%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM175^1 : 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 : n012.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 08:41:51 AM UTC 2026
% Result : Theorem 6.78s 2.13s
% Output : Refutation 6.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : COM175^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.27 % Computer : n012.cluster.edu
% 0.06/0.27 % Model : x86_64 x86_64
% 0.06/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.27 % Memory : 8042.1875MB
% 0.06/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.27 % CPULimit : 300
% 0.06/0.27 % WCLimit : 300
% 0.06/0.27 % DateTime : Tue Feb 24 04:16:00 EST 2026
% 0.06/0.27 % CPUTime :
% 0.06/0.27 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.36 ---- Original DTF file ---
% 0.13/0.36 thf(spec,logic,$$dhol).
% 0.13/0.36 %------------------------------------------------------------------------------
% 0.13/0.36 % File : COM175^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.36 % Domain : Computing Theory
% 0.13/0.36 % Problem : Koenig's lemma 115
% 0.13/0.36 % Version : [Bla16] axioms : Especial.
% 0.13/0.36 % English :
% 0.13/0.36
% 0.13/0.36 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.13/0.36 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.13/0.36 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.13/0.36 % Source : [Bla16]
% 0.13/0.36 % Names : koenigslemma__115.p [Bla16]
% 0.13/0.36
% 0.13/0.36 % Status : Theorem
% 0.13/0.36 % Rating : 0.33 v9.0.0, 0.00 v8.1.0, 0.25 v7.5.0, 0.00 v7.3.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.13/0.36 % Syntax : Number of formulae : 326 ( 117 unt; 47 typ; 0 def)
% 0.13/0.36 % Number of atoms : 815 ( 241 equ; 0 cnn)
% 0.13/0.36 % Maximal formula atoms : 13 ( 2 avg)
% 0.13/0.36 % Number of connectives : 4283 ( 86 ~; 39 |; 81 &;3671 @)
% 0.13/0.36 % ( 0 <=>; 406 =>; 0 <=; 0 <~>)
% 0.13/0.36 % Maximal formula depth : 22 ( 9 avg)
% 0.13/0.36 % Number of types : 2 ( 1 usr)
% 0.13/0.36 % Number of type conns : 283 ( 283 >; 0 *; 0 +; 0 <<)
% 0.13/0.36 % Number of symbols : 49 ( 46 usr; 8 con; 0-8 aty)
% 0.13/0.36 % Number of variables : 1143 ( 60 ^; 971 !; 74 ?;1143 :)
% 0.13/0.36 % ( 38 !>; 0 ?*; 0 @-; 0 @+)
% 0.13/0.36 % SPC : TH1_THM_EQU_NAR
% 0.13/0.36
% 0.13/0.36 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.13/0.36 % 2016-07-13 14:46:24.599
% 0.13/0.36 %------------------------------------------------------------------------------
% 0.13/0.36 %----Could-be-implicit typings (4)
% 0.13/0.36 thf(ty_t_Coinductive__List_Ollist,type,
% 0.13/0.36 coinductive_llist: $tType > $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_Set_Oset,type,
% 0.13/0.36 set: $tType > $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_t_itself,type,
% 0.13/0.36 itself: $tType > $tType ).
% 0.13/0.36
% 0.13/0.36 thf(ty_tf_a,type,
% 0.13/0.36 a: $tType ).
% 0.13/0.36
% 0.13/0.36 %----Explicit typings (43)
% 0.13/0.36 thf(sy_cl_HOL_Otype,type,
% 0.13/0.36 type:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Oord,type,
% 0.13/0.36 ord:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Oorder,type,
% 0.13/0.36 order:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Lattices_Olattice,type,
% 0.13/0.36 lattice:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Olinorder,type,
% 0.13/0.36 linorder:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Orderings_Opreorder,type,
% 0.13/0.36 preorder:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.13/0.36 semilattice_sup:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.13/0.36 comple187826305attice:
% 0.13/0.36 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.13/0.36 coindu328551480prefix:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 0.13/0.36 coinductive_gen_lset:
% 0.13/0.36 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Olappend,type,
% 0.13/0.36 coinductive_lappend:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Oldistinct,type,
% 0.13/0.36 coindu351974385stinct:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Olfilter,type,
% 0.13/0.36 coinductive_lfilter:
% 0.13/0.36 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.13/0.36 coinductive_lfinite:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollast,type,
% 0.13/0.36 coinductive_llast:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollexord,type,
% 0.13/0.36 coinductive_llexord:
% 0.13/0.36 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.13/0.36 coinductive_LCons:
% 0.13/0.36 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.13/0.36 coinductive_LNil:
% 0.13/0.36 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollist_Ocorec__llist,type,
% 0.13/0.36 coindu1259883913_llist:
% 0.13/0.36 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 0.13/0.36 coinductive_lhd:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.13/0.36 coinductive_lnull:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 0.13/0.36 coinductive_lset:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Olmember,type,
% 0.13/0.36 coinductive_lmember:
% 0.13/0.36 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.13/0.36 coindu1478340336prefix:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Oord__class_Olsorted,type,
% 0.13/0.36 coindu63249387sorted:
% 0.13/0.36 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Coinductive__List_Ounfold__llist,type,
% 0.13/0.36 coindu1441602521_llist:
% 0.13/0.36 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coinductive_llist @ B ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_If,type,
% 0.13/0.36 if:
% 0.13/0.36 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opaths,type,
% 0.13/0.36 koenig916195507_paths:
% 0.13/0.36 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ ( coinductive_llist @ Node ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opathsp,type,
% 0.13/0.36 koenig2031690877pathsp:
% 0.13/0.36 !>[Node: $tType] : ( ( Node > Node > $o ) > ( coinductive_llist @ Node ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oreachable__via,type,
% 0.13/0.36 koenig317145564le_via:
% 0.13/0.36 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ Node ) > Node > ( set @ Node ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oreachable__viap,type,
% 0.13/0.36 koenig1757754772e_viap:
% 0.13/0.36 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ Node ) > Node > Node > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.13/0.36 sup_sup:
% 0.13/0.36 !>[A: $tType] : ( A > A > A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.13/0.36 ord_less_eq:
% 0.13/0.36 !>[A: $tType] : ( A > A > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Pure_Otype,type,
% 0.13/0.36 type2:
% 0.13/0.36 !>[A: $tType] : ( itself @ A ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_Set_OCollect,type,
% 0.13/0.36 collect:
% 0.13/0.36 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_c_member,type,
% 0.13/0.36 member:
% 0.13/0.36 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_graph,type,
% 0.13/0.36 graph: a > a > $o ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_n,type,
% 0.13/0.36 n: a ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_n_H____,type,
% 0.13/0.36 n2: a ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_ns,type,
% 0.13/0.36 ns: set @ a ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_x____,type,
% 0.13/0.36 x: a ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_xs_H____,type,
% 0.13/0.36 xs: coinductive_llist @ a ).
% 0.13/0.36
% 0.13/0.36 thf(sy_v_xs____,type,
% 0.13/0.36 xs2: coinductive_llist @ a ).
% 0.13/0.36
% 0.13/0.36 %----Relevant facts (256)
% 0.13/0.36 thf(fact_0__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062,axiom,
% 0.13/0.36 member @ a @ x @ ( coinductive_lset @ a @ xs2 ) ).
% 0.13/0.36
% 0.13/0.36 % \<open>x \<in> lset xs\<close>
% 0.13/0.36 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.13/0.36 ~ ! [N: a,Xs: coinductive_llist @ a] :
% 0.13/0.36 ( xs2
% 0.13/0.36 != ( coinductive_LCons @ a @ N @ Xs ) ) ).
% 0.13/0.36
% 0.13/0.36 % \<open>\<And>thesis. (\<And>n' xs'. xs = LCons n' xs' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.13/0.36 thf(fact_2_xs,axiom,
% 0.13/0.36 ( xs2
% 0.13/0.36 = ( coinductive_LCons @ a @ n2 @ xs ) ) ).
% 0.13/0.36
% 0.13/0.36 % xs
% 0.13/0.36 thf(fact_3__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062,axiom,
% 0.13/0.36 ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns ).
% 0.13/0.36
% 0.13/0.36 % \<open>lset xs \<subseteq> ns\<close>
% 0.13/0.36 thf(fact_4_calculation,axiom,
% 0.13/0.36 graph @ n @ n2 ).
% 0.13/0.36
% 0.13/0.36 % calculation
% 0.13/0.36 thf(fact_5__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062,axiom,
% 0.13/0.36 member @ a @ x @ ( koenig317145564le_via @ a @ graph @ ns @ n ) ).
% 0.13/0.36
% 0.13/0.36 % \<open>x \<in> reachable_via graph ns n\<close>
% 0.13/0.36 thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.13/0.36 ~ ! [Xs2: coinductive_llist @ a] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ Xs2 ) @ ( koenig916195507_paths @ a @ graph ) )
% 0.13/0.36 => ( ( member @ a @ x @ ( coinductive_lset @ a @ Xs2 ) )
% 0.13/0.36 => ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ Xs2 ) @ ns ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % \<open>\<And>thesis. (\<And>xs. \<lbrakk>LCons n xs \<in> paths graph; x \<in> lset xs; lset xs \<subseteq> ns\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.13/0.36 thf(fact_7_path,axiom,
% 0.13/0.36 member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs2 ) @ ( koenig916195507_paths @ a @ graph ) ).
% 0.13/0.36
% 0.13/0.36 % path
% 0.13/0.36 thf(fact_8_paths_OLCons,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,X: Node,Y: Node,Xs3: coinductive_llist @ Node] :
% 0.13/0.36 ( ( Graph @ X @ Y )
% 0.13/0.36 => ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y @ Xs3 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 => ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LCons @ Node @ Y @ Xs3 ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths.LCons
% 0.13/0.36 thf(fact_9_paths__LConsD,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,Graph: A > A > $o] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.13/0.36 => ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths_LConsD
% 0.13/0.36 thf(fact_10_path__avoid__node,axiom,
% 0.13/0.36 ! [A: $tType,N2: A,Xs3: coinductive_llist @ A,Graph: A > A > $o,X: A] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ N2 @ Xs3 ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.13/0.36 => ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( ( N2 != X )
% 0.13/0.36 => ? [Xs: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ N2 @ Xs ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.13/0.36 & ( ord_less_eq @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 & ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.13/0.36 & ~ ( member @ A @ N2 @ ( coinductive_lset @ A @ Xs ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % path_avoid_node
% 0.13/0.36 thf(fact_11_reachable__via_Ocases,axiom,
% 0.13/0.36 ! [Node: $tType,A2: Node,Graph: Node > Node > $o,Ns: set @ Node,N2: Node] :
% 0.13/0.36 ( ( member @ Node @ A2 @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) )
% 0.13/0.36 => ~ ! [Xs2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 => ( ( member @ Node @ A2 @ ( coinductive_lset @ Node @ Xs2 ) )
% 0.13/0.36 => ~ ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_via.cases
% 0.13/0.36 thf(fact_12_reachable__via_Osimps,axiom,
% 0.13/0.36 ! [Node: $tType,A2: Node,Graph: Node > Node > $o,Ns: set @ Node,N2: Node] :
% 0.13/0.36 ( ( member @ Node @ A2 @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) )
% 0.13/0.36 = ( ? [Xs4: coinductive_llist @ Node,N3: Node] :
% 0.13/0.36 ( ( A2 = N3 )
% 0.13/0.36 & ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs4 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 & ( member @ Node @ N3 @ ( coinductive_lset @ Node @ Xs4 ) )
% 0.13/0.36 & ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs4 ) @ Ns ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_via.simps
% 0.13/0.36 thf(fact_13_reachable__via_Ointros,axiom,
% 0.13/0.36 ! [Node: $tType,N2: Node,Xs3: coinductive_llist @ Node,Graph: Node > Node > $o,N4: Node,Ns: set @ Node] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs3 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 => ( ( member @ Node @ N4 @ ( coinductive_lset @ Node @ Xs3 ) )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs3 ) @ Ns )
% 0.13/0.36 => ( member @ Node @ N4 @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_via.intros
% 0.13/0.36 thf(fact_14_reachable__via_Oinducts,axiom,
% 0.13/0.36 ! [Node: $tType,X: Node,Graph: Node > Node > $o,Ns: set @ Node,N2: Node,P: Node > $o] :
% 0.13/0.36 ( ( member @ Node @ X @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) )
% 0.13/0.36 => ( ! [Xs2: coinductive_llist @ Node,N: Node] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 => ( ( member @ Node @ N @ ( coinductive_lset @ Node @ Xs2 ) )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns )
% 0.13/0.36 => ( P @ N ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_via.inducts
% 0.13/0.36 thf(fact_15_llist_Oinject,axiom,
% 0.13/0.36 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.13/0.36 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.13/0.36 = ( ( X21 = Y21 )
% 0.13/0.36 & ( X22 = Y22 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.inject
% 0.13/0.36 thf(fact_16_subsetI,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ A3 )
% 0.13/0.36 => ( member @ A @ X2 @ B2 ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % subsetI
% 0.13/0.36 thf(fact_17_subset__antisym,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A3 )
% 0.13/0.36 => ( A3 = B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_antisym
% 0.13/0.36 thf(fact_18_order__refl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_refl
% 0.13/0.36 thf(fact_19_lset__intros_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,X3: A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_intros(2)
% 0.13/0.36 thf(fact_20_lset__intros_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_intros(1)
% 0.13/0.36 thf(fact_21_llist_Oset__intros_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 0.13/0.36 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.set_intros(2)
% 0.13/0.36 thf(fact_22_llist_Oset__intros_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.set_intros(1)
% 0.13/0.36 thf(fact_23_lset__cases,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( ! [Xs: coinductive_llist @ A] :
% 0.13/0.36 ( Xs3
% 0.13/0.36 != ( coinductive_LCons @ A @ X @ Xs ) )
% 0.13/0.36 => ~ ! [X4: A,Xs: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs3
% 0.13/0.36 = ( coinductive_LCons @ A @ X4 @ Xs ) )
% 0.13/0.36 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_cases
% 0.13/0.36 thf(fact_24_lset__induct,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 0.13/0.36 => ( ! [X4: A,Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 0.13/0.36 => ( ( X != X4 )
% 0.13/0.36 => ( ( P @ Xs2 )
% 0.13/0.36 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs2 ) ) ) ) )
% 0.13/0.36 => ( P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_induct
% 0.13/0.36 thf(fact_25_lset__induct_H,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 0.13/0.36 => ( ! [X4: A,Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 0.13/0.36 => ( ( P @ Xs2 )
% 0.13/0.36 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs2 ) ) ) )
% 0.13/0.36 => ( P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_induct'
% 0.13/0.36 thf(fact_26_dual__order_Oantisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( A2 = B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.antisym
% 0.13/0.36 thf(fact_27_dual__order_Otrans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,A2: A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.trans
% 0.13/0.36 thf(fact_28_linorder__wlog,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [P: A > A > $o,A2: A,B3: A] :
% 0.13/0.36 ( ! [A4: A,B4: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.13/0.36 => ( P @ A4 @ B4 ) )
% 0.13/0.36 => ( ! [A4: A,B4: A] :
% 0.13/0.36 ( ( P @ B4 @ A4 )
% 0.13/0.36 => ( P @ A4 @ B4 ) )
% 0.13/0.36 => ( P @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % linorder_wlog
% 0.13/0.36 thf(fact_29_dual__order_Orefl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % dual_order.refl
% 0.13/0.36 thf(fact_30_order__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_trans
% 0.13/0.36 thf(fact_31_order__class_Oorder_Oantisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ( A2 = B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_class.order.antisym
% 0.13/0.36 thf(fact_32_ord__le__eq__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( ( B3 = C2 )
% 0.13/0.36 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_le_eq_trans
% 0.13/0.36 thf(fact_33_ord__eq__le__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A,C2: A] :
% 0.13/0.36 ( ( A2 = B3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.13/0.36 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_eq_le_trans
% 0.13/0.36 thf(fact_34_antisym__conv,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 = ( X = Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % antisym_conv
% 0.13/0.36 thf(fact_35_le__cases3,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.13/0.36 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.13/0.36 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_cases3
% 0.13/0.36 thf(fact_36_order_Otrans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.13/0.36 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order.trans
% 0.13/0.36 thf(fact_37_le__cases,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_cases
% 0.13/0.36 thf(fact_38_wlog__linorder__le,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [P: A > A > $o,B3: A,A2: A] :
% 0.13/0.36 ( ! [A4: A,B4: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.13/0.36 => ( P @ A4 @ B4 ) )
% 0.13/0.36 => ( ( ( P @ B3 @ A2 )
% 0.13/0.36 => ( P @ A2 @ B3 ) )
% 0.13/0.36 => ( P @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % wlog_linorder_le
% 0.13/0.36 thf(fact_39_eq__refl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( X = Y )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % eq_refl
% 0.13/0.36 thf(fact_40_linear,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % linear
% 0.13/0.36 thf(fact_41_antisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( X = Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % antisym
% 0.13/0.36 thf(fact_42_eq__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( order @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [X5: A,Y3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X5 @ Y3 )
% 0.13/0.36 & ( ord_less_eq @ A @ Y3 @ X5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % eq_iff
% 0.13/0.36 thf(fact_43_ord__le__eq__subst,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType] :
% 0.13/0.36 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.13/0.36 & ( ord @ A @ ( type2 @ A ) ) )
% 0.13/0.36 => ! [A2: A,B3: A,F: A > B,C2: B] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( ( ( F @ B3 )
% 0.13/0.36 = C2 )
% 0.13/0.36 => ( ! [X2: A,Y4: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_le_eq_subst
% 0.13/0.36 thf(fact_44_ord__eq__le__subst,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType] :
% 0.13/0.36 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.13/0.36 & ( ord @ A @ ( type2 @ A ) ) )
% 0.13/0.36 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( F @ B3 ) )
% 0.13/0.36 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.13/0.36 => ( ! [X2: B,Y4: B] :
% 0.13/0.36 ( ( ord_less_eq @ B @ X2 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ord_eq_le_subst
% 0.13/0.36 thf(fact_45_mem__Collect__eq,axiom,
% 0.13/0.36 ! [A: $tType,A2: A,P: A > $o] :
% 0.13/0.36 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.13/0.36 = ( P @ A2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % mem_Collect_eq
% 0.13/0.36 thf(fact_46_Collect__mem__eq,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A] :
% 0.13/0.36 ( ( collect @ A
% 0.13/0.36 @ ^ [X5: A] : ( member @ A @ X5 @ A3 ) )
% 0.13/0.36 = A3 ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_mem_eq
% 0.13/0.36 thf(fact_47_Collect__cong,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ! [X2: A] :
% 0.13/0.36 ( ( P @ X2 )
% 0.13/0.36 = ( Q @ X2 ) )
% 0.13/0.36 => ( ( collect @ A @ P )
% 0.13/0.36 = ( collect @ A @ Q ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_cong
% 0.13/0.36 thf(fact_48_ext,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.13/0.36 ( ! [X2: A] :
% 0.13/0.36 ( ( F @ X2 )
% 0.13/0.36 = ( G @ X2 ) )
% 0.13/0.36 => ( F = G ) ) ).
