 thf(func_def_11, type, coindu300403952lexord: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.84/1.83 thf(func_def_12, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_13, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_14, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.84/1.83 thf(func_def_15, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 2.84/1.83 thf(func_def_16, type, coindu1112613586e_lset: !>[X0: $tType]:(coindu1593790203_llist @ X0 > set @ X0)).
% 2.84/1.83 thf(func_def_17, type, coindu1079202755ist_of: !>[X0: $tType]:(list @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_18, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 2.84/1.83 thf(func_def_19, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 2.84/1.83 thf(func_def_20, type, undefined: !>[X0: $tType]:(X0)).
% 2.84/1.83 thf(func_def_21, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.84/1.83 thf(func_def_22, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_23, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 2.84/1.83 thf(func_def_24, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_25, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_26, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_27, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_28, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.84/1.83 thf(func_def_29, type, case_list: !>[X0: $tType, X1: $tType]:(X0 > (X1 > list @ X1 > X0) > list @ X1 > X0)).
% 2.84/1.83 thf(func_def_30, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_31, type, map: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 2.84/1.83 thf(func_def_32, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_33, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 2.84/1.83 thf(func_def_34, type, map_tailrec: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 2.84/1.83 thf(func_def_35, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1 > list @ X1)).
% 2.84/1.83 thf(func_def_36, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 2.84/1.83 thf(func_def_37, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.84/1.83 thf(func_def_38, type, remdups_adj: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_39, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_40, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_41, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.84/1.83 thf(func_def_42, type, type: !>[X0: $tType]:(itself @ X0)).
% 2.84/1.83 thf(func_def_43, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.84/1.83 thf(func_def_44, type, prefixes: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.84/1.83 thf(func_def_45, type, prefixes_rel: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.84/1.83 thf(func_def_46, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 2.84/1.83 thf(func_def_47, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.84/1.83 thf(func_def_48, type, xs: list @ a).
% 2.84/1.83 thf(func_def_49, type, r: a > a > $o).
% 2.84/1.83 thf(func_def_51, type, xs2: list @ a).
% 2.84/1.83 thf(func_def_52, type, xs3: coindu1593790203_llist @ a).
% 2.84/1.83 thf(func_def_53, type, y: a).
% 2.84/1.83 thf(func_def_54, type, ys: list @ a).
% 2.84/1.83 thf(func_def_55, type, ys2: coindu1593790203_llist @ a).
% 2.84/1.83 thf(func_def_56, type, zs: list @ a).
% 2.84/1.83 thf(func_def_57, type, zs2: coindu1593790203_llist @ a).
% 2.84/1.83 thf(func_def_73, type, sP0: !>[X0: $tType]:(list @ X0 > list @ list @ X0 > $o)).
% 2.84/1.83 thf(func_def_74, type, sP1: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > $o)).
% 2.84/1.83 thf(func_def_75, type, sK2: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_76, type, sK3: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_77, type, sK4: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.84/1.83 thf(func_def_78, type, sK5: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_79, type, sK6: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > X0)).
% 2.84/1.83 thf(func_def_80, type, sK7: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_81, type, sK8: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_82, type, sK9: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_83, type, sK10: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > X1)).
% 2.84/1.83 thf(func_def_84, type, sK11: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > list @ X1)).
% 2.84/1.83 thf(func_def_85, type, sK12: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_86, type, sK13: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_87, type, sK14: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_88, type, sK15: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_89, type, sK16: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_90, type, sK17: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0 > X0)).
% 2.84/1.83 thf(func_def_91, type, sK18: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_92, type, sK19: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_93, type, sK20: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_94, type, sK21: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_95, type, sK22: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_96, type, sK23: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_97, type, sK24: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_98, type, sK25: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_99, type, sK26: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_100, type, sK27: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_101, type, sK28: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_102, type, sK29: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_103, type, sK30: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_104, type, sK31: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_105, type, sK32: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_106, type, sK33: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_107, type, sK34: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_108, type, sK35: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.84/1.83 thf(func_def_109, type, sK36: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_110, type, sK37: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.84/1.83 thf(func_def_111, type, sK38: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.84/1.83 thf(func_def_112, type, sK39: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.84/1.83 thf(func_def_113, type, sK40: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.84/1.83 thf(func_def_114, type, sK41: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.84/1.83 thf(func_def_115, type, sK42: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_116, type, sK43: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_117, type, sK44: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.84/1.83 thf(func_def_118, type, sK45: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_119, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.84/1.83 thf(func_def_120, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.84/1.83 thf(func_def_121, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.84/1.83 thf(func_def_122, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 2.84/1.83 thf(func_def_123, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_124, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.84/1.83 thf(func_def_125, type, sK52: list @ a).