% 0.13/0.36
% 0.13/0.36 % ext
% 0.13/0.36 thf(fact_49_order__subst2,axiom,
% 0.13/0.36 ! [A: $tType,C: $tType] :
% 0.13/0.36 ( ( ( order @ C @ ( type2 @ C ) )
% 0.13/0.36 & ( order @ A @ ( type2 @ A ) ) )
% 0.13/0.36 => ! [A2: A,B3: A,F: A > C,C2: C] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C2 )
% 0.13/0.36 => ( ! [X2: A,Y4: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_subst2
% 0.13/0.36 thf(fact_50_order__subst1,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType] :
% 0.13/0.36 ( ( ( order @ B @ ( type2 @ B ) )
% 0.13/0.36 & ( order @ A @ ( type2 @ A ) ) )
% 0.13/0.36 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 0.13/0.36 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.13/0.36 => ( ! [X2: B,Y4: B] :
% 0.13/0.36 ( ( ord_less_eq @ B @ X2 @ Y4 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.13/0.36 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % order_subst1
% 0.13/0.36 thf(fact_51_le__fun__def,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B @ ( type2 @ B ) )
% 0.13/0.36 => ( ( ord_less_eq @ ( A > B ) )
% 0.13/0.36 = ( ^ [F2: A > B,G2: A > B] :
% 0.13/0.36 ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_fun_def
% 0.13/0.36 thf(fact_52_le__funI,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B @ ( type2 @ B ) )
% 0.13/0.36 => ! [F: A > B,G: A > B] :
% 0.13/0.36 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.13/0.36 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_funI
% 0.13/0.36 thf(fact_53_le__funE,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B @ ( type2 @ B ) )
% 0.13/0.36 => ! [F: A > B,G: A > B,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_funE
% 0.13/0.36 thf(fact_54_le__funD,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( ord @ B @ ( type2 @ B ) )
% 0.13/0.36 => ! [F: A > B,G: A > B,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.13/0.36 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_funD
% 0.13/0.36 thf(fact_55_Collect__mono__iff,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.13/0.36 = ( ! [X5: A] :
% 0.13/0.36 ( ( P @ X5 )
% 0.13/0.36 => ( Q @ X5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_mono_iff
% 0.13/0.36 thf(fact_56_contra__subsetD,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ~ ( member @ A @ C2 @ B2 )
% 0.13/0.36 => ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % contra_subsetD
% 0.13/0.36 thf(fact_57_set__eq__subset,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ^ [Y2: set @ A,Z2: set @ A] : ( Y2 = Z2 ) )
% 0.13/0.36 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 0.13/0.36 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % set_eq_subset
% 0.13/0.36 thf(fact_58_subset__trans,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_trans
% 0.13/0.36 thf(fact_59_Collect__mono,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ! [X2: A] :
% 0.13/0.36 ( ( P @ X2 )
% 0.13/0.36 => ( Q @ X2 ) )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Collect_mono
% 0.13/0.36 thf(fact_60_subset__refl,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.13/0.36
% 0.13/0.36 % subset_refl
% 0.13/0.36 thf(fact_61_rev__subsetD,axiom,
% 0.13/0.36 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C2 @ A3 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % rev_subsetD
% 0.13/0.36 thf(fact_62_subset__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.13/0.36 ! [T: A] :
% 0.13/0.36 ( ( member @ A @ T @ A5 )
% 0.13/0.36 => ( member @ A @ T @ B5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_iff
% 0.13/0.36 thf(fact_63_set__rev__mp,axiom,
% 0.13/0.36 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ X @ A3 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( member @ A @ X @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % set_rev_mp
% 0.13/0.36 thf(fact_64_equalityD2,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( A3 = B2 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ B2 @ A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % equalityD2
% 0.13/0.36 thf(fact_65_equalityD1,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( A3 = B2 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % equalityD1
% 0.13/0.36 thf(fact_66_subset__eq,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.13/0.36 ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ A5 )
% 0.13/0.36 => ( member @ A @ X5 @ B5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_eq
% 0.13/0.36 thf(fact_67_equalityE,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( A3 = B2 )
% 0.13/0.36 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % equalityE
% 0.13/0.36 thf(fact_68_subsetCE,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( member @ A @ C2 @ A3 )
% 0.13/0.36 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subsetCE
% 0.13/0.36 thf(fact_69_subsetD,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( member @ A @ C2 @ A3 )
% 0.13/0.36 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subsetD
% 0.13/0.36 thf(fact_70_in__mono,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( member @ A @ X @ A3 )
% 0.13/0.36 => ( member @ A @ X @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % in_mono
% 0.13/0.36 thf(fact_71_set__mp,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( member @ A @ X @ A3 )
% 0.13/0.36 => ( member @ A @ X @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % set_mp
% 0.13/0.36 thf(fact_72_llist_Oset__induct,axiom,
% 0.13/0.36 ! [A: $tType,X: A,A2: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ A2 ) )
% 0.13/0.36 => ( ! [Z1: A,Z22: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 0.13/0.36 => ( ! [Z1: A,Z22: coinductive_llist @ A,Xa: A] :
% 0.13/0.36 ( ( member @ A @ Xa @ ( coinductive_lset @ A @ Z22 ) )
% 0.13/0.36 => ( ( P @ Xa @ Z22 )
% 0.13/0.36 => ( P @ Xa @ ( coinductive_LCons @ A @ Z1 @ Z22 ) ) ) )
% 0.13/0.36 => ( P @ X @ A2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.set_induct
% 0.13/0.36 thf(fact_73_llist_Oset__cases,axiom,
% 0.13/0.36 ! [A: $tType,E: A,A2: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ E @ ( coinductive_lset @ A @ A2 ) )
% 0.13/0.36 => ( ! [Z22: coinductive_llist @ A] :
% 0.13/0.36 ( A2
% 0.13/0.36 != ( coinductive_LCons @ A @ E @ Z22 ) )
% 0.13/0.36 => ~ ! [Z1: A,Z22: coinductive_llist @ A] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 0.13/0.36 => ~ ( member @ A @ E @ ( coinductive_lset @ A @ Z22 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.set_cases
% 0.13/0.36 thf(fact_74_reachable__viap__reachable__via__eq,axiom,
% 0.13/0.36 ! [Node: $tType] :
% 0.13/0.36 ( ( koenig1757754772e_viap @ Node )
% 0.13/0.36 = ( ^ [Graph2: Node > Node > $o,Ns2: set @ Node,N5: Node,X5: Node] : ( member @ Node @ X5 @ ( koenig317145564le_via @ Node @ Graph2 @ Ns2 @ N5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_viap_reachable_via_eq
% 0.13/0.36 thf(fact_75_lset__lmember,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 = ( coinductive_lmember @ A @ X @ Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_lmember
% 0.13/0.36 thf(fact_76_lsorted__LCons,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( ( coindu63249387sorted @ A @ Xs3 )
% 0.13/0.36 & ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ X5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted_LCons
% 0.13/0.36 thf(fact_77_lmember__code_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Y: A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lmember @ A @ X @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.13/0.36 = ( ( X = Y )
% 0.13/0.36 | ( coinductive_lmember @ A @ X @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lmember_code(2)
% 0.13/0.36 thf(fact_78_lfp_Oleq__antisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( X = Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfp.leq_antisym
% 0.13/0.36 thf(fact_79_gfp_Oleq__antisym,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( X = Y ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % gfp.leq_antisym
% 0.13/0.36 thf(fact_80_lfp_Oleq__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfp.leq_trans
% 0.13/0.36 thf(fact_81_gfp_Oleq__trans,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Z @ Y )
% 0.13/0.36 => ( ord_less_eq @ A @ Z @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % gfp.leq_trans
% 0.13/0.36 thf(fact_82_lfp_Oleq__refl,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfp.leq_refl
% 0.13/0.36 thf(fact_83_lsorted__LCons__LCons,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) )
% 0.13/0.36 = ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 & ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted_LCons_LCons
% 0.13/0.36 thf(fact_84_LCons__LCons,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y @ Xs3 ) )
% 0.13/0.36 => ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % LCons_LCons
% 0.13/0.36 thf(fact_85_reachable__viap_Ocases,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,Ns: set @ Node,N2: Node,A2: Node] :
% 0.13/0.36 ( ( koenig1757754772e_viap @ Node @ Graph @ Ns @ N2 @ A2 )
% 0.13/0.36 => ~ ! [Xs2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) )
% 0.13/0.36 => ( ( member @ Node @ A2 @ ( coinductive_lset @ Node @ Xs2 ) )
% 0.13/0.36 => ~ ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_viap.cases
% 0.13/0.36 thf(fact_86_reachable__viap_Osimps,axiom,
% 0.13/0.36 ! [Node: $tType] :
% 0.13/0.36 ( ( koenig1757754772e_viap @ Node )
% 0.13/0.36 = ( ^ [Graph2: Node > Node > $o,Ns2: set @ Node,N5: Node,A6: Node] :
% 0.13/0.36 ? [Xs4: coinductive_llist @ Node,N3: Node] :
% 0.13/0.36 ( ( A6 = N3 )
% 0.13/0.36 & ( koenig2031690877pathsp @ Node @ Graph2 @ ( coinductive_LCons @ Node @ N5 @ Xs4 ) )
% 0.13/0.36 & ( member @ Node @ N3 @ ( coinductive_lset @ Node @ Xs4 ) )
% 0.13/0.36 & ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs4 ) @ Ns2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_viap.simps
% 0.13/0.36 thf(fact_87_reachable__viap_Ointros,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,N2: Node,Xs3: coinductive_llist @ Node,N4: Node,Ns: set @ Node] :
% 0.13/0.36 ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ N2 @ Xs3 ) )
% 0.13/0.36 => ( ( member @ Node @ N4 @ ( coinductive_lset @ Node @ Xs3 ) )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs3 ) @ Ns )
% 0.13/0.36 => ( koenig1757754772e_viap @ Node @ Graph @ Ns @ N2 @ N4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_viap.intros
% 0.13/0.36 thf(fact_88_reachable__viap_Oinducts,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,Ns: set @ Node,N2: Node,X: Node,P: Node > $o] :
% 0.13/0.36 ( ( koenig1757754772e_viap @ Node @ Graph @ Ns @ N2 @ X )
% 0.13/0.36 => ( ! [Xs2: coinductive_llist @ Node,N: Node] :
% 0.13/0.36 ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) )
% 0.13/0.36 => ( ( member @ Node @ N @ ( coinductive_lset @ Node @ Xs2 ) )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns )
% 0.13/0.36 => ( P @ N ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % reachable_viap.inducts
% 0.13/0.36 thf(fact_89_lsorted_Ocases,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu63249387sorted @ A @ A2 )
% 0.13/0.36 => ( ( A2
% 0.13/0.36 != ( coinductive_LNil @ A ) )
% 0.13/0.36 => ( ! [X2: A] :
% 0.13/0.36 ( A2
% 0.13/0.36 != ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) )
% 0.13/0.36 => ~ ! [X2: A,Y4: A,Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( coinductive_LCons @ A @ X2 @ ( coinductive_LCons @ A @ Y4 @ Xs2 ) ) )
% 0.13/0.36 => ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.13/0.36 => ~ ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted.cases
% 0.13/0.36 thf(fact_90_lsorted_Osimps,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( ( coindu63249387sorted @ A )
% 0.13/0.36 = ( ^ [A6: coinductive_llist @ A] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ? [X5: A] :
% 0.13/0.36 ( A6
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) )
% 0.13/0.36 | ? [X5: A,Y3: A,Xs4: coinductive_llist @ A] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ ( coinductive_LCons @ A @ Y3 @ Xs4 ) ) )
% 0.13/0.36 & ( ord_less_eq @ A @ X5 @ Y3 )
% 0.13/0.36 & ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y3 @ Xs4 ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted.simps
% 0.13/0.36 thf(fact_91_lsorted__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( coindu63249387sorted @ A @ ( coinductive_LNil @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted_code(1)
% 0.13/0.36 thf(fact_92_lsorted__code_I2_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A] : ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted_code(2)
% 0.13/0.36 thf(fact_93_pathsp_Ocases,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,A2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( koenig2031690877pathsp @ Node @ Graph @ A2 )
% 0.13/0.36 => ( ( A2
% 0.13/0.36 != ( coinductive_LNil @ Node ) )
% 0.13/0.36 => ( ! [X2: Node] :
% 0.13/0.36 ( A2
% 0.13/0.36 != ( coinductive_LCons @ Node @ X2 @ ( coinductive_LNil @ Node ) ) )
% 0.13/0.36 => ~ ! [X2: Node,Y4: Node,Xs2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( coinductive_LCons @ Node @ X2 @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) ) )
% 0.13/0.36 => ( ( Graph @ X2 @ Y4 )
% 0.13/0.36 => ~ ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp.cases
% 0.13/0.36 thf(fact_94_pathsp_Osimps,axiom,
% 0.13/0.36 ! [Node: $tType] :
% 0.13/0.36 ( ( koenig2031690877pathsp @ Node )
% 0.13/0.36 = ( ^ [Graph2: Node > Node > $o,A6: coinductive_llist @ Node] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LNil @ Node ) )
% 0.13/0.36 | ? [X5: Node] :
% 0.13/0.36 ( A6
% 0.13/0.36 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LNil @ Node ) ) )
% 0.13/0.36 | ? [X5: Node,Y3: Node,Xs4: coinductive_llist @ Node] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) ) )
% 0.13/0.36 & ( Graph2 @ X5 @ Y3 )
% 0.13/0.36 & ( koenig2031690877pathsp @ Node @ Graph2 @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp.simps
% 0.13/0.36 thf(fact_95_pathsp_OSingle,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,X: Node] : ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ X @ ( coinductive_LNil @ Node ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp.Single
% 0.13/0.36 thf(fact_96_pathsp_Ocoinduct,axiom,
% 0.13/0.36 ! [Node: $tType,X6: ( coinductive_llist @ Node ) > $o,X: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.13/0.36 ( ( X6 @ X )
% 0.13/0.36 => ( ! [X2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( X6 @ X2 )
% 0.13/0.36 => ( ( X2
% 0.13/0.36 = ( coinductive_LNil @ Node ) )
% 0.13/0.36 | ? [Xa2: Node] :
% 0.13/0.36 ( X2
% 0.13/0.36 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LNil @ Node ) ) )
% 0.13/0.36 | ? [Xa2: Node,Y5: Node,Xs5: coinductive_llist @ Node] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) ) )
% 0.13/0.36 & ( Graph @ Xa2 @ Y5 )
% 0.13/0.36 & ( ( X6 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) )
% 0.13/0.36 | ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) ) ) ) ) )
% 0.13/0.36 => ( koenig2031690877pathsp @ Node @ Graph @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp.coinduct
% 0.13/0.36 thf(fact_97_pathsp_OEmpty,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o] : ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LNil @ Node ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp.Empty
% 0.13/0.36 thf(fact_98_neq__LNil__conv,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs3
% 0.13/0.36 != ( coinductive_LNil @ A ) )
% 0.13/0.36 = ( ? [X5: A,Xs6: coinductive_llist @ A] :
% 0.13/0.36 ( Xs3
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ Xs6 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % neq_LNil_conv
% 0.13/0.36 thf(fact_99_llist_Oexhaust,axiom,
% 0.13/0.36 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.13/0.36 ( ( Y
% 0.13/0.36 != ( coinductive_LNil @ A ) )
% 0.13/0.36 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.13/0.36 ( Y
% 0.13/0.36 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.exhaust
% 0.13/0.36 thf(fact_100_llist_Odistinct_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_LNil @ A )
% 0.13/0.36 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.distinct(1)
% 0.13/0.36 thf(fact_101_LNil,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( coindu63249387sorted @ A @ ( coinductive_LNil @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % LNil
% 0.13/0.36 thf(fact_102_paths_OEmpty,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LNil @ Node ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths.Empty
% 0.13/0.36 thf(fact_103_pathsp_OLCons,axiom,
% 0.13/0.36 ! [Node: $tType,Graph: Node > Node > $o,X: Node,Y: Node,Xs3: coinductive_llist @ Node] :
% 0.13/0.36 ( ( Graph @ X @ Y )
% 0.13/0.36 => ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ Y @ Xs3 ) )
% 0.13/0.36 => ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ X @ ( coinductive_LCons @ Node @ Y @ Xs3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp.LCons
% 0.13/0.36 thf(fact_104_lmember__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,X: A] :
% 0.13/0.36 ~ ( coinductive_lmember @ A @ X @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % lmember_code(1)
% 0.13/0.36 thf(fact_105_pathsp__paths__eq,axiom,
% 0.13/0.36 ! [Node: $tType] :
% 0.13/0.36 ( ( koenig2031690877pathsp @ Node )
% 0.13/0.36 = ( ^ [Graph2: Node > Node > $o,X5: coinductive_llist @ Node] : ( member @ ( coinductive_llist @ Node ) @ X5 @ ( koenig916195507_paths @ Node @ Graph2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % pathsp_paths_eq
% 0.13/0.36 thf(fact_106_Singleton,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A] : ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Singleton
% 0.13/0.36 thf(fact_107_paths_Ocoinduct,axiom,
% 0.13/0.36 ! [Node: $tType,X6: ( coinductive_llist @ Node ) > $o,X: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.13/0.36 ( ( X6 @ X )
% 0.13/0.36 => ( ! [X2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( X6 @ X2 )
% 0.13/0.36 => ( ( X2
% 0.13/0.36 = ( coinductive_LNil @ Node ) )
% 0.13/0.36 | ? [Xa2: Node] :
% 0.13/0.36 ( X2
% 0.13/0.36 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LNil @ Node ) ) )
% 0.13/0.36 | ? [Xa2: Node,Y5: Node,Xs5: coinductive_llist @ Node] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) ) )
% 0.13/0.36 & ( Graph @ Xa2 @ Y5 )
% 0.13/0.36 & ( ( X6 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) )
% 0.13/0.36 | ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) )
% 0.13/0.36 => ( member @ ( coinductive_llist @ Node ) @ X @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths.coinduct
% 0.13/0.36 thf(fact_108_paths_OSingle,axiom,
% 0.13/0.36 ! [Node: $tType,X: Node,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LNil @ Node ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths.Single
% 0.13/0.36 thf(fact_109_paths_Osimps,axiom,
% 0.13/0.36 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 = ( ( A2
% 0.13/0.36 = ( coinductive_LNil @ Node ) )
% 0.13/0.36 | ? [X5: Node] :
% 0.13/0.36 ( A2
% 0.13/0.36 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LNil @ Node ) ) )
% 0.13/0.36 | ? [X5: Node,Y3: Node,Xs4: coinductive_llist @ Node] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) ) )
% 0.13/0.36 & ( Graph @ X5 @ Y3 )
% 0.13/0.36 & ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths.simps
% 0.13/0.36 thf(fact_110_paths_Ocases,axiom,
% 0.13/0.36 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.13/0.36 => ( ( A2
% 0.13/0.36 != ( coinductive_LNil @ Node ) )
% 0.13/0.36 => ( ! [X2: Node] :
% 0.13/0.36 ( A2
% 0.13/0.36 != ( coinductive_LCons @ Node @ X2 @ ( coinductive_LNil @ Node ) ) )
% 0.13/0.36 => ~ ! [X2: Node,Y4: Node,Xs2: coinductive_llist @ Node] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( coinductive_LCons @ Node @ X2 @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) ) )
% 0.13/0.36 => ( ( Graph @ X2 @ Y4 )
% 0.13/0.36 => ~ ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths.cases
% 0.13/0.36 thf(fact_111_lsorted_Ocoinduct,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X6: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A] :
% 0.13/0.36 ( ( X6 @ X )
% 0.13/0.36 => ( ! [X2: coinductive_llist @ A] :
% 0.13/0.36 ( ( X6 @ X2 )
% 0.13/0.36 => ( ( X2
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ? [Xa2: A] :
% 0.13/0.36 ( X2
% 0.13/0.36 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_LNil @ A ) ) )
% 0.13/0.36 | ? [Xa2: A,Y5: A,Xs5: coinductive_llist @ A] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_LCons @ A @ Y5 @ Xs5 ) ) )
% 0.13/0.36 & ( ord_less_eq @ A @ Xa2 @ Y5 )
% 0.13/0.36 & ( ( X6 @ ( coinductive_LCons @ A @ Y5 @ Xs5 ) )
% 0.13/0.36 | ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y5 @ Xs5 ) ) ) ) ) )
% 0.13/0.36 => ( coindu63249387sorted @ A @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted.coinduct
% 0.13/0.36 thf(fact_112_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu328551480prefix @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.13/0.36 = ( ( Xs3
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ? [Xs6: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs3
% 0.13/0.36 = ( coinductive_LCons @ A @ Y @ Xs6 ) )
% 0.13/0.36 & ( coindu328551480prefix @ A @ Xs6 @ Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.13/0.36 thf(fact_113_lstrict__prefix__code_I2_J,axiom,
% 0.13/0.36 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.13/0.36
% 0.13/0.36 % lstrict_prefix_code(2)
% 0.13/0.36 thf(fact_114_lstrict__prefix__code_I3_J,axiom,
% 0.13/0.36 ! [B: $tType,X: B,Xs3: coinductive_llist @ B] :
% 0.13/0.36 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs3 ) @ ( coinductive_LNil @ B ) ) ).
% 0.13/0.36
% 0.13/0.36 % lstrict_prefix_code(3)
% 0.13/0.36 thf(fact_115_llast__singleton,axiom,
% 0.13/0.36 ! [A: $tType,X: A] :
% 0.13/0.36 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.13/0.36 = X ) ).
% 0.13/0.36
% 0.13/0.36 % llast_singleton
% 0.13/0.36 thf(fact_116_ldistinct_Ocoinduct,axiom,
% 0.13/0.36 ! [A: $tType,X6: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A] :
% 0.13/0.36 ( ( X6 @ X )
% 0.13/0.36 => ( ! [X2: coinductive_llist @ A] :
% 0.13/0.36 ( ( X6 @ X2 )
% 0.13/0.36 => ( ( X2
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ? [Xa2: A,Xs5: coinductive_llist @ A] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LCons @ A @ Xa2 @ Xs5 ) )
% 0.13/0.36 & ~ ( member @ A @ Xa2 @ ( coinductive_lset @ A @ Xs5 ) )
% 0.13/0.36 & ( ( X6 @ Xs5 )
% 0.13/0.36 | ( coindu351974385stinct @ A @ Xs5 ) ) ) ) )
% 0.13/0.36 => ( coindu351974385stinct @ A @ X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct.coinduct
% 0.13/0.36 thf(fact_117_ldistinct_Osimps,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( coindu351974385stinct @ A )
% 0.13/0.36 = ( ^ [A6: coinductive_llist @ A] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ? [X5: A,Xs4: coinductive_llist @ A] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 0.13/0.36 & ~ ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs4 ) )
% 0.13/0.36 & ( coindu351974385stinct @ A @ Xs4 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct.simps
% 0.13/0.36 thf(fact_118_ldistinct__LNil__code,axiom,
% 0.13/0.36 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct_LNil_code
% 0.13/0.36 thf(fact_119_llast__LCons2,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Y: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) )
% 0.13/0.36 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llast_LCons2
% 0.13/0.36 thf(fact_120_lstrict__prefix__code_I4_J,axiom,
% 0.13/0.36 ! [B: $tType,X: B,Xs3: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.13/0.36 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs3 ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.13/0.36 = ( ( X = Y )
% 0.13/0.36 & ( coindu1478340336prefix @ B @ Xs3 @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lstrict_prefix_code(4)
% 0.13/0.36 thf(fact_121_lstrict__prefix__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % lstrict_prefix_code(1)
% 0.13/0.36 thf(fact_122_ldistinct__LCons,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 & ( coindu351974385stinct @ A @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct_LCons
% 0.13/0.36 thf(fact_123_llist__less__induct,axiom,
% 0.13/0.36 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ! [Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ! [Ys2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs2 )
% 0.13/0.36 => ( P @ Ys2 ) )
% 0.13/0.36 => ( P @ Xs2 ) )
% 0.13/0.36 => ( P @ Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist_less_induct
% 0.13/0.36 thf(fact_124_ldistinct_OLNil,axiom,
% 0.13/0.36 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct.LNil
% 0.13/0.36 thf(fact_125_ldistinct_OLCons,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( ( coindu351974385stinct @ A @ Xs3 )
% 0.13/0.36 => ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct.LCons
% 0.13/0.36 thf(fact_126_lsorted__ldistinct__lset__unique,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( linorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu63249387sorted @ A @ Xs3 )
% 0.13/0.36 => ( ( coindu351974385stinct @ A @ Xs3 )
% 0.13/0.36 => ( ( coindu63249387sorted @ A @ Ys )
% 0.13/0.36 => ( ( coindu351974385stinct @ A @ Ys )
% 0.13/0.36 => ( ( ( coinductive_lset @ A @ Xs3 )
% 0.13/0.36 = ( coinductive_lset @ A @ Ys ) )
% 0.13/0.36 => ( Xs3 = Ys ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted_ldistinct_lset_unique
% 0.13/0.36 thf(fact_127_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu328551480prefix @ A @ Xs3 @ ( coinductive_LNil @ A ) )
% 0.13/0.36 = ( Xs3
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.13/0.36 thf(fact_128_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs3 ) ).
% 0.13/0.36
% 0.13/0.36 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.13/0.36 thf(fact_129_ldistinct_Ocases,axiom,
% 0.13/0.36 ! [A: $tType,A2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu351974385stinct @ A @ A2 )
% 0.13/0.36 => ( ( A2
% 0.13/0.36 != ( coinductive_LNil @ A ) )
% 0.13/0.36 => ~ ! [X2: A,Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 0.13/0.36 => ( ~ ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs2 ) )
% 0.13/0.36 => ~ ( coindu351974385stinct @ A @ Xs2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct.cases
% 0.13/0.36 thf(fact_130_llimit__induct,axiom,
% 0.13/0.36 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( P @ ( coinductive_LNil @ A ) )
% 0.13/0.36 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.13/0.36 => ( ( P @ Xs2 )
% 0.13/0.36 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.13/0.36 => ( ( ! [Ys2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.13/0.36 => ( P @ Ys2 ) )
% 0.13/0.36 => ( P @ Xs3 ) )
% 0.13/0.36 => ( P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llimit_induct
% 0.13/0.36 thf(fact_131_gen__lset__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A] :
% 0.13/0.36 ( ( coinductive_gen_lset @ A @ A3 @ ( coinductive_LNil @ A ) )
% 0.13/0.36 = A3 ) ).
% 0.13/0.36
% 0.13/0.36 % gen_lset_code(1)
% 0.13/0.36 thf(fact_132_llist_Ocorec__code,axiom,
% 0.13/0.36 ! [A: $tType,C: $tType] :
% 0.13/0.36 ( ( coindu1259883913_llist @ C @ A )
% 0.13/0.36 = ( ^ [P2: C > $o,G21: C > A,Q22: C > $o,G221: C > ( coinductive_llist @ A ),G222: C > C,A6: C] : ( if @ ( coinductive_llist @ A ) @ ( P2 @ A6 ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ ( G21 @ A6 ) @ ( if @ ( coinductive_llist @ A ) @ ( Q22 @ A6 ) @ ( G221 @ A6 ) @ ( coindu1259883913_llist @ C @ A @ P2 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A6 ) ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.corec_code
% 0.13/0.36 thf(fact_133_unfold__llist_Ocode,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType] :
% 0.13/0.36 ( ( coindu1441602521_llist @ A @ B )
% 0.13/0.36 = ( ^ [P2: A > $o,G21: A > B,G22: A > A,A6: A] : ( if @ ( coinductive_llist @ B ) @ ( P2 @ A6 ) @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ ( G21 @ A6 ) @ ( coindu1441602521_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A6 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % unfold_llist.code
% 0.13/0.36 thf(fact_134_lfinite__code_I2_J,axiom,
% 0.13/0.36 ! [B: $tType,X: B,Xs3: coinductive_llist @ B] :
% 0.13/0.36 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs3 ) )
% 0.13/0.36 = ( coinductive_lfinite @ B @ Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_code(2)
% 0.13/0.36 thf(fact_135_lfinite__LCons,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( coinductive_lfinite @ A @ Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_LCons
% 0.13/0.36 thf(fact_136_lfinite__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_code(1)
% 0.13/0.36 thf(fact_137_unfold__llist__eq__LCons,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B3 )
% 0.13/0.36 = ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( ~ ( IS_LNIL @ B3 )
% 0.13/0.36 & ( X
% 0.13/0.36 = ( LHD @ B3 ) )
% 0.13/0.36 & ( Xs3
% 0.13/0.36 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % unfold_llist_eq_LCons
% 0.13/0.36 thf(fact_138_lfinite__LConsI,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,X: A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_LConsI
% 0.13/0.36 thf(fact_139_lfinite__LNil,axiom,
% 0.13/0.36 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_LNil
% 0.13/0.36 thf(fact_140_lstrict__prefix__lfinite1,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu1478340336prefix @ A @ Xs3 @ Ys )
% 0.13/0.36 => ( coinductive_lfinite @ A @ Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % lstrict_prefix_lfinite1
% 0.13/0.36 thf(fact_141_unfold__llist_Octr_I2_J,axiom,
% 0.13/0.36 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.13/0.36 ( ~ ( P3 @ A2 )
% 0.13/0.36 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 0.13/0.36 = ( coinductive_LCons @ B @ ( G212 @ A2 ) @ ( coindu1441602521_llist @ A @ B @ P3 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % unfold_llist.ctr(2)
% 0.13/0.36 thf(fact_142_unfold__llist_Octr_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 0.13/0.36 ( ( P3 @ A2 )
% 0.13/0.36 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 0.13/0.36 = ( coinductive_LNil @ B ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % unfold_llist.ctr(1)
% 0.13/0.36 thf(fact_143_llist_Ocorec_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coinductive_llist @ A ),G2222: C > C] :
% 0.13/0.36 ( ~ ( P3 @ A2 )
% 0.13/0.36 => ( ( coindu1259883913_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.13/0.36 = ( coinductive_LCons @ A @ ( G212 @ A2 ) @ ( if @ ( coinductive_llist @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( coindu1259883913_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.corec(2)
% 0.13/0.36 thf(fact_144_llist_Ocorec_I1_J,axiom,
% 0.13/0.36 ! [C: $tType,A: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coinductive_llist @ A ),G2222: C > C] :
% 0.13/0.36 ( ( P3 @ A2 )
% 0.13/0.36 => ( ( coindu1259883913_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llist.corec(1)
% 0.13/0.36 thf(fact_145_lfinite_Oinducts,axiom,
% 0.13/0.36 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ X )
% 0.13/0.36 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.13/0.36 => ( ! [Xs2: coinductive_llist @ A,X2: A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.13/0.36 => ( ( P @ Xs2 )
% 0.13/0.36 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.13/0.36 => ( P @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite.inducts
% 0.13/0.36 thf(fact_146_lfinite_Osimps,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( coinductive_lfinite @ A )
% 0.13/0.36 = ( ^ [A6: coinductive_llist @ A] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ? [Xs4: coinductive_llist @ A,X5: A] :
% 0.13/0.36 ( ( A6
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 0.13/0.36 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite.simps
% 0.13/0.36 thf(fact_147_lfinite_Ocases,axiom,
% 0.13/0.36 ! [A: $tType,A2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ A2 )
% 0.13/0.36 => ( ( A2
% 0.13/0.36 != ( coinductive_LNil @ A ) )
% 0.13/0.36 => ~ ! [Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ? [X2: A] :
% 0.13/0.36 ( A2
% 0.13/0.36 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 0.13/0.36 => ~ ( coinductive_lfinite @ A @ Xs2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite.cases
% 0.13/0.36 thf(fact_148_llast__lappend__LCons,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 0.13/0.36 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llast_lappend_LCons
% 0.13/0.36 thf(fact_149_split__llist,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ? [Ys3: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs3
% 0.13/0.36 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 0.13/0.36 & ( coinductive_lfinite @ A @ Ys3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % split_llist
% 0.13/0.36 thf(fact_150_split__llist__first,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ? [Ys3: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs3
% 0.13/0.36 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 0.13/0.36 & ( coinductive_lfinite @ A @ Ys3 )
% 0.13/0.36 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % split_llist_first
% 0.13/0.36 thf(fact_151_lfinite__rev__induct,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.13/0.36 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.13/0.36 => ( ( P @ Xs2 )
% 0.13/0.36 => ( P @ ( coinductive_lappend @ A @ Xs2 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 0.13/0.36 => ( P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_rev_induct
% 0.13/0.36 thf(fact_152_lappend__code_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,Xa3: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa3 @ X ) @ Ys )
% 0.13/0.36 = ( coinductive_LCons @ A @ Xa3 @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_code(2)
% 0.13/0.36 thf(fact_153_lappend__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.13/0.36 = Ys ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_code(1)
% 0.13/0.36 thf(fact_154_lappend__LNil2,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LNil @ A ) )
% 0.13/0.36 = Xs3 ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_LNil2
% 0.13/0.36 thf(fact_155_lfinite__lappend,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_lappend
% 0.13/0.36 thf(fact_156_lappend__inf,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( coinductive_lappend @ A @ Xs3 @ Ys )
% 0.13/0.36 = Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_inf
% 0.13/0.36 thf(fact_157_lappend__assoc,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ Zs2 )
% 0.13/0.36 = ( coinductive_lappend @ A @ Xs3 @ ( coinductive_lappend @ A @ Ys @ Zs2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_assoc
% 0.13/0.36 thf(fact_158_paths__lappendD1,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 0.13/0.36 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.13/0.36 => ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths_lappendD1
% 0.13/0.36 thf(fact_159_lappend__LNil__LNil,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_LNil_LNil
% 0.13/0.36 thf(fact_160_LNil__eq__lappend__iff,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_LNil @ A )
% 0.13/0.36 = ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( ( Xs3
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 & ( Ys
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % LNil_eq_lappend_iff
% 0.13/0.36 thf(fact_161_lappend__eq__LNil__iff,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_lappend @ A @ Xs3 @ Ys )
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 = ( ( Xs3
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 & ( Ys
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_eq_LNil_iff
% 0.13/0.36 thf(fact_162_lset__lappend1,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_lappend1
% 0.13/0.36 thf(fact_163_lappend__snocL1__conv__LCons2,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.13/0.36 = ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lappend_snocL1_conv_LCons2
% 0.13/0.36 thf(fact_164_in__lset__lappend__iff,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) )
% 0.13/0.36 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 | ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % in_lset_lappend_iff
% 0.13/0.36 thf(fact_165_paths__lappendD2,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.13/0.36 => ( member @ ( coinductive_llist @ A ) @ Ys @ ( koenig916195507_paths @ A @ Graph ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % paths_lappendD2
% 0.13/0.36 thf(fact_166_lfilter__eq__LConsD,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Ys: coinductive_llist @ A,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_lfilter @ A @ P @ Ys )
% 0.13/0.36 = ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 0.13/0.36 ( ( Ys
% 0.13/0.36 = ( coinductive_lappend @ A @ Us @ ( coinductive_LCons @ A @ X @ Vs ) ) )
% 0.13/0.36 & ( coinductive_lfinite @ A @ Us )
% 0.13/0.36 & ! [X7: A] :
% 0.13/0.36 ( ( member @ A @ X7 @ ( coinductive_lset @ A @ Us ) )
% 0.13/0.36 => ~ ( P @ X7 ) )
% 0.13/0.36 & ( P @ X )
% 0.13/0.36 & ( Xs3
% 0.13/0.36 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_eq_LConsD
% 0.13/0.36 thf(fact_167_lset__lappend__lfinite,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_lappend_lfinite
% 0.13/0.36 thf(fact_168_llexord__lappend__leftD,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( coinductive_lappend @ A @ Xs3 @ Zs2 ) )
% 0.13/0.36 => ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ~ ( R @ X2 @ X2 ) )
% 0.13/0.36 => ( coinductive_llexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_lappend_leftD
% 0.13/0.36 thf(fact_169_UnCI,axiom,
% 0.13/0.36 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 0.13/0.36 ( ( ~ ( member @ A @ C2 @ B2 )
% 0.13/0.36 => ( member @ A @ C2 @ A3 ) )
% 0.13/0.36 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnCI
% 0.13/0.36 thf(fact_170_Un__iff,axiom,
% 0.13/0.36 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.13/0.36 = ( ( member @ A @ C2 @ A3 )
% 0.13/0.36 | ( member @ A @ C2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_iff
% 0.13/0.36 thf(fact_171_lfilter__idem,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs3 ) )
% 0.13/0.36 = ( coinductive_lfilter @ A @ P @ Xs3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_idem
% 0.13/0.36 thf(fact_172_llexord__refl,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs3 @ Xs3 ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_refl
% 0.13/0.36 thf(fact_173_Un__subset__iff,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C3 )
% 0.13/0.36 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C3 )
% 0.13/0.36 & ( ord_less_eq @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_subset_iff