% 2.84/1.83 thf(func_def_126, type, sK53: !>[X0: $tType, X1: $tType]:(list @ X0 > X0 > list @ X1 > (X1 > X0) > X1)).
% 2.84/1.83 thf(func_def_127, type, sK54: !>[X0: $tType, X1: $tType]:(list @ X0 > X0 > list @ X1 > (X1 > X0) > list @ X1)).
% 2.84/1.83 thf(func_def_128, type, sK55: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > X0)).
% 2.84/1.83 thf(func_def_129, type, sK56: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_130, type, sK57: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0)).
% 2.84/1.83 thf(func_def_131, type, sK58: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_132, type, sK59: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_133, type, sK60: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_134, type, sK61: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_135, type, sK62: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_136, type, sK63: list @ a).
% 2.84/1.83 thf(func_def_137, type, sK64: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > X0)).
% 2.84/1.83 thf(func_def_138, type, sK65: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_139, type, sK66: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_140, type, sK67: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_141, type, sK68: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > (X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_142, type, sK69: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_143, type, sK70: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_144, type, sK71: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_145, type, sK72: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_146, type, sK73: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_147, type, sK74: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_148, type, sK75: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > X0)).
% 2.84/1.83 thf(func_def_149, type, sK76: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_150, type, sK77: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_151, type, sK78: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_152, type, sK79: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_153, type, sK80: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_154, type, sK81: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_155, type, sK82: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_156, type, sK83: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_157, type, sK84: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_158, type, sK85: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_159, type, sK86: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_160, type, sK87: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_161, type, sK88: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_162, type, sK89: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_163, type, sK90: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_164, type, sK91: !>[X0: $tType, X1: $tType]:(list @ X1 > X1 > list @ X0 > (X0 > X1) > X0)).
% 2.84/1.83 thf(func_def_165, type, sK92: !>[X0: $tType, X1: $tType]:(list @ X1 > X1 > list @ X0 > (X0 > X1) > list @ X0)).
% 2.84/1.83 thf(func_def_166, type, sK93: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_167, type, sK94: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_168, type, sK95: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_169, type, sK96: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_170, type, sK97: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_171, type, sK98: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_172, type, sK99: !>[X0: $tType]:(list @ X0 > X0)).
% 2.84/1.83 thf(func_def_173, type, sK100: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_174, type, sK101: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_175, type, sK102: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > X0)).
% 2.84/1.83 thf(func_def_176, type, sK103: !>[X0: $tType]:(list @ list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_177, type, sK104: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_178, type, sK105: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_179, type, sK106: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_180, type, sK107: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_181, type, sK108: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_182, type, sK109: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_183, type, sK110: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_184, type, sK111: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 2.84/1.83 thf(func_def_185, type, sK112: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_186, type, sK113: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.84/1.83 thf(func_def_187, type, sK114: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.84/1.83 thf(func_def_188, type, sK115: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_189, type, sK116: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_190, type, sK117: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_191, type, sK118: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0 > X0)).
% 2.84/1.83 thf(func_def_192, type, sK119: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_193, type, sK120: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > X1)).
% 2.84/1.83 thf(func_def_194, type, sK121: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > list @ X1)).
% 2.84/1.83 thf(func_def_195, type, sK122: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_196, type, sK123: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_197, type, sK124: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_198, type, sK125: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_199, type, sK126: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_200, type, sK127: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_201, type, sK128: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_202, type, sK129: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_203, type, sK130: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_204, type, sK131: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_205, type, sK132: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_206, type, sK133: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_207, type, sK134: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_208, type, sK135: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_209, type, sK136: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.84/1.83 thf(func_def_210, type, sK137: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 2.84/1.83 thf(func_def_211, type, sK138: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_212, type, sK139: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_213, type, sK140: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.84/1.83 thf(func_def_214, type, sK141: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_215, type, sK142: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.84/1.83 thf(func_def_216, type, sK143: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_217, type, sK144: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 2.84/1.83 thf(func_def_218, type, sK145: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X1 > list @ X0 > (X0 > X1) > X0)).
% 2.84/1.83 thf(func_def_219, type, sK146: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X1 > list @ X0 > (X0 > X1) > list @ X0)).