% 0.13/0.36 thf(fact_174_lfilter__LCons,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( P @ X )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) )
% 0.13/0.36 & ( ~ ( P @ X )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_LCons
% 0.13/0.36 thf(fact_175_lfilter__LNil,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o] :
% 0.13/0.36 ( ( coinductive_lfilter @ A @ P @ ( coinductive_LNil @ A ) )
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_LNil
% 0.13/0.36 thf(fact_176_llexord__LCons__LCons,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.13/0.36 = ( ( ( X = Y )
% 0.13/0.36 & ( coinductive_llexord @ A @ R @ Xs3 @ Ys ) )
% 0.13/0.36 | ( R @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_LCons_LCons
% 0.13/0.36 thf(fact_177_llexord__code_I1_J,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_code(1)
% 0.13/0.36 thf(fact_178_diverge__lfilter__LNil,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o] :
% 0.13/0.36 ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ~ ( P @ X2 ) )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 0.13/0.36 = ( coinductive_LNil @ A ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % diverge_lfilter_LNil
% 0.13/0.36 thf(fact_179_lfilter__lappend__lfinite,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( coinductive_lappend @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_lappend_lfinite
% 0.13/0.36 thf(fact_180_llexord__lappend__leftI,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ Ys @ Zs2 )
% 0.13/0.36 => ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( coinductive_lappend @ A @ Xs3 @ Zs2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_lappend_leftI
% 0.13/0.36 thf(fact_181_llexord__append__right,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs3 @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_append_right
% 0.13/0.36 thf(fact_182_ldistinct__lfilterI,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o] :
% 0.13/0.36 ( ( coindu351974385stinct @ A @ Xs3 )
% 0.13/0.36 => ( coindu351974385stinct @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ldistinct_lfilterI
% 0.13/0.36 thf(fact_183_lfilter__LCons__seek,axiom,
% 0.13/0.36 ! [A: $tType,P3: A > $o,X: A,L: coinductive_llist @ A] :
% 0.13/0.36 ( ~ ( P3 @ X )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P3 @ ( coinductive_LCons @ A @ X @ L ) )
% 0.13/0.36 = ( coinductive_lfilter @ A @ P3 @ L ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_LCons_seek
% 0.13/0.36 thf(fact_184_lfilter__LCons__found,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( P @ X )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 0.13/0.36 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_LCons_found
% 0.13/0.36 thf(fact_185_lfilter__cong,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o,Q: A > $o] :
% 0.13/0.36 ( ( Xs3 = Ys )
% 0.13/0.36 => ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Ys ) )
% 0.13/0.36 => ( ( P @ X2 )
% 0.13/0.36 = ( Q @ X2 ) ) )
% 0.13/0.36 => ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 0.13/0.36 = ( coinductive_lfilter @ A @ Q @ Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_cong
% 0.13/0.36 thf(fact_186_lfilter__id__conv,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 0.13/0.36 = Xs3 )
% 0.13/0.36 = ( ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ( P @ X5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_id_conv
% 0.13/0.36 thf(fact_187_Un__mono,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,C3: set @ A,B2: set @ A,D: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C3 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C3 @ D ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_mono
% 0.13/0.36 thf(fact_188_Un__least,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,C3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C3 )
% 0.13/0.36 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 0.13/0.36 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_least
% 0.13/0.36 thf(fact_189_Un__upper1,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_upper1
% 0.13/0.36 thf(fact_190_Un__upper2,axiom,
% 0.13/0.36 ! [A: $tType,B2: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_upper2
% 0.13/0.36 thf(fact_191_Un__absorb1,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 => ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 = B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_absorb1
% 0.13/0.36 thf(fact_192_Un__absorb2,axiom,
% 0.13/0.36 ! [A: $tType,B2: set @ A,A3: set @ A] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A3 )
% 0.13/0.36 => ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 0.13/0.36 = A3 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_absorb2
% 0.13/0.36 thf(fact_193_subset__Un__eq,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( ord_less_eq @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A5 @ B5 )
% 0.13/0.36 = B5 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % subset_Un_eq
% 0.13/0.36 thf(fact_194_lsorted__lfilterI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( preorder @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Xs3: coinductive_llist @ A,P: A > $o] :
% 0.13/0.36 ( ( coindu63249387sorted @ A @ Xs3 )
% 0.13/0.36 => ( coindu63249387sorted @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lsorted_lfilterI
% 0.13/0.36 thf(fact_195_llexord__code_I3_J,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.13/0.36 = ( ( R @ X @ Y )
% 0.13/0.36 | ( ( X = Y )
% 0.13/0.36 & ( coinductive_llexord @ A @ R @ Xs3 @ Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_code(3)
% 0.13/0.36 thf(fact_196_llexord__LCons__left,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ Ys )
% 0.13/0.36 = ( ? [Y3: A,Ys4: coinductive_llist @ A] :
% 0.13/0.36 ( ( Ys
% 0.13/0.36 = ( coinductive_LCons @ A @ Y3 @ Ys4 ) )
% 0.13/0.36 & ( ( ( X = Y3 )
% 0.13/0.36 & ( coinductive_llexord @ A @ R @ Xs3 @ Ys4 ) )
% 0.13/0.36 | ( R @ X @ Y3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_LCons_left
% 0.13/0.36 thf(fact_197_llexord__LCons__eq,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 0.13/0.36 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_LCons_eq
% 0.13/0.36 thf(fact_198_llexord__LCons__less,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( R @ X @ Y )
% 0.13/0.36 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_LCons_less
% 0.13/0.36 thf(fact_199_llexord__LNil,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_LNil
% 0.13/0.36 thf(fact_200_UnE,axiom,
% 0.13/0.36 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.13/0.36 => ( ~ ( member @ A @ C2 @ A3 )
% 0.13/0.36 => ( member @ A @ C2 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnE
% 0.13/0.36 thf(fact_201_UnI1,axiom,
% 0.13/0.36 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( member @ A @ C2 @ A3 )
% 0.13/0.36 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnI1
% 0.13/0.36 thf(fact_202_UnI2,axiom,
% 0.13/0.36 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 0.13/0.36 ( ( member @ A @ C2 @ B2 )
% 0.13/0.36 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % UnI2
% 0.13/0.36 thf(fact_203_bex__Un,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 0.13/0.36 ( ( ? [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.13/0.36 & ( P @ X5 ) ) )
% 0.13/0.36 = ( ? [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ A3 )
% 0.13/0.36 & ( P @ X5 ) )
% 0.13/0.36 | ? [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ B2 )
% 0.13/0.36 & ( P @ X5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % bex_Un
% 0.13/0.36 thf(fact_204_ball__Un,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 0.13/0.36 ( ( ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.13/0.36 => ( P @ X5 ) ) )
% 0.13/0.36 = ( ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ A3 )
% 0.13/0.36 => ( P @ X5 ) )
% 0.13/0.36 & ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ B2 )
% 0.13/0.36 => ( P @ X5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % ball_Un
% 0.13/0.36 thf(fact_205_Un__assoc,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C3 )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_assoc
% 0.13/0.36 thf(fact_206_Un__absorb,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.13/0.36 = A3 ) ).
% 0.13/0.36
% 0.13/0.36 % Un_absorb
% 0.13/0.36 thf(fact_207_Un__commute,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) )
% 0.13/0.36 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_commute
% 0.13/0.36 thf(fact_208_Un__left__absorb,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_left_absorb
% 0.13/0.36 thf(fact_209_Un__left__commute,axiom,
% 0.13/0.36 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 0.13/0.36 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % Un_left_commute
% 0.13/0.36 thf(fact_210_llexord__trans,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 0.13/0.36 => ( ( coinductive_llexord @ A @ R @ Ys @ Zs2 )
% 0.13/0.36 => ( ! [A4: A,B4: A,C4: A] :
% 0.13/0.36 ( ( R @ A4 @ B4 )
% 0.13/0.36 => ( ( R @ B4 @ C4 )
% 0.13/0.36 => ( R @ A4 @ C4 ) ) )
% 0.13/0.36 => ( coinductive_llexord @ A @ R @ Xs3 @ Zs2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_trans
% 0.13/0.36 thf(fact_211_llexord__linear,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ! [X2: A,Y4: A] :
% 0.13/0.36 ( ( R @ X2 @ Y4 )
% 0.13/0.36 | ( X2 = Y4 )
% 0.13/0.36 | ( R @ Y4 @ X2 ) )
% 0.13/0.36 => ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 0.13/0.36 | ( coinductive_llexord @ A @ R @ Ys @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_linear
% 0.13/0.36 thf(fact_212_llexord__antisym,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 0.13/0.36 => ( ( coinductive_llexord @ A @ R @ Ys @ Xs3 )
% 0.13/0.36 => ( ! [A4: A,B4: A] :
% 0.13/0.36 ( ( R @ A4 @ B4 )
% 0.13/0.36 => ~ ( R @ B4 @ A4 ) )
% 0.13/0.36 => ( Xs3 = Ys ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_antisym
% 0.13/0.36 thf(fact_213_lfinite__lfilterI,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( coinductive_lfinite @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfinite_lfilterI
% 0.13/0.36 thf(fact_214_lfilter__empty__conv,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 = ( ! [X5: A] :
% 0.13/0.36 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ~ ( P @ X5 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_empty_conv
% 0.13/0.36 thf(fact_215_lfilter__eq__lappend__lfiniteD,axiom,
% 0.13/0.36 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 0.13/0.36 = ( coinductive_lappend @ A @ Ys @ Zs2 ) )
% 0.13/0.36 => ( ( coinductive_lfinite @ A @ Ys )
% 0.13/0.36 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs3
% 0.13/0.36 = ( coinductive_lappend @ A @ Us @ Vs ) )
% 0.13/0.36 & ( coinductive_lfinite @ A @ Us )
% 0.13/0.36 & ( Ys
% 0.13/0.36 = ( coinductive_lfilter @ A @ P @ Us ) )
% 0.13/0.36 & ( Zs2
% 0.13/0.36 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lfilter_eq_lappend_lfiniteD
% 0.13/0.36 thf(fact_216_llexord_Ocoinduct,axiom,
% 0.13/0.36 ! [A: $tType,X6: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa3: coinductive_llist @ A,R: A > A > $o] :
% 0.13/0.36 ( ( X6 @ X @ Xa3 )
% 0.13/0.36 => ( ! [X2: coinductive_llist @ A,Xa: coinductive_llist @ A] :
% 0.13/0.36 ( ( X6 @ X2 @ Xa )
% 0.13/0.36 => ( ? [Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A,Xb: A] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 0.13/0.36 & ( Xa
% 0.13/0.36 = ( coinductive_LCons @ A @ Xb @ Ys2 ) )
% 0.13/0.36 & ( ( X6 @ Xs5 @ Ys2 )
% 0.13/0.36 | ( coinductive_llexord @ A @ R @ Xs5 @ Ys2 ) ) )
% 0.13/0.36 | ? [Xb: A,Y5: A,Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 0.13/0.36 & ( Xa
% 0.13/0.36 = ( coinductive_LCons @ A @ Y5 @ Ys2 ) )
% 0.13/0.36 & ( R @ Xb @ Y5 ) )
% 0.13/0.36 | ? [Ys2: coinductive_llist @ A] :
% 0.13/0.36 ( ( X2
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 & ( Xa = Ys2 ) ) ) )
% 0.13/0.36 => ( coinductive_llexord @ A @ R @ X @ Xa3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord.coinduct
% 0.13/0.36 thf(fact_217_llexord_Osimps,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( coinductive_llexord @ A )
% 0.13/0.36 = ( ^ [R2: A > A > $o,A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 0.13/0.36 ( ? [Xs4: coinductive_llist @ A,Ys5: coinductive_llist @ A,X5: A] :
% 0.13/0.36 ( ( A12
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 0.13/0.36 & ( A23
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ Ys5 ) )
% 0.13/0.36 & ( coinductive_llexord @ A @ R2 @ Xs4 @ Ys5 ) )
% 0.13/0.36 | ? [X5: A,Y3: A,Xs4: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 0.13/0.36 ( ( A12
% 0.13/0.36 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 0.13/0.36 & ( A23
% 0.13/0.36 = ( coinductive_LCons @ A @ Y3 @ Ys5 ) )
% 0.13/0.36 & ( R2 @ X5 @ Y3 ) )
% 0.13/0.36 | ? [Ys5: coinductive_llist @ A] :
% 0.13/0.36 ( ( A12
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 & ( A23 = Ys5 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord.simps
% 0.13/0.36 thf(fact_218_llexord_Ocases,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_llexord @ A @ R @ A1 @ A22 )
% 0.13/0.36 => ( ! [Xs2: coinductive_llist @ A,Ys3: coinductive_llist @ A,X2: A] :
% 0.13/0.36 ( ( A1
% 0.13/0.36 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 0.13/0.36 => ( ( A22
% 0.13/0.36 = ( coinductive_LCons @ A @ X2 @ Ys3 ) )
% 0.13/0.36 => ~ ( coinductive_llexord @ A @ R @ Xs2 @ Ys3 ) ) )
% 0.13/0.36 => ( ! [X2: A] :
% 0.13/0.36 ( ? [Xs2: coinductive_llist @ A] :
% 0.13/0.36 ( A1
% 0.13/0.36 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 0.13/0.36 => ! [Y4: A] :
% 0.13/0.36 ( ? [Ys3: coinductive_llist @ A] :
% 0.13/0.36 ( A22
% 0.13/0.36 = ( coinductive_LCons @ A @ Y4 @ Ys3 ) )
% 0.13/0.36 => ~ ( R @ X2 @ Y4 ) ) )
% 0.13/0.36 => ~ ( ( A1
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 => ! [Ys3: coinductive_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord.cases
% 0.13/0.36 thf(fact_219_llexord__code_I2_J,axiom,
% 0.13/0.36 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A] :
% 0.13/0.36 ~ ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LNil @ A ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_code(2)
% 0.13/0.36 thf(fact_220_gen__lset__def,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( coinductive_gen_lset @ A )
% 0.13/0.36 = ( ^ [A5: set @ A,Xs4: coinductive_llist @ A] : ( sup_sup @ ( set @ A ) @ A5 @ ( coinductive_lset @ A @ Xs4 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % gen_lset_def
% 0.13/0.36 thf(fact_221_lset__lappend,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) @ ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_lappend
% 0.13/0.36 thf(fact_222_lset__lappend__conv,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ Ys ) ) ) )
% 0.13/0.36 & ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( coinductive_lset @ A @ Xs3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lset_lappend_conv
% 0.13/0.36 thf(fact_223_llexord__lappend__left,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,R: A > A > $o,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 => ( ! [X2: A] :
% 0.13/0.36 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs3 ) )
% 0.13/0.36 => ~ ( R @ X2 @ X2 ) )
% 0.13/0.36 => ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( coinductive_lappend @ A @ Xs3 @ Zs2 ) )
% 0.13/0.36 = ( coinductive_llexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_lappend_left
% 0.13/0.36 thf(fact_224_le__sup__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.13/0.36 = ( ( ord_less_eq @ A @ X @ Z )
% 0.13/0.36 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_sup_iff
% 0.13/0.36 thf(fact_225_sup_Obounded__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,C2: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 )
% 0.13/0.36 = ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.bounded_iff
% 0.13/0.36 thf(fact_226_sup_OcoboundedI2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [C2: A,B3: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.coboundedI2
% 0.13/0.36 thf(fact_227_inf__sup__ord_I4_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_ord(4)
% 0.13/0.36 thf(fact_228_inf__sup__ord_I3_J,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( lattice @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % inf_sup_ord(3)
% 0.13/0.36 thf(fact_229_le__supE,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X )
% 0.13/0.36 => ~ ( ( ord_less_eq @ A @ A2 @ X )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ B3 @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supE
% 0.13/0.36 thf(fact_230_le__supI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,X: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ X )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supI
% 0.13/0.36 thf(fact_231_sup__ge1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_ge1
% 0.13/0.36 thf(fact_232_sup__ge2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_ge2
% 0.13/0.36 thf(fact_233_le__supI1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,A2: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ A2 )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supI1
% 0.13/0.36 thf(fact_234_le__supI2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,B3: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_supI2
% 0.13/0.36 thf(fact_235_sup_Omono,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [C2: A,A2: A,D2: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ D2 @ B3 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ C2 @ D2 ) @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.mono
% 0.13/0.36 thf(fact_236_sup__mono,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,C2: A,B3: A,D2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ B3 @ D2 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ ( sup_sup @ A @ C2 @ D2 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_mono
% 0.13/0.36 thf(fact_237_sup__least,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A,Z: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Z @ X )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_least
% 0.13/0.36 thf(fact_238_le__iff__sup,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [X5: A,Y3: A] :
% 0.13/0.36 ( ( sup_sup @ A @ X5 @ Y3 )
% 0.13/0.36 = Y3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % le_iff_sup
% 0.13/0.36 thf(fact_239_sup_OorderE,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ( A2
% 0.13/0.36 = ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.orderE
% 0.13/0.36 thf(fact_240_sup_OorderI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A] :
% 0.13/0.36 ( ( A2
% 0.13/0.36 = ( sup_sup @ A @ A2 @ B3 ) )
% 0.13/0.36 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.orderI
% 0.13/0.36 thf(fact_241_sup__unique,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [F: A > A > A,X: A,Y: A] :
% 0.13/0.36 ( ! [X2: A,Y4: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y4 ) )
% 0.13/0.36 => ( ! [X2: A,Y4: A] : ( ord_less_eq @ A @ Y4 @ ( F @ X2 @ Y4 ) )
% 0.13/0.36 => ( ! [X2: A,Y4: A,Z3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y4 @ X2 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 0.13/0.36 => ( ( sup_sup @ A @ X @ Y )
% 0.13/0.36 = ( F @ X @ Y ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_unique
% 0.13/0.36 thf(fact_242_sup_Oabsorb1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ( ( sup_sup @ A @ A2 @ B3 )
% 0.13/0.36 = A2 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb1
% 0.13/0.36 thf(fact_243_sup_Oabsorb2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ A2 @ B3 )
% 0.13/0.36 => ( ( sup_sup @ A @ A2 @ B3 )
% 0.13/0.36 = B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb2
% 0.13/0.36 thf(fact_244_sup__absorb1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [Y: A,X: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ Y @ X )
% 0.13/0.36 => ( ( sup_sup @ A @ X @ Y )
% 0.13/0.36 = X ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_absorb1
% 0.13/0.36 thf(fact_245_sup__absorb2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [X: A,Y: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ X @ Y )
% 0.13/0.36 => ( ( sup_sup @ A @ X @ Y )
% 0.13/0.36 = Y ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup_absorb2
% 0.13/0.36 thf(fact_246_sup_OboundedE,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,C2: A,A2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 )
% 0.13/0.36 => ~ ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ~ ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.boundedE
% 0.13/0.36 thf(fact_247_sup_OboundedI,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,A2: A,C2: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ B3 @ A2 )
% 0.13/0.36 => ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.13/0.36 => ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.boundedI
% 0.13/0.36 thf(fact_248_sup_Oorder__iff,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [B6: A,A6: A] :
% 0.13/0.36 ( A6
% 0.13/0.36 = ( sup_sup @ A @ A6 @ B6 ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.order_iff
% 0.13/0.36 thf(fact_249_sup_Ocobounded1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.cobounded1
% 0.13/0.36 thf(fact_250_sup_Ocobounded2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [B3: A,A2: A] : ( ord_less_eq @ A @ B3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.cobounded2
% 0.13/0.36 thf(fact_251_sup_Oabsorb__iff1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [B6: A,A6: A] :
% 0.13/0.36 ( ( sup_sup @ A @ A6 @ B6 )
% 0.13/0.36 = A6 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb_iff1
% 0.13/0.36 thf(fact_252_sup_Oabsorb__iff2,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ( ( ord_less_eq @ A )
% 0.13/0.36 = ( ^ [A6: A,B6: A] :
% 0.13/0.36 ( ( sup_sup @ A @ A6 @ B6 )
% 0.13/0.36 = B6 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.absorb_iff2
% 0.13/0.36 thf(fact_253_sup_OcoboundedI1,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.13/0.36 => ! [C2: A,A2: A,B3: A] :
% 0.13/0.36 ( ( ord_less_eq @ A @ C2 @ A2 )
% 0.13/0.36 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % sup.coboundedI1
% 0.13/0.36 thf(fact_254_llexord__conv,axiom,
% 0.13/0.36 ! [A: $tType] :
% 0.13/0.36 ( ( coinductive_llexord @ A )
% 0.13/0.36 = ( ^ [R2: A > A > $o,Xs4: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 0.13/0.36 ( ( Xs4 = Ys5 )
% 0.13/0.36 | ? [Zs3: coinductive_llist @ A,Xs6: coinductive_llist @ A,Y3: A,Ys4: coinductive_llist @ A] :
% 0.13/0.36 ( ( coinductive_lfinite @ A @ Zs3 )
% 0.13/0.36 & ( Xs4
% 0.13/0.36 = ( coinductive_lappend @ A @ Zs3 @ Xs6 ) )
% 0.13/0.36 & ( Ys5
% 0.13/0.36 = ( coinductive_lappend @ A @ Zs3 @ ( coinductive_LCons @ A @ Y3 @ Ys4 ) ) )
% 0.13/0.36 & ( ( Xs6
% 0.13/0.36 = ( coinductive_LNil @ A ) )
% 0.13/0.36 | ( R2 @ ( coinductive_lhd @ A @ Xs6 ) @ Y3 ) ) ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % llexord_conv
% 0.13/0.36 thf(fact_255_lstrict__prefix__lappend__conv,axiom,
% 0.13/0.36 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.13/0.36 ( ( coindu1478340336prefix @ A @ Xs3 @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 0.13/0.36 = ( ( coinductive_lfinite @ A @ Xs3 )
% 0.13/0.36 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.13/0.36
% 0.13/0.36 % lstrict_prefix_lappend_conv
% 0.13/0.36
% 0.13/0.36 %----Type constructors (19)
% 0.13/0.36 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.13/0.36 ! [A7: $tType,A8: $tType] :
% 0.13/0.36 ( ( comple187826305attice @ A8 @ ( type2 @ A8 ) )
% 0.13/0.36 => ( comple187826305attice @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.13/0.36 ! [A7: $tType,A8: $tType] :
% 0.13/0.36 ( ( semilattice_sup @ A8 @ ( type2 @ A8 ) )
% 0.13/0.36 => ( semilattice_sup @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.13/0.36 ! [A7: $tType,A8: $tType] :
% 0.13/0.36 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.13/0.36 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.13/0.36 ! [A7: $tType,A8: $tType] :
% 0.13/0.36 ( ( lattice @ A8 @ ( type2 @ A8 ) )
% 0.13/0.36 => ( lattice @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.13/0.36 ! [A7: $tType,A8: $tType] :
% 0.13/0.36 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.13/0.36 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_fun___Orderings_Oord,axiom,
% 0.13/0.36 ! [A7: $tType,A8: $tType] :
% 0.13/0.36 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.13/0.36 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 0.13/0.36 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_2,axiom,
% 0.13/0.36 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Orderings_Opreorder_3,axiom,
% 0.13/0.36 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Lattices_Olattice_4,axiom,
% 0.13/0.36 ! [A7: $tType] : ( lattice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.13/0.36 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.13/0.36 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7,axiom,
% 0.13/0.36 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_8,axiom,
% 0.13/0.36 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Opreorder_9,axiom,
% 0.13/0.36 preorder @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.13/0.36 linorder @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 0.13/0.36 lattice @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 0.13/0.36 order @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 0.13/0.36 ord @ $o @ ( type2 @ $o ) ).
% 0.13/0.36
% 0.13/0.36 %----Helper facts (3)
% 0.13/0.36 thf(help_If_3_1_T,axiom,
% 0.13/0.36 ! [P: $o] :
% 0.13/0.36 ( ( P = $true )
% 0.13/0.36 | ( P = $false ) ) ).
% 0.13/0.36
% 0.13/0.36 thf(help_If_2_1_T,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Y: A] :
% 0.13/0.36 ( ( if @ A @ $false @ X @ Y )
% 0.13/0.36 = Y ) ).
% 0.13/0.36
% 0.13/0.36 thf(help_If_1_1_T,axiom,
% 0.13/0.36 ! [A: $tType,X: A,Y: A] :
% 0.13/0.36 ( ( if @ A @ $true @ X @ Y )
% 0.13/0.36 = X ) ).
% 0.13/0.36
% 0.13/0.36 %----Conjectures (1)
% 0.13/0.36 thf(conj_0,conjecture,
% 0.13/0.36 member @ a @ n2 @ ns ).
% 0.13/0.36
% 0.13/0.36 %------------------------------------------------------------------------------
% 0.13/0.36 ------------------------
% 2.71/1.46 ---- Embedded in THF ---
% 2.71/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.71/1.46 %%% Generated on Tue Feb 24 04:16:01 EST 2026
% 2.71/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.71/1.46 %%% Logic specification used:
% 2.71/1.46 %%% thf(spec, logic, $$dhol).
% 2.71/1.46
% 2.71/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2DTF21052.p
% 2.71/1.46 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.71/1.46 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.71/1.46 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.71/1.46 thf(ty_tf_a, type, a: $tType).
% 2.71/1.46 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ogen__lset, type, coinductive_gen_lset: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ A)))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Oldistinct, type, coindu351974385stinct: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Olfilter, type, coinductive_lfilter: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollexord, type, coinductive_llexord: (!> [A:$tType]: (((A > (A > $o)) > ((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollist_Ocorec__llist, type, coindu1259883913_llist: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (coinductive_llist @ A)) > ((C > C) > (C > (coinductive_llist @ A)))))))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollist_Olhd, type, coinductive_lhd: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ollist_Olset, type, coinductive_lset: (!> [A:$tType]: (((coinductive_llist @ A) > (set @ A))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Olmember, type, coinductive_lmember: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > $o))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Oord__class_Olsorted, type, coindu63249387sorted: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.71/1.46 thf(sy_c_Coinductive__List_Ounfold__llist, type, coindu1441602521_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coinductive_llist @ B)))))))).
% 2.71/1.46 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.71/1.46 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opaths, type, koenig916195507_paths: (!> [Node:$tType]: (((Node > (Node > $o)) > (set @ (coinductive_llist @ Node)))))).
% 2.71/1.46 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opathsp, type, koenig2031690877pathsp: (!> [Node:$tType]: (((Node > (Node > $o)) > ((coinductive_llist @ Node) > $o))))).
% 2.71/1.46 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oreachable__via, type, koenig317145564le_via: (!> [Node:$tType]: (((Node > (Node > $o)) > ((set @ Node) > (Node > (set @ Node))))))).
% 2.71/1.46 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oreachable__viap, type, koenig1757754772e_viap: (!> [Node:$tType]: (((Node > (Node > $o)) > ((set @ Node) > (Node > (Node > $o))))))).
% 2.71/1.46 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.71/1.46 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.71/1.46 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.71/1.46 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.71/1.46 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.71/1.46 thf(sy_v_graph, type, graph: (a > (a > $o))).
% 2.71/1.46 thf(sy_v_n, type, n: a).
% 2.71/1.46 thf(sy_v_n_H____, type, n2: a).
% 2.71/1.46 thf(sy_v_ns, type, ns: (set @ a)).
% 2.71/1.46 thf(sy_v_x____, type, x: a).
% 2.71/1.46 thf(sy_v_xs_H____, type, xs: (coinductive_llist @ a)).
% 2.71/1.46 thf(sy_v_xs____, type, xs2: (coinductive_llist @ a)).
% 2.71/1.46 thf(fact_0__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062, axiom, (((member @ a) @ x) @ ((coinductive_lset @ a) @ xs2))).
% 2.71/1.46 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [N:a,Xs:(coinductive_llist @ a)]: ((xs2 != (((coinductive_LCons @ a) @ N) @ Xs))))))).
% 2.71/1.46 thf(fact_2_xs, axiom, (xs2 = (((coinductive_LCons @ a) @ n2) @ xs))).
% 2.71/1.46 thf(fact_3__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062, axiom, (((ord_less_eq @ (set @ a)) @ ((coinductive_lset @ a) @ xs2)) @ ns)).
% 2.71/1.46 thf(fact_4_calculation, axiom, ((graph @ n) @ n2)).
% 2.71/1.46 thf(fact_5__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062, axiom, (((member @ a) @ x) @ ((((koenig317145564le_via @ a) @ graph) @ ns) @ n))).
% 2.71/1.46 thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Xs2:(coinductive_llist @ a)]: (((((member @ (coinductive_llist @ a)) @ (((coinductive_LCons @ a) @ n) @ Xs2)) @ ((koenig916195507_paths @ a) @ graph)) => ((((member @ a) @ x) @ ((coinductive_lset @ a) @ Xs2)) => (~ ((((ord_less_eq @ (set @ a)) @ ((coinductive_lset @ a) @ Xs2)) @ ns)))))))))).
% 2.71/1.46 thf(fact_7_path, axiom, (((member @ (coinductive_llist @ a)) @ (((coinductive_LCons @ a) @ n) @ xs2)) @ ((koenig916195507_paths @ a) @ graph))).
% 2.71/1.46 thf(fact_8_paths_OLCons, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),X:Node,Y:Node,Xs3:(coinductive_llist @ Node)]: ((((Graph @ X) @ Y) => ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y) @ Xs3)) @ ((koenig916195507_paths @ Node) @ Graph)) => (((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ X) @ (((coinductive_LCons @ Node) @ Y) @ Xs3))) @ ((koenig916195507_paths @ Node) @ Graph))))))).
% 2.71/1.46 thf(fact_9_paths__LConsD, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A),Graph:(A > (A > $o))]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ ((koenig916195507_paths @ A) @ Graph)) => (((member @ (coinductive_llist @ A)) @ Xs3) @ ((koenig916195507_paths @ A) @ Graph)))))).
% 2.71/1.46 thf(fact_10_path__avoid__node, axiom, (! [A:$tType,N2:A,Xs3:(coinductive_llist @ A),Graph:(A > (A > $o)),X:A]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ N2) @ Xs3)) @ ((koenig916195507_paths @ A) @ Graph)) => ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => ((N2 != X) => (? [Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ N2) @ Xs)) @ ((koenig916195507_paths @ A) @ Graph)) & ((((ord_less_eq @ (set @ A)) @ ((coinductive_lset @ A) @ Xs)) @ ((coinductive_lset @ A) @ Xs3)) & ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) & (~ ((((member @ A) @ N2) @ ((coinductive_lset @ A) @ Xs))))))))))))))).
% 2.71/1.46 thf(fact_11_reachable__via_Ocases, axiom, (! [Node:$tType,A2:Node,Graph:(Node > (Node > $o)),Ns:(set @ Node),N2:Node]: (((((member @ Node) @ A2) @ ((((koenig317145564le_via @ Node) @ Graph) @ Ns) @ N2)) => (~ ((! [Xs2:(coinductive_llist @ Node)]: (((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ N2) @ Xs2)) @ ((koenig916195507_paths @ Node) @ Graph)) => ((((member @ Node) @ A2) @ ((coinductive_lset @ Node) @ Xs2)) => (~ ((((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs2)) @ Ns))))))))))))).
% 2.71/1.46 thf(fact_12_reachable__via_Osimps, axiom, (! [Node:$tType,A2:Node,Graph:(Node > (Node > $o)),Ns:(set @ Node),N2:Node]: (((((member @ Node) @ A2) @ ((((koenig317145564le_via @ Node) @ Graph) @ Ns) @ N2)) = (? [Xs4:(coinductive_llist @ Node),N3:Node]: (((A2 = N3) & ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ N2) @ Xs4)) @ ((koenig916195507_paths @ Node) @ Graph)) & ((((member @ Node) @ N3) @ ((coinductive_lset @ Node) @ Xs4)) & (((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs4)) @ Ns)))))))))).
% 2.71/1.46 thf(fact_13_reachable__via_Ointros, axiom, (! [Node:$tType,N2:Node,Xs3:(coinductive_llist @ Node),Graph:(Node > (Node > $o)),N4:Node,Ns:(set @ Node)]: (((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ N2) @ Xs3)) @ ((koenig916195507_paths @ Node) @ Graph)) => ((((member @ Node) @ N4) @ ((coinductive_lset @ Node) @ Xs3)) => ((((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs3)) @ Ns) => (((member @ Node) @ N4) @ ((((koenig317145564le_via @ Node) @ Graph) @ Ns) @ N2)))))))).
% 2.71/1.46 thf(fact_14_reachable__via_Oinducts, axiom, (! [Node:$tType,X:Node,Graph:(Node > (Node > $o)),Ns:(set @ Node),N2:Node,P:(Node > $o)]: (((((member @ Node) @ X) @ ((((koenig317145564le_via @ Node) @ Graph) @ Ns) @ N2)) => ((! [Xs2:(coinductive_llist @ Node),N:Node]: (((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ N2) @ Xs2)) @ ((koenig916195507_paths @ Node) @ Graph)) => ((((member @ Node) @ N) @ ((coinductive_lset @ Node) @ Xs2)) => ((((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs2)) @ Ns) => (P @ N)))))) => (P @ X)))))).
% 2.71/1.46 thf(fact_15_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.71/1.46 thf(fact_16_subsetI, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A3) => (((member @ A) @ X2) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B2))))).
% 2.71/1.46 thf(fact_17_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A3) => (A3 = B2)))))).
% 2.71/1.46 thf(fact_18_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.71/1.46 thf(fact_19_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A),X3:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X3) @ Xs3))))))).
% 2.71/1.46 thf(fact_20_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: ((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X) @ Xs3)))))).
% 2.71/1.46 thf(fact_21_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(coinductive_llist @ A),A1:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A22)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22))))))).
% 2.71/1.46 thf(fact_22_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coinductive_llist @ A)]: ((((member @ A) @ A1) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22)))))).
% 2.71/1.46 thf(fact_23_lset__cases, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => ((! [Xs:(coinductive_llist @ A)]: ((Xs3 != (((coinductive_LCons @ A) @ X) @ Xs)))) => (~ ((! [X4:A,Xs:(coinductive_llist @ A)]: (((Xs3 = (((coinductive_LCons @ A) @ X4) @ Xs)) => (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)))))))))))))).
% 2.71/1.46 thf(fact_24_lset__induct, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => ((! [Xs2:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs2)))) => ((! [X4:A,Xs2:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs2)) => ((X != X4) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X4) @ Xs2))))))) => (P @ Xs3))))))).
% 2.71/1.46 thf(fact_25_lset__induct_H, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => ((! [Xs2:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs2)))) => ((! [X4:A,Xs2:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs2)) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X4) @ Xs2)))))) => (P @ Xs3))))))).
% 2.71/1.46 thf(fact_26_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ A2) @ B3) => (A2 = B3))))))))).
% 2.71/1.46 thf(fact_27_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C2) @ B3) => (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.71/1.46 thf(fact_28_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B3:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_29_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.71/1.46 thf(fact_30_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 2.71/1.46 thf(fact_31_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ A2) => (A2 = B3))))))))).
% 2.71/1.46 thf(fact_32_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((B3 = C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.71/1.46 thf(fact_33_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((A2 = B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.71/1.46 thf(fact_34_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.71/1.46 thf(fact_35_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.71/1.46 thf(fact_36_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less_eq @ A) @ A2) @ C2))))))))).
% 2.71/1.46 thf(fact_37_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.71/1.46 thf(fact_38_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B3:A,A2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((((P @ B3) @ A2) => ((P @ A2) @ B3)) => ((P @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_39_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.71/1.46 thf(fact_40_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.71/1.46 thf(fact_41_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.71/1.46 thf(fact_42_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [X5:A,Y3:A]: (((((ord_less_eq @ A) @ X5) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X5))))))))).
% 2.71/1.46 thf(fact_43_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A2) @ B3) => (((F @ B3) = C2) => ((! [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C2)))))))))).
% 2.71/1.46 thf(fact_44_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C2:B]: (((A2 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X2:B,Y4:B]: (((((ord_less_eq @ B) @ X2) @ Y4) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.71/1.46 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.71/1.46 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member @ A) @ X5) @ A3)))) = A3)))).
% 2.71/1.46 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.71/1.46 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.71/1.46 thf(fact_49_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B3:A,F:(A > C),C2:C]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C2) => ((! [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) => (((ord_less_eq @ C) @ (F @ X2)) @ (F @ Y4))))) => (((ord_less_eq @ C) @ (F @ A2)) @ C2)))))))))).
% 2.71/1.46 thf(fact_50_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B3:B,C2:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X2:B,Y4:B]: (((((ord_less_eq @ B) @ X2) @ Y4) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C2))))))))))).
% 2.71/1.46 thf(fact_51_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X5:A]: ((((ord_less_eq @ B) @ (F2 @ X5)) @ (G2 @ X5))))))))))).
% 2.71/1.46 thf(fact_52_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.71/1.46 thf(fact_53_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.71/1.46 thf(fact_54_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.71/1.46 thf(fact_55_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X5:A]: (((P @ X5) => (Q @ X5)))))))).
% 2.71/1.46 thf(fact_56_contra__subsetD, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((~ ((((member @ A) @ C2) @ B2))) => (~ ((((member @ A) @ C2) @ A3)))))))).
% 2.71/1.46 thf(fact_57_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y2:(set @ A),Z2:(set @ A)]: ((Y2 = Z2))) = (^ [A5:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A5)))))))).
% 2.71/1.46 thf(fact_58_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => (((ord_less_eq @ (set @ A)) @ A3) @ C3)))))).
% 2.71/1.46 thf(fact_59_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.71/1.46 thf(fact_60_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 2.71/1.46 thf(fact_61_rev__subsetD, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A3) => ((((ord_less_eq @ (set @ A)) @ A3) @ B2) => (((member @ A) @ C2) @ B2)))))).
% 2.71/1.46 thf(fact_62_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A5) => (((member @ A) @ T) @ B5)))))))))).
% 2.71/1.46 thf(fact_63_set__rev__mp, axiom, (! [A:$tType,X:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ X) @ A3) => ((((ord_less_eq @ (set @ A)) @ A3) @ B2) => (((member @ A) @ X) @ B2)))))).
% 2.71/1.46 thf(fact_64_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((A3 = B2) => (((ord_less_eq @ (set @ A)) @ B2) @ A3))))).
% 2.71/1.46 thf(fact_65_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((A3 = B2) => (((ord_less_eq @ (set @ A)) @ A3) @ B2))))).
% 2.71/1.46 thf(fact_66_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((! [X5:A]: (((((member @ A) @ X5) @ A5) => (((member @ A) @ X5) @ B5)))))))))).
% 2.71/1.46 thf(fact_67_equalityE, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((A3 = B2) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => (~ ((((ord_less_eq @ (set @ A)) @ B2) @ A3)))))))))).
% 2.71/1.46 thf(fact_68_subsetCE, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B2)))))).
% 2.71/1.46 thf(fact_69_subsetD, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ B2)))))).
% 2.71/1.46 thf(fact_70_in__mono, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((member @ A) @ X) @ A3) => (((member @ A) @ X) @ B2)))))).
% 2.71/1.46 thf(fact_71_set__mp, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((member @ A) @ X) @ A3) => (((member @ A) @ X) @ B2)))))).
% 2.71/1.46 thf(fact_72_llist_Oset__induct, axiom, (! [A:$tType,X:A,A2:(coinductive_llist @ A),P:(A > ((coinductive_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A2)) => ((! [Z1:A,Z22:(coinductive_llist @ A)]: (((P @ Z1) @ (((coinductive_LCons @ A) @ Z1) @ Z22)))) => ((! [Z1:A,Z22:(coinductive_llist @ A),Xa:A]: (((((member @ A) @ Xa) @ ((coinductive_lset @ A) @ Z22)) => (((P @ Xa) @ Z22) => ((P @ Xa) @ (((coinductive_LCons @ A) @ Z1) @ Z22)))))) => ((P @ X) @ A2))))))).
% 2.71/1.46 thf(fact_73_llist_Oset__cases, axiom, (! [A:$tType,E:A,A2:(coinductive_llist @ A)]: (((((member @ A) @ E) @ ((coinductive_lset @ A) @ A2)) => ((! [Z22:(coinductive_llist @ A)]: ((A2 != (((coinductive_LCons @ A) @ E) @ Z22)))) => (~ ((! [Z1:A,Z22:(coinductive_llist @ A)]: (((A2 = (((coinductive_LCons @ A) @ Z1) @ Z22)) => (~ ((((member @ A) @ E) @ ((coinductive_lset @ A) @ Z22)))))))))))))).
% 2.71/1.46 thf(fact_74_reachable__viap__reachable__via__eq, axiom, (! [Node:$tType]: (((koenig1757754772e_viap @ Node) = (^ [Graph2:(Node > (Node > $o)),Ns2:(set @ Node),N5:Node,X5:Node]: ((((member @ Node) @ X5) @ ((((koenig317145564le_via @ Node) @ Graph2) @ Ns2) @ N5)))))))).
% 2.71/1.46 thf(fact_75_lset__lmember, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) = (((coinductive_lmember @ A) @ X) @ Xs3))))).
% 2.71/1.46 thf(fact_76_lsorted__LCons, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Xs3:(coinductive_llist @ A)]: ((((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ X) @ Xs3)) = (((coindu63249387sorted @ A) @ Xs3) & (! [X5:A]: (((((member @ A) @ X5) @ ((coinductive_lset @ A) @ Xs3)) => (((ord_less_eq @ A) @ X) @ X5)))))))))))).
% 2.71/1.46 thf(fact_77_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lmember @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coinductive_lmember @ A) @ X) @ Ys)))))).
% 2.71/1.46 thf(fact_78_lfp_Oleq__antisym, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.71/1.46 thf(fact_79_gfp_Oleq__antisym, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) => (X = Y))))))))).
% 2.71/1.46 thf(fact_80_lfp_Oleq__trans, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 2.71/1.46 thf(fact_81_gfp_Oleq__trans, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [Y:A,X:A,Z:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ Z) @ Y) => (((ord_less_eq @ A) @ Z) @ X))))))))).
% 2.71/1.46 thf(fact_82_lfp_Oleq__refl, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.71/1.46 thf(fact_83_lsorted__LCons__LCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs3:(coinductive_llist @ A)]: ((((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs3))) = ((((ord_less_eq @ A) @ X) @ Y) & ((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs3)))))))))).
% 2.71/1.46 thf(fact_84_LCons__LCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs3:(coinductive_llist @ A)]: (((((ord_less_eq @ A) @ X) @ Y) => (((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs3)) => ((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs3))))))))))).
% 2.71/1.46 thf(fact_85_reachable__viap_Ocases, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),Ns:(set @ Node),N2:Node,A2:Node]: (((((((koenig1757754772e_viap @ Node) @ Graph) @ Ns) @ N2) @ A2) => (~ ((! [Xs2:(coinductive_llist @ Node)]: (((((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ N2) @ Xs2)) => ((((member @ Node) @ A2) @ ((coinductive_lset @ Node) @ Xs2)) => (~ ((((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs2)) @ Ns))))))))))))).
% 2.71/1.46 thf(fact_86_reachable__viap_Osimps, axiom, (! [Node:$tType]: (((koenig1757754772e_viap @ Node) = (^ [Graph2:(Node > (Node > $o)),Ns2:(set @ Node),N5:Node,A6:Node]: ((? [Xs4:(coinductive_llist @ Node),N3:Node]: (((A6 = N3) & ((((koenig2031690877pathsp @ Node) @ Graph2) @ (((coinductive_LCons @ Node) @ N5) @ Xs4)) & ((((member @ Node) @ N3) @ ((coinductive_lset @ Node) @ Xs4)) & (((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs4)) @ Ns2)))))))))))).
% 2.71/1.46 thf(fact_87_reachable__viap_Ointros, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),N2:Node,Xs3:(coinductive_llist @ Node),N4:Node,Ns:(set @ Node)]: (((((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ N2) @ Xs3)) => ((((member @ Node) @ N4) @ ((coinductive_lset @ Node) @ Xs3)) => ((((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs3)) @ Ns) => (((((koenig1757754772e_viap @ Node) @ Graph) @ Ns) @ N2) @ N4))))))).
% 2.71/1.46 thf(fact_88_reachable__viap_Oinducts, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),Ns:(set @ Node),N2:Node,X:Node,P:(Node > $o)]: (((((((koenig1757754772e_viap @ Node) @ Graph) @ Ns) @ N2) @ X) => ((! [Xs2:(coinductive_llist @ Node),N:Node]: (((((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ N2) @ Xs2)) => ((((member @ Node) @ N) @ ((coinductive_lset @ Node) @ Xs2)) => ((((ord_less_eq @ (set @ Node)) @ ((coinductive_lset @ Node) @ Xs2)) @ Ns) => (P @ N)))))) => (P @ X)))))).
% 2.71/1.46 thf(fact_89_lsorted_Ocases, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:(coinductive_llist @ A)]: ((((coindu63249387sorted @ A) @ A2) => ((A2 != (coinductive_LNil @ A)) => ((! [X2:A]: ((A2 != (((coinductive_LCons @ A) @ X2) @ (coinductive_LNil @ A))))) => (~ ((! [X2:A,Y4:A,Xs2:(coinductive_llist @ A)]: (((A2 = (((coinductive_LCons @ A) @ X2) @ (((coinductive_LCons @ A) @ Y4) @ Xs2))) => ((((ord_less_eq @ A) @ X2) @ Y4) => (~ (((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ Y4) @ Xs2))))))))))))))))))).
% 2.71/1.46 thf(fact_90_lsorted_Osimps, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((coindu63249387sorted @ A) = (^ [A6:(coinductive_llist @ A)]: (((A6 = (coinductive_LNil @ A)) | ((? [X5:A]: ((A6 = (((coinductive_LCons @ A) @ X5) @ (coinductive_LNil @ A))))) | (? [X5:A,Y3:A,Xs4:(coinductive_llist @ A)]: (((A6 = (((coinductive_LCons @ A) @ X5) @ (((coinductive_LCons @ A) @ Y3) @ Xs4))) & ((((ord_less_eq @ A) @ X5) @ Y3) & ((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ Y3) @ Xs4))))))))))))))).
% 2.71/1.46 thf(fact_91_lsorted__code_I1_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((coindu63249387sorted @ A) @ (coinductive_LNil @ A)))))).
% 2.71/1.46 thf(fact_92_lsorted__code_I2_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A]: (((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))))))))).
% 2.71/1.46 thf(fact_93_pathsp_Ocases, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),A2:(coinductive_llist @ Node)]: (((((koenig2031690877pathsp @ Node) @ Graph) @ A2) => ((A2 != (coinductive_LNil @ Node)) => ((! [X2:Node]: ((A2 != (((coinductive_LCons @ Node) @ X2) @ (coinductive_LNil @ Node))))) => (~ ((! [X2:Node,Y4:Node,Xs2:(coinductive_llist @ Node)]: (((A2 = (((coinductive_LCons @ Node) @ X2) @ (((coinductive_LCons @ Node) @ Y4) @ Xs2))) => (((Graph @ X2) @ Y4) => (~ ((((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ Y4) @ Xs2)))))))))))))))).
% 2.71/1.46 thf(fact_94_pathsp_Osimps, axiom, (! [Node:$tType]: (((koenig2031690877pathsp @ Node) = (^ [Graph2:(Node > (Node > $o)),A6:(coinductive_llist @ Node)]: (((A6 = (coinductive_LNil @ Node)) | ((? [X5:Node]: ((A6 = (((coinductive_LCons @ Node) @ X5) @ (coinductive_LNil @ Node))))) | (? [X5:Node,Y3:Node,Xs4:(coinductive_llist @ Node)]: (((A6 = (((coinductive_LCons @ Node) @ X5) @ (((coinductive_LCons @ Node) @ Y3) @ Xs4))) & (((Graph2 @ X5) @ Y3) & (((koenig2031690877pathsp @ Node) @ Graph2) @ (((coinductive_LCons @ Node) @ Y3) @ Xs4)))))))))))))).
% 2.71/1.46 thf(fact_95_pathsp_OSingle, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),X:Node]: ((((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ X) @ (coinductive_LNil @ Node)))))).
% 2.71/1.46 thf(fact_96_pathsp_Ocoinduct, axiom, (! [Node:$tType,X6:((coinductive_llist @ Node) > $o),X:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((X6 @ X) => ((! [X2:(coinductive_llist @ Node)]: (((X6 @ X2) => ((X2 = (coinductive_LNil @ Node)) | ((? [Xa2:Node]: ((X2 = (((coinductive_LCons @ Node) @ Xa2) @ (coinductive_LNil @ Node))))) | (? [Xa2:Node,Y5:Node,Xs5:(coinductive_llist @ Node)]: (((X2 = (((coinductive_LCons @ Node) @ Xa2) @ (((coinductive_LCons @ Node) @ Y5) @ Xs5))) & (((Graph @ Xa2) @ Y5) & ((X6 @ (((coinductive_LCons @ Node) @ Y5) @ Xs5)) | (((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ Y5) @ Xs5)))))))))))) => (((koenig2031690877pathsp @ Node) @ Graph) @ X)))))).
% 2.71/1.46 thf(fact_97_pathsp_OEmpty, axiom, (! [Node:$tType,Graph:(Node > (Node > $o))]: ((((koenig2031690877pathsp @ Node) @ Graph) @ (coinductive_LNil @ Node))))).
% 2.71/1.46 thf(fact_98_neq__LNil__conv, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A)]: (((Xs3 != (coinductive_LNil @ A)) = (? [X5:A,Xs6:(coinductive_llist @ A)]: ((Xs3 = (((coinductive_LCons @ A) @ X5) @ Xs6)))))))).
% 2.71/1.46 thf(fact_99_llist_Oexhaust, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 2.71/1.46 thf(fact_100_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 2.71/1.46 thf(fact_101_LNil, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((coindu63249387sorted @ A) @ (coinductive_LNil @ A)))))).
% 2.71/1.46 thf(fact_102_paths_OEmpty, axiom, (! [Node:$tType,Graph:(Node > (Node > $o))]: ((((member @ (coinductive_llist @ Node)) @ (coinductive_LNil @ Node)) @ ((koenig916195507_paths @ Node) @ Graph))))).
% 2.71/1.46 thf(fact_103_pathsp_OLCons, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),X:Node,Y:Node,Xs3:(coinductive_llist @ Node)]: ((((Graph @ X) @ Y) => ((((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ Y) @ Xs3)) => (((koenig2031690877pathsp @ Node) @ Graph) @ (((coinductive_LCons @ Node) @ X) @ (((coinductive_LCons @ Node) @ Y) @ Xs3)))))))).
% 2.71/1.46 thf(fact_104_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coinductive_lmember @ A) @ X) @ (coinductive_LNil @ A))))))).
% 2.71/1.46 thf(fact_105_pathsp__paths__eq, axiom, (! [Node:$tType]: (((koenig2031690877pathsp @ Node) = (^ [Graph2:(Node > (Node > $o)),X5:(coinductive_llist @ Node)]: ((((member @ (coinductive_llist @ Node)) @ X5) @ ((koenig916195507_paths @ Node) @ Graph2)))))))).
% 2.71/1.46 thf(fact_106_Singleton, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A]: (((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))))))))).
% 2.71/1.46 thf(fact_107_paths_Ocoinduct, axiom, (! [Node:$tType,X6:((coinductive_llist @ Node) > $o),X:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((X6 @ X) => ((! [X2:(coinductive_llist @ Node)]: (((X6 @ X2) => ((X2 = (coinductive_LNil @ Node)) | ((? [Xa2:Node]: ((X2 = (((coinductive_LCons @ Node) @ Xa2) @ (coinductive_LNil @ Node))))) | (? [Xa2:Node,Y5:Node,Xs5:(coinductive_llist @ Node)]: (((X2 = (((coinductive_LCons @ Node) @ Xa2) @ (((coinductive_LCons @ Node) @ Y5) @ Xs5))) & (((Graph @ Xa2) @ Y5) & ((X6 @ (((coinductive_LCons @ Node) @ Y5) @ Xs5)) | (((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y5) @ Xs5)) @ ((koenig916195507_paths @ Node) @ Graph)))))))))))) => (((member @ (coinductive_llist @ Node)) @ X) @ ((koenig916195507_paths @ Node) @ Graph))))))).
% 2.71/1.46 thf(fact_108_paths_OSingle, axiom, (! [Node:$tType,X:Node,Graph:(Node > (Node > $o))]: ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ X) @ (coinductive_LNil @ Node))) @ ((koenig916195507_paths @ Node) @ Graph))))).
% 2.71/1.46 thf(fact_109_paths_Osimps, axiom, (! [Node:$tType,A2:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((((member @ (coinductive_llist @ Node)) @ A2) @ ((koenig916195507_paths @ Node) @ Graph)) = ((A2 = (coinductive_LNil @ Node)) | ((? [X5:Node]: ((A2 = (((coinductive_LCons @ Node) @ X5) @ (coinductive_LNil @ Node))))) | (? [X5:Node,Y3:Node,Xs4:(coinductive_llist @ Node)]: (((A2 = (((coinductive_LCons @ Node) @ X5) @ (((coinductive_LCons @ Node) @ Y3) @ Xs4))) & (((Graph @ X5) @ Y3) & (((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y3) @ Xs4)) @ ((koenig916195507_paths @ Node) @ Graph)))))))))))).
% 2.71/1.46 thf(fact_110_paths_Ocases, axiom, (! [Node:$tType,A2:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((((member @ (coinductive_llist @ Node)) @ A2) @ ((koenig916195507_paths @ Node) @ Graph)) => ((A2 != (coinductive_LNil @ Node)) => ((! [X2:Node]: ((A2 != (((coinductive_LCons @ Node) @ X2) @ (coinductive_LNil @ Node))))) => (~ ((! [X2:Node,Y4:Node,Xs2:(coinductive_llist @ Node)]: (((A2 = (((coinductive_LCons @ Node) @ X2) @ (((coinductive_LCons @ Node) @ Y4) @ Xs2))) => (((Graph @ X2) @ Y4) => (~ ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y4) @ Xs2)) @ ((koenig916195507_paths @ Node) @ Graph)))))))))))))))).
% 2.71/1.46 thf(fact_111_lsorted_Ocoinduct, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X6:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A)]: (((X6 @ X) => ((! [X2:(coinductive_llist @ A)]: (((X6 @ X2) => ((X2 = (coinductive_LNil @ A)) | ((? [Xa2:A]: ((X2 = (((coinductive_LCons @ A) @ Xa2) @ (coinductive_LNil @ A))))) | (? [Xa2:A,Y5:A,Xs5:(coinductive_llist @ A)]: (((X2 = (((coinductive_LCons @ A) @ Xa2) @ (((coinductive_LCons @ A) @ Y5) @ Xs5))) & ((((ord_less_eq @ A) @ Xa2) @ Y5) & ((X6 @ (((coinductive_LCons @ A) @ Y5) @ Xs5)) | ((coindu63249387sorted @ A) @ (((coinductive_LCons @ A) @ Y5) @ Xs5)))))))))))) => ((coindu63249387sorted @ A) @ X))))))))).
% 2.71/1.46 thf(fact_112_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs3) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs3 = (coinductive_LNil @ A)) | (? [Xs6:(coinductive_llist @ A)]: (((Xs3 = (((coinductive_LCons @ A) @ Y) @ Xs6)) & (((coindu328551480prefix @ A) @ Xs6) @ Ys))))))))).
% 2.71/1.46 thf(fact_113_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 2.71/1.46 thf(fact_114_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs3:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs3)) @ (coinductive_LNil @ B))))))).
% 2.71/1.46 thf(fact_115_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 2.71/1.46 thf(fact_116_ldistinct_Ocoinduct, axiom, (! [A:$tType,X6:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A)]: (((X6 @ X) => ((! [X2:(coinductive_llist @ A)]: (((X6 @ X2) => ((X2 = (coinductive_LNil @ A)) | (? [Xa2:A,Xs5:(coinductive_llist @ A)]: (((X2 = (((coinductive_LCons @ A) @ Xa2) @ Xs5)) & ((~ ((((member @ A) @ Xa2) @ ((coinductive_lset @ A) @ Xs5)))) & ((X6 @ Xs5) | ((coindu351974385stinct @ A) @ Xs5)))))))))) => ((coindu351974385stinct @ A) @ X)))))).
% 2.71/1.46 thf(fact_117_ldistinct_Osimps, axiom, (! [A:$tType]: (((coindu351974385stinct @ A) = (^ [A6:(coinductive_llist @ A)]: (((A6 = (coinductive_LNil @ A)) | (? [X5:A,Xs4:(coinductive_llist @ A)]: (((A6 = (((coinductive_LCons @ A) @ X5) @ Xs4)) & ((~ ((((member @ A) @ X5) @ ((coinductive_lset @ A) @ Xs4)))) & ((coindu351974385stinct @ A) @ Xs4)))))))))))).
% 2.71/1.46 thf(fact_118_ldistinct__LNil__code, axiom, (! [A:$tType]: (((coindu351974385stinct @ A) @ (coinductive_LNil @ A))))).
% 2.71/1.46 thf(fact_119_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs3))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs3)))))).
% 2.71/1.46 thf(fact_120_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs3:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs3)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu1478340336prefix @ B) @ Xs3) @ Ys)))))).
% 2.71/1.46 thf(fact_121_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.71/1.46 thf(fact_122_ldistinct__LCons, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: ((((coindu351974385stinct @ A) @ (((coinductive_LCons @ A) @ X) @ Xs3)) = ((~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)))) & ((coindu351974385stinct @ A) @ Xs3)))))).
% 2.71/1.46 thf(fact_123_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs3:(coinductive_llist @ A)]: (((! [Xs2:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs2) => (P @ Ys2)))) => (P @ Xs2)))) => (P @ Xs3))))).
% 2.71/1.46 thf(fact_124_ldistinct_OLNil, axiom, (! [A:$tType]: (((coindu351974385stinct @ A) @ (coinductive_LNil @ A))))).
% 2.71/1.46 thf(fact_125_ldistinct_OLCons, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: (((~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)))) => (((coindu351974385stinct @ A) @ Xs3) => ((coindu351974385stinct @ A) @ (((coinductive_LCons @ A) @ X) @ Xs3))))))).
% 2.71/1.46 thf(fact_126_lsorted__ldistinct__lset__unique, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coindu63249387sorted @ A) @ Xs3) => (((coindu351974385stinct @ A) @ Xs3) => (((coindu63249387sorted @ A) @ Ys) => (((coindu351974385stinct @ A) @ Ys) => ((((coinductive_lset @ A) @ Xs3) = ((coinductive_lset @ A) @ Ys)) => (Xs3 = Ys)))))))))))).
% 2.71/1.46 thf(fact_127_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs3) @ (coinductive_LNil @ A)) = (Xs3 = (coinductive_LNil @ A)))))).
% 2.71/1.46 thf(fact_128_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs3)))).
% 2.71/1.46 thf(fact_129_ldistinct_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A)]: ((((coindu351974385stinct @ A) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [X2:A,Xs2:(coinductive_llist @ A)]: (((A2 = (((coinductive_LCons @ A) @ X2) @ Xs2)) => ((~ ((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs2)))) => (~ (((coindu351974385stinct @ A) @ Xs2)))))))))))))).
% 2.71/1.46 thf(fact_130_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs3:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X2) @ Xs2)))))) => (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)) => (P @ Xs3))))))).
% 2.71/1.46 thf(fact_131_gen__lset__code_I1_J, axiom, (! [A:$tType,A3:(set @ A)]: (((((coinductive_gen_lset @ A) @ A3) @ (coinductive_LNil @ A)) = A3)))).
% 2.71/1.46 thf(fact_132_llist_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((coindu1259883913_llist @ C) @ A) = (^ [P2:(C > $o),G21:(C > A),Q22:(C > $o),G221:(C > (coinductive_llist @ A)),G222:(C > C),A6:C]: (((((if @ (coinductive_llist @ A)) @ (P2 @ A6)) @ (coinductive_LNil @ A)) @ (((coinductive_LCons @ A) @ (G21 @ A6)) @ ((((if @ (coinductive_llist @ A)) @ (Q22 @ A6)) @ (G221 @ A6)) @ ((((((((coindu1259883913_llist @ C) @ A) @ P2) @ G21) @ Q22) @ G221) @ G222) @ (G222 @ A6))))))))))).
% 2.71/1.46 thf(fact_133_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1441602521_llist @ A) @ B) = (^ [P2:(A > $o),G21:(A > B),G22:(A > A),A6:A]: (((((if @ (coinductive_llist @ B)) @ (P2 @ A6)) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ (G21 @ A6)) @ ((((((coindu1441602521_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A6)))))))))).
% 2.71/1.46 thf(fact_134_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs3:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs3)) = ((coinductive_lfinite @ B) @ Xs3))))).
% 2.71/1.46 thf(fact_135_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs3)) = ((coinductive_lfinite @ A) @ Xs3))))).
% 2.71/1.46 thf(fact_136_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.71/1.46 thf(fact_137_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B3:B,X:A,Xs3:(coinductive_llist @ A)]: (((((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B3) = (((coinductive_LCons @ A) @ X) @ Xs3)) = ((~ ((IS_LNIL @ B3))) & ((X = (LHD @ B3)) & (Xs3 = ((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B3))))))))).
% 2.71/1.46 thf(fact_138_lfinite__LConsI, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs3) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs3)))))).
% 2.71/1.46 thf(fact_139_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.71/1.46 thf(fact_140_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs3) @ Ys) => ((coinductive_lfinite @ A) @ Xs3))))).
% 2.71/1.46 thf(fact_141_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((~ ((P3 @ A2))) => (((((((coindu1441602521_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2) = (((coinductive_LCons @ B) @ (G212 @ A2)) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G212) @ G223) @ (G223 @ A2)))))))).
% 2.71/1.46 thf(fact_142_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P3:(A > $o),A2:A,G212:(A > B),G223:(A > A)]: (((P3 @ A2) => (((((((coindu1441602521_llist @ A) @ B) @ P3) @ G212) @ G223) @ A2) = (coinductive_LNil @ B)))))).
% 2.71/1.46 thf(fact_143_llist_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coinductive_llist @ A)),G2222:(C > C)]: (((~ ((P3 @ A2))) => (((((((((coindu1259883913_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = (((coinductive_LCons @ A) @ (G212 @ A2)) @ ((((if @ (coinductive_llist @ A)) @ (Q222 @ A2)) @ (G2212 @ A2)) @ ((((((((coindu1259883913_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ (G2222 @ A2))))))))).
% 2.71/1.46 thf(fact_144_llist_Ocorec_I1_J, axiom, (! [C:$tType,A:$tType,P3:(C > $o),A2:C,G212:(C > A),Q222:(C > $o),G2212:(C > (coinductive_llist @ A)),G2222:(C > C)]: (((P3 @ A2) => (((((((((coindu1259883913_llist @ C) @ A) @ P3) @ G212) @ Q222) @ G2212) @ G2222) @ A2) = (coinductive_LNil @ A)))))).
% 2.71/1.46 thf(fact_145_lfinite_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [Xs2:(coinductive_llist @ A),X2:A]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X2) @ Xs2)))))) => (P @ X))))))).
% 2.71/1.46 thf(fact_146_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A6:(coinductive_llist @ A)]: (((A6 = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A),X5:A]: (((A6 = (((coinductive_LCons @ A) @ X5) @ Xs4)) & ((coinductive_lfinite @ A) @ Xs4))))))))))).
% 2.71/1.46 thf(fact_147_lfinite_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [Xs2:(coinductive_llist @ A)]: (((? [X2:A]: ((A2 = (((coinductive_LCons @ A) @ X2) @ Xs2)))) => (~ (((coinductive_lfinite @ A) @ Xs2))))))))))))).
% 2.71/1.46 thf(fact_148_llast__lappend__LCons, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ Y) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Ys))))))).
% 2.71/1.46 thf(fact_149_split__llist, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => (? [Ys3:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((Xs3 = (((coinductive_lappend @ A) @ Ys3) @ (((coinductive_LCons @ A) @ X) @ Zs))) & ((coinductive_lfinite @ A) @ Ys3)))))))).
% 2.71/1.46 thf(fact_150_split__llist__first, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) => (? [Ys3:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((Xs3 = (((coinductive_lappend @ A) @ Ys3) @ (((coinductive_LCons @ A) @ X) @ Zs))) & (((coinductive_lfinite @ A) @ Ys3) & (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys3)))))))))))).
% 2.71/1.46 thf(fact_151_lfinite__rev__induct, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs3) => ((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_lappend @ A) @ Xs2) @ (((coinductive_LCons @ A) @ X2) @ (coinductive_LNil @ A)))))))) => (P @ Xs3))))))).
% 2.71/1.46 thf(fact_152_lappend__code_I2_J, axiom, (! [A:$tType,Xa3:A,X:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa3) @ X)) @ Ys) = (((coinductive_LCons @ A) @ Xa3) @ (((coinductive_lappend @ A) @ X) @ Ys)))))).
% 2.71/1.46 thf(fact_153_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.71/1.46 thf(fact_154_lappend__LNil2, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs3) @ (coinductive_LNil @ A)) = Xs3)))).
% 2.71/1.46 thf(fact_155_lfinite__lappend, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) = (((coinductive_lfinite @ A) @ Xs3) & ((coinductive_lfinite @ A) @ Ys)))))).
% 2.71/1.46 thf(fact_156_lappend__inf, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs3))) => ((((coinductive_lappend @ A) @ Xs3) @ Ys) = Xs3))))).
% 2.71/1.46 thf(fact_157_lappend__assoc, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) @ Zs2) = (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_lappend @ A) @ Ys) @ Zs2)))))).
% 2.71/1.46 thf(fact_158_paths__lappendD1, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Graph:(A > (A > $o))]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) @ ((koenig916195507_paths @ A) @ Graph)) => (((member @ (coinductive_llist @ A)) @ Xs3) @ ((koenig916195507_paths @ A) @ Graph)))))).
% 2.71/1.46 thf(fact_159_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.71/1.46 thf(fact_160_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs3) @ Ys)) = ((Xs3 = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.71/1.46 thf(fact_161_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs3) @ Ys) = (coinductive_LNil @ A)) = ((Xs3 = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.71/1.46 thf(fact_162_lset__lappend1, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((ord_less_eq @ (set @ A)) @ ((coinductive_lset @ A) @ Xs3)) @ ((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)))))).
% 2.71/1.46 thf(fact_163_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.71/1.46 thf(fact_164_in__lset__lappend__iff, axiom, (! [A:$tType,X:A,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys))) = ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs3)) | (((coinductive_lfinite @ A) @ Xs3) & (((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys)))))))).
% 2.71/1.46 thf(fact_165_paths__lappendD2, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Graph:(A > (A > $o))]: ((((coinductive_lfinite @ A) @ Xs3) => ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) @ ((koenig916195507_paths @ A) @ Graph)) => (((member @ (coinductive_llist @ A)) @ Ys) @ ((koenig916195507_paths @ A) @ Graph))))))).
% 2.71/1.46 thf(fact_166_lfilter__eq__LConsD, axiom, (! [A:$tType,P:(A > $o),Ys:(coinductive_llist @ A),X:A,Xs3:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Ys) = (((coinductive_LCons @ A) @ X) @ Xs3)) => (? [Us:(coinductive_llist @ A),Vs:(coinductive_llist @ A)]: (((Ys = (((coinductive_lappend @ A) @ Us) @ (((coinductive_LCons @ A) @ X) @ Vs))) & (((coinductive_lfinite @ A) @ Us) & ((! [X7:A]: (((((member @ A) @ X7) @ ((coinductive_lset @ A) @ Us)) => (~ ((P @ X7)))))) & ((P @ X) & (Xs3 = (((coinductive_lfilter @ A) @ P) @ Vs)))))))))))).
% 2.71/1.46 thf(fact_167_lset__lappend__lfinite, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs3)) @ ((coinductive_lset @ A) @ Ys))))))).
% 2.71/1.46 thf(fact_168_llexord__lappend__leftD, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) @ (((coinductive_lappend @ A) @ Xs3) @ Zs2)) => (((coinductive_lfinite @ A) @ Xs3) => ((! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs3)) => (~ (((R @ X2) @ X2)))))) => ((((coinductive_llexord @ A) @ R) @ Ys) @ Zs2))))))).
% 2.71/1.46 thf(fact_169_UnCI, axiom, (! [A:$tType,C2:A,B2:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B2))) => (((member @ A) @ C2) @ A3)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 2.71/1.46 thf(fact_170_Un__iff, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) = ((((member @ A) @ C2) @ A3) | (((member @ A) @ C2) @ B2)))))).
% 2.71/1.46 thf(fact_171_lfilter__idem, axiom, (! [A:$tType,P:(A > $o),Xs3:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ P) @ (((coinductive_lfilter @ A) @ P) @ Xs3)) = (((coinductive_lfilter @ A) @ P) @ Xs3))))).
% 2.71/1.46 thf(fact_172_llexord__refl, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ Xs3) @ Xs3)))).
% 2.71/1.46 thf(fact_173_Un__subset__iff, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) @ C3) = ((((ord_less_eq @ (set @ A)) @ A3) @ C3) & (((ord_less_eq @ (set @ A)) @ B2) @ C3)))))).
% 2.71/1.46 thf(fact_174_lfilter__LCons, axiom, (! [A:$tType,P:(A > $o),X:A,Xs3:(coinductive_llist @ A)]: ((((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs3)) = (((coinductive_LCons @ A) @ X) @ (((coinductive_lfilter @ A) @ P) @ Xs3)))) & ((~ ((P @ X))) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs3)) = (((coinductive_lfilter @ A) @ P) @ Xs3))))))).
% 2.71/1.46 thf(fact_175_lfilter__LNil, axiom, (! [A:$tType,P:(A > $o)]: (((((coinductive_lfilter @ A) @ P) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.71/1.46 thf(fact_176_llexord__LCons__LCons, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs3:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((X = Y) & ((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys)) | ((R @ X) @ Y)))))).
% 2.71/1.46 thf(fact_177_llexord__code_I1_J, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ (coinductive_LNil @ A)) @ Ys)))).
% 2.71/1.46 thf(fact_178_diverge__lfilter__LNil, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs3)) => (~ ((P @ X2)))))) => ((((coinductive_lfilter @ A) @ P) @ Xs3) = (coinductive_LNil @ A)))))).
% 2.71/1.46 thf(fact_179_lfilter__lappend__lfinite, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),P:(A > $o),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) = (((coinductive_lappend @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs3)) @ (((coinductive_lfilter @ A) @ P) @ Ys))))))).
% 2.71/1.46 thf(fact_180_llexord__lappend__leftI, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A),Xs3:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ Ys) @ Zs2) => ((((coinductive_llexord @ A) @ R) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) @ (((coinductive_lappend @ A) @ Xs3) @ Zs2)))))).
% 2.71/1.46 thf(fact_181_llexord__append__right, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ Xs3) @ (((coinductive_lappend @ A) @ Xs3) @ Ys))))).
% 2.71/1.46 thf(fact_182_ldistinct__lfilterI, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),P:(A > $o)]: ((((coindu351974385stinct @ A) @ Xs3) => ((coindu351974385stinct @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs3)))))).
% 2.71/1.46 thf(fact_183_lfilter__LCons__seek, axiom, (! [A:$tType,P3:(A > $o),X:A,L:(coinductive_llist @ A)]: (((~ ((P3 @ X))) => ((((coinductive_lfilter @ A) @ P3) @ (((coinductive_LCons @ A) @ X) @ L)) = (((coinductive_lfilter @ A) @ P3) @ L)))))).
% 2.71/1.46 thf(fact_184_lfilter__LCons__found, axiom, (! [A:$tType,P:(A > $o),X:A,Xs3:(coinductive_llist @ A)]: (((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs3)) = (((coinductive_LCons @ A) @ X) @ (((coinductive_lfilter @ A) @ P) @ Xs3))))))).
% 2.71/1.46 thf(fact_185_lfilter__cong, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),P:(A > $o),Q:(A > $o)]: (((Xs3 = Ys) => ((! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Ys)) => ((P @ X2) = (Q @ X2))))) => ((((coinductive_lfilter @ A) @ P) @ Xs3) = (((coinductive_lfilter @ A) @ Q) @ Ys))))))).
% 2.71/1.46 thf(fact_186_lfilter__id__conv, axiom, (! [A:$tType,P:(A > $o),Xs3:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs3) = Xs3) = (! [X5:A]: (((((member @ A) @ X5) @ ((coinductive_lset @ A) @ Xs3)) => (P @ X5)))))))).
% 2.71/1.46 thf(fact_187_Un__mono, axiom, (! [A:$tType,A3:(set @ A),C3:(set @ A),B2:(set @ A),D:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C3) => ((((ord_less_eq @ (set @ A)) @ B2) @ D) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) @ (((sup_sup @ (set @ A)) @ C3) @ D))))))).
% 2.71/1.46 thf(fact_188_Un__least, axiom, (! [A:$tType,A3:(set @ A),C3:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C3) => ((((ord_less_eq @ (set @ A)) @ B2) @ C3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) @ C3)))))).
% 2.71/1.46 thf(fact_189_Un__upper1, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B2))))).
% 2.71/1.46 thf(fact_190_Un__upper2, axiom, (! [A:$tType,B2:(set @ A),A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A3) @ B2))))).
% 2.71/1.46 thf(fact_191_Un__absorb1, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B2) => ((((sup_sup @ (set @ A)) @ A3) @ B2) = B2))))).
% 2.71/1.46 thf(fact_192_Un__absorb2, axiom, (! [A:$tType,B2:(set @ A),A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A3) => ((((sup_sup @ (set @ A)) @ A3) @ B2) = A3))))).
% 2.71/1.46 thf(fact_193_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ B5) = B5))))))).
% 2.71/1.46 thf(fact_194_lsorted__lfilterI, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [Xs3:(coinductive_llist @ A),P:(A > $o)]: ((((coindu63249387sorted @ A) @ Xs3) => ((coindu63249387sorted @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs3))))))))).
% 2.71/1.46 thf(fact_195_llexord__code_I3_J, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs3:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((R @ X) @ Y) | ((X = Y) & ((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys))))))).
% 2.71/1.46 thf(fact_196_llexord__LCons__left, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ Ys) = (? [Y3:A,Ys4:(coinductive_llist @ A)]: (((Ys = (((coinductive_LCons @ A) @ Y3) @ Ys4)) & (((X = Y3) & ((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys4)) | ((R @ X) @ Y3))))))))).
% 2.71/1.46 thf(fact_197_llexord__LCons__eq, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),X:A]: ((((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys) => ((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ (((coinductive_LCons @ A) @ X) @ Ys)))))).
% 2.71/1.46 thf(fact_198_llexord__LCons__less, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Y:A,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((R @ X) @ Y) => ((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.71/1.46 thf(fact_199_llexord__LNil, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R) @ (coinductive_LNil @ A)) @ Ys)))).
% 2.71/1.46 thf(fact_200_UnE, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => ((~ ((((member @ A) @ C2) @ A3))) => (((member @ A) @ C2) @ B2)))))).
% 2.71/1.46 thf(fact_201_UnI1, axiom, (! [A:$tType,C2:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C2) @ A3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 2.71/1.46 thf(fact_202_UnI2, axiom, (! [A:$tType,C2:A,B2:(set @ A),A3:(set @ A)]: (((((member @ A) @ C2) @ B2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 2.71/1.46 thf(fact_203_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X5:A]: (((((member @ A) @ X5) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) & (P @ X5)))) = ((? [X5:A]: (((((member @ A) @ X5) @ A3) & (P @ X5)))) | (? [X5:A]: (((((member @ A) @ X5) @ B2) & (P @ X5))))))))).
% 2.71/1.46 thf(fact_204_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X5:A]: (((((member @ A) @ X5) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => (P @ X5)))) = ((! [X5:A]: (((((member @ A) @ X5) @ A3) => (P @ X5)))) & (! [X5:A]: (((((member @ A) @ X5) @ B2) => (P @ X5))))))))).
% 2.71/1.46 thf(fact_205_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) @ C3) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C3)))))).
% 2.71/1.46 thf(fact_206_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 2.71/1.46 thf(fact_207_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A5))))))).
% 2.71/1.46 thf(fact_208_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) = (((sup_sup @ (set @ A)) @ A3) @ B2))))).
% 2.71/1.46 thf(fact_209_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C3)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A3) @ C3)))))).
% 2.71/1.46 thf(fact_210_llexord__trans, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys) => (((((coinductive_llexord @ A) @ R) @ Ys) @ Zs2) => ((! [A4:A,B4:A,C4:A]: ((((R @ A4) @ B4) => (((R @ B4) @ C4) => ((R @ A4) @ C4))))) => ((((coinductive_llexord @ A) @ R) @ Xs3) @ Zs2))))))).
% 2.71/1.46 thf(fact_211_llexord__linear, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((! [X2:A,Y4:A]: ((((R @ X2) @ Y4) | ((X2 = Y4) | ((R @ Y4) @ X2))))) => (((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys) | ((((coinductive_llexord @ A) @ R) @ Ys) @ Xs3)))))).
% 2.71/1.46 thf(fact_212_llexord__antisym, axiom, (! [A:$tType,R:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ Xs3) @ Ys) => (((((coinductive_llexord @ A) @ R) @ Ys) @ Xs3) => ((! [A4:A,B4:A]: ((((R @ A4) @ B4) => (~ (((R @ B4) @ A4)))))) => (Xs3 = Ys))))))).
% 2.71/1.46 thf(fact_213_lfinite__lfilterI, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),P:(A > $o)]: ((((coinductive_lfinite @ A) @ Xs3) => ((coinductive_lfinite @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs3)))))).
% 2.71/1.46 thf(fact_214_lfilter__empty__conv, axiom, (! [A:$tType,P:(A > $o),Xs3:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs3) = (coinductive_LNil @ A)) = (! [X5:A]: (((((member @ A) @ X5) @ ((coinductive_lset @ A) @ Xs3)) => (~ ((P @ X5)))))))))).
% 2.71/1.46 thf(fact_215_lfilter__eq__lappend__lfiniteD, axiom, (! [A:$tType,P:(A > $o),Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs3) = (((coinductive_lappend @ A) @ Ys) @ Zs2)) => (((coinductive_lfinite @ A) @ Ys) => (? [Us:(coinductive_llist @ A),Vs:(coinductive_llist @ A)]: (((Xs3 = (((coinductive_lappend @ A) @ Us) @ Vs)) & (((coinductive_lfinite @ A) @ Us) & ((Ys = (((coinductive_lfilter @ A) @ P) @ Us)) & (Zs2 = (((coinductive_lfilter @ A) @ P) @ Vs)))))))))))).
% 2.71/1.46 thf(fact_216_llexord_Ocoinduct, axiom, (! [A:$tType,X6:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),X:(coinductive_llist @ A),Xa3:(coinductive_llist @ A),R:(A > (A > $o))]: ((((X6 @ X) @ Xa3) => ((! [X2:(coinductive_llist @ A),Xa:(coinductive_llist @ A)]: ((((X6 @ X2) @ Xa) => ((? [Xs5:(coinductive_llist @ A),Ys2:(coinductive_llist @ A),Xb:A]: (((X2 = (((coinductive_LCons @ A) @ Xb) @ Xs5)) & ((Xa = (((coinductive_LCons @ A) @ Xb) @ Ys2)) & (((X6 @ Xs5) @ Ys2) | ((((coinductive_llexord @ A) @ R) @ Xs5) @ Ys2)))))) | ((? [Xb:A,Y5:A,Xs5:(coinductive_llist @ A),Ys2:(coinductive_llist @ A)]: (((X2 = (((coinductive_LCons @ A) @ Xb) @ Xs5)) & ((Xa = (((coinductive_LCons @ A) @ Y5) @ Ys2)) & ((R @ Xb) @ Y5))))) | (? [Ys2:(coinductive_llist @ A)]: (((X2 = (coinductive_LNil @ A)) & (Xa = Ys2))))))))) => ((((coinductive_llexord @ A) @ R) @ X) @ Xa3)))))).
% 2.71/1.46 thf(fact_217_llexord_Osimps, axiom, (! [A:$tType]: (((coinductive_llexord @ A) = (^ [R2:(A > (A > $o)),A12:(coinductive_llist @ A),A23:(coinductive_llist @ A)]: (((? [Xs4:(coinductive_llist @ A),Ys5:(coinductive_llist @ A),X5:A]: (((A12 = (((coinductive_LCons @ A) @ X5) @ Xs4)) & ((A23 = (((coinductive_LCons @ A) @ X5) @ Ys5)) & ((((coinductive_llexord @ A) @ R2) @ Xs4) @ Ys5))))) | ((? [X5:A,Y3:A,Xs4:(coinductive_llist @ A),Ys5:(coinductive_llist @ A)]: (((A12 = (((coinductive_LCons @ A) @ X5) @ Xs4)) & ((A23 = (((coinductive_LCons @ A) @ Y3) @ Ys5)) & ((R2 @ X5) @ Y3))))) | (? [Ys5:(coinductive_llist @ A)]: (((A12 = (coinductive_LNil @ A)) & (A23 = Ys5)))))))))))).
% 2.71/1.46 thf(fact_218_llexord_Ocases, axiom, (! [A:$tType,R:(A > (A > $o)),A1:(coinductive_llist @ A),A22:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R) @ A1) @ A22) => ((! [Xs2:(coinductive_llist @ A),Ys3:(coinductive_llist @ A),X2:A]: (((A1 = (((coinductive_LCons @ A) @ X2) @ Xs2)) => ((A22 = (((coinductive_LCons @ A) @ X2) @ Ys3)) => (~ (((((coinductive_llexord @ A) @ R) @ Xs2) @ Ys3))))))) => ((! [X2:A]: (((? [Xs2:(coinductive_llist @ A)]: ((A1 = (((coinductive_LCons @ A) @ X2) @ Xs2)))) => (! [Y4:A]: (((? [Ys3:(coinductive_llist @ A)]: ((A22 = (((coinductive_LCons @ A) @ Y4) @ Ys3)))) => (~ (((R @ X2) @ Y4))))))))) => (~ (((A1 = (coinductive_LNil @ A)) => (! [Ys3:(coinductive_llist @ A)]: ((A22 != Ys3)))))))))))).
% 2.71/1.46 thf(fact_219_llexord__code_I2_J, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs3:(coinductive_llist @ A)]: ((~ (((((coinductive_llexord @ A) @ R) @ (((coinductive_LCons @ A) @ X) @ Xs3)) @ (coinductive_LNil @ A))))))).
% 2.71/1.46 thf(fact_220_gen__lset__def, axiom, (! [A:$tType]: (((coinductive_gen_lset @ A) = (^ [A5:(set @ A),Xs4:(coinductive_llist @ A)]: ((((sup_sup @ (set @ A)) @ A5) @ ((coinductive_lset @ A) @ Xs4)))))))).
% 2.71/1.46 thf(fact_221_lset__lappend, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((ord_less_eq @ (set @ A)) @ ((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys))) @ (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs3)) @ ((coinductive_lset @ A) @ Ys)))))).
% 2.71/1.46 thf(fact_222_lset__lappend__conv, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lfinite @ A) @ Xs3) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs3)) @ ((coinductive_lset @ A) @ Ys)))) & ((~ (((coinductive_lfinite @ A) @ Xs3))) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) = ((coinductive_lset @ A) @ Xs3))))))).
% 2.71/1.46 thf(fact_223_llexord__lappend__left, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),R:(A > (A > $o)),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs3) => ((! [X2:A]: (((((member @ A) @ X2) @ ((coinductive_lset @ A) @ Xs3)) => (~ (((R @ X2) @ X2)))))) => (((((coinductive_llexord @ A) @ R) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) @ (((coinductive_lappend @ A) @ Xs3) @ Zs2)) = ((((coinductive_llexord @ A) @ R) @ Ys) @ Zs2))))))).
% 2.71/1.46 thf(fact_224_le__sup__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = ((((ord_less_eq @ A) @ X) @ Z) & (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 2.71/1.46 thf(fact_225_sup_Obounded__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C2)) @ A2) = ((((ord_less_eq @ A) @ B3) @ A2) & (((ord_less_eq @ A) @ C2) @ A2))))))))).
% 2.71/1.46 thf(fact_226_sup_OcoboundedI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,B3:A,A2:A]: (((((ord_less_eq @ A) @ C2) @ B3) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_227_inf__sup__ord_I4_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.71/1.46 thf(fact_228_inf__sup__ord_I3_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.71/1.46 thf(fact_229_le__supE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A,X:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ X) => (~ (((((ord_less_eq @ A) @ A2) @ X) => (~ ((((ord_less_eq @ A) @ B3) @ X))))))))))))).
% 2.71/1.46 thf(fact_230_le__supI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,X:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ X) => ((((ord_less_eq @ A) @ B3) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ X))))))))).
% 2.71/1.46 thf(fact_231_sup__ge1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.71/1.46 thf(fact_232_sup__ge2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A]: ((((ord_less_eq @ A) @ Y) @ (((sup_sup @ A) @ X) @ Y)))))))).
% 2.71/1.46 thf(fact_233_le__supI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,A2:A,B3:A]: (((((ord_less_eq @ A) @ X) @ A2) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_234_le__supI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,B3:A,A2:A]: (((((ord_less_eq @ A) @ X) @ B3) => (((ord_less_eq @ A) @ X) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_235_sup_Omono, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,A2:A,D2:A,B3:A]: (((((ord_less_eq @ A) @ C2) @ A2) => ((((ord_less_eq @ A) @ D2) @ B3) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ C2) @ D2)) @ (((sup_sup @ A) @ A2) @ B3)))))))))).
% 2.71/1.46 thf(fact_236_sup__mono, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,C2:A,B3:A,D2:A]: (((((ord