% 2.84/1.83 thf(func_def_220, type, sK147: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 2.84/1.83 thf(func_def_221, type, sK148: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 2.84/1.83 thf(func_def_223, type, ph150: !>[X0: $tType]:(X0)).
% 2.84/1.83 thf(f1732,plain,(
% 2.84/1.83 $false),
% 2.84/1.83 inference(avatar_sat_refutation,[status(thm)],[f1647,f1648,f1704])).
% 2.84/1.83 thf(f1704,plain,(
% 2.84/1.83 ~spl149_2),
% 2.84/1.83 inference(avatar_contradiction_clause,[status(thm)],[f1703])).
% 2.84/1.83 thf(f1703,plain,(
% 2.84/1.83 $false | ~spl149_2),
% 2.84/1.83 inference(trivial_inequality_removal,[status(thm)],[f1666])).
% 2.84/1.83 thf(f1666,plain,(
% 2.84/1.83 (ys2 != ys2) | ($true != $true) | ~spl149_2),
% 2.84/1.83 inference(superposition,[status(thm)],[f1656,f1195])).
% 2.84/1.83 thf(f1195,plain,(
% 2.84/1.83 ((coindu1213758845finite @ a @ ys2) = $true)),
% 2.84/1.83 inference(cnf_transformation,[status(thm)],[f435])).
% 2.84/1.83 thf(f435,plain,(
% 2.84/1.83 ((coindu1213758845finite @ a @ ys2) = $true)),
% 2.84/1.83 inference(fool_elimination,[status(thm)],[f434])).
% 2.84/1.83 thf(f434,plain,(
% 2.84/1.83 (coindu1213758845finite @ a @ ys2)),
% 2.84/1.83 inference(rectify,[status(thm)],[f4])).
% 2.84/1.83 thf(f4,axiom,(
% 2.84/1.83 (coindu1213758845finite @ a @ ys2)),
% 2.84/1.83 file('/export/starexec/sandbox/tmp/tmp.SSpVV69JSc/DTF2THF_1697.p',fact_3__092_060open_062lfinite_Ays_H_092_060close_062)).
% 2.84/1.83 thf(f1656,plain,(
% 2.84/1.83 ( ! [X0 : coindu1593790203_llist @ a] : (($true != (coindu1213758845finite @ a @ X0)) | (ys2 != X0)) ) | ~spl149_2),
% 2.84/1.83 inference(superposition,[status(thm)],[f1646,f1274])).
% 2.84/1.83 thf(f1274,plain,(
% 2.84/1.83 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((coindu1079202755ist_of @ X0 @ (coindu1736001939ist_of @ X0 @ X1)) = X1) | ($true != (coindu1213758845finite @ X0 @ X1))) )),
% 2.84/1.83 inference(cnf_transformation,[status(thm)],[f676])).
% 2.84/1.83 thf(f676,plain,(
% 2.84/1.83 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((coindu1079202755ist_of @ X0 @ (coindu1736001939ist_of @ X0 @ X1)) = X1) | ($true != (coindu1213758845finite @ X0 @ X1)))),
% 2.84/1.83 inference(ennf_transformation,[status(thm)],[f313])).
% 2.84/1.83 thf(f313,plain,(
% 2.84/1.83 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = (coindu1213758845finite @ X0 @ X1)) => ((coindu1079202755ist_of @ X0 @ (coindu1736001939ist_of @ X0 @ X1)) = X1))),
% 2.84/1.83 inference(fool_elimination,[status(thm)],[f312])).
% 2.84/1.83 thf(f312,plain,(
% 2.84/1.83 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((coindu1213758845finite @ X0 @ X1) => ((coindu1079202755ist_of @ X0 @ (coindu1736001939ist_of @ X0 @ X1)) = X1))),
% 2.84/1.83 inference(rectify,[status(thm)],[f25])).
% 2.84/1.83 thf(f25,axiom,(
% 2.84/1.83 ! [X0 : $tType,X3 : coindu1593790203_llist @ X0] : ((coindu1213758845finite @ X0 @ X3) => ((coindu1079202755ist_of @ X0 @ (coindu1736001939ist_of @ X0 @ X3)) = X3))),
% 2.84/1.83 file('/export/starexec/sandbox/tmp/tmp.SSpVV69JSc/DTF2THF_1697.p',fact_24_llist__of__list__of)).
% 2.84/1.83 thf(f1646,plain,(
% 2.84/1.83 ( ! [X0 : list @ a] : ((ys2 != (coindu1079202755ist_of @ a @ X0))) ) | ~spl149_2),
% 2.84/1.83 inference(avatar_component_clause,[status(thm)],[f1645])).
% 2.84/1.83 thf(f1645,definition,(
% 2.84/1.83 spl149_2 <=> ! [X0 : list @ a] : (ys2 != (coindu1079202755ist_of @ a @ X0))),
% 2.84/1.83 introduced(definition,[new_symbols(naming,[spl149_2])],[avatar_definition])).
% 2.84/1.83 thf(f1648,plain,(
% 2.84/1.83 ~spl149_1),
% 2.84/1.83 inference(avatar_split_clause,[status(thm)],[f1431,f1641])).
% 2.84/1.83 thf(f1641,definition,(
% 2.84/1.83 spl149_1 <=> (thesis = $true)),
% 2.84/1.83 introduced(definition,[new_symbols(naming,[spl149_1])],[avatar_definition])).
% 2.84/1.83 thf(f1431,plain,(
% 2.84/1.83 (thesis != $true)),
% 2.84/1.83 inference(cnf_transformation,[status(thm)],[f622])).
% 2.84/1.83 thf(f622,plain,(
% 2.84/1.83 (thesis != $true)),
% 2.84/1.83 inference(flattening,[status(thm)],[f453])).
% 2.84/1.83 thf(f453,plain,(
% 2.84/1.83 ~(thesis = $true)),
% 2.84/1.83 inference(fool_elimination,[status(thm)],[f452])).
% 2.84/1.83 thf(f452,plain,(
% 2.84/1.83 ~thesis),
% 2.84/1.83 inference(rectify,[status(thm)],[f260])).
% 2.84/1.83 thf(f260,negated_conjecture,(
% 2.84/1.83 ~thesis),
% 2.84/1.83 inference(negated_conjecture,[status(cth)],[f259])).
% 2.84/1.83 thf(f259,conjecture,(
% 2.84/1.83 thesis),
% 2.84/1.83 file('/export/starexec/sandbox/tmp/tmp.SSpVV69JSc/DTF2THF_1697.p',conj_1)).
% 2.84/1.83 thf(f1647,plain,(
% 2.84/1.83 spl149_1 | spl149_2),
% 2.84/1.83 inference(avatar_split_clause,[status(thm)],[f1465,f1645,f1641])).
% 2.84/1.83 thf(f1465,plain,(
% 2.84/1.83 ( ! [X0 : list @ a] : ((ys2 != (coindu1079202755ist_of @ a @ X0)) | (thesis = $true)) )),
% 2.84/1.83 inference(cnf_transformation,[status(thm)],[f742])).
% 2.84/1.83 thf(f742,plain,(
% 2.84/1.83 ! [X0 : list @ a] : ((thesis = $true) | (ys2 != (coindu1079202755ist_of @ a @ X0)))),
% 2.84/1.83 inference(ennf_transformation,[status(thm)],[f463])).
% 2.84/1.83 thf(f463,plain,(
% 2.84/1.83 ! [X0 : list @ a] : ((ys2 = (coindu1079202755ist_of @ a @ X0)) => (thesis = $true))),
% 2.84/1.83 inference(fool_elimination,[status(thm)],[f462])).
% 2.84/1.83 thf(f462,plain,(
% 2.84/1.83 ! [X0 : list @ a] : ((ys2 = (coindu1079202755ist_of @ a @ X0)) => thesis)),
% 2.84/1.83 inference(rectify,[status(thm)],[f258])).
% 2.84/1.83 thf(f258,axiom,(
% 2.84/1.83 ! [X90 : list @ a] : ((ys2 = (coindu1079202755ist_of @ a @ X90)) => thesis)),
% 2.84/1.83 file('/export/starexec/sandbox/tmp/tmp.SSpVV69JSc/DTF2THF_1697.p',conj_0)).
% 2.84/1.83 % SZS output end Proof for DTF2THF_1697
% 2.84/1.83 % (1823)------------------------------
% 2.84/1.83 % (1823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.83 % (1823)Termination reason: Refutation
% 2.84/1.83
% 2.84/1.83 % (1823)Memory used [KB]: 7419
% 2.84/1.83 % (1823)Time elapsed: 0.074 s
% 2.84/1.83 % (1823)Instructions burned: 146 (million)
% 2.84/1.83 % (1823)------------------------------
% 2.84/1.83 % (1823)------------------------------
% 2.84/1.83 % (1800)Success in time 0.174 s
%------------------------------------------------------------------------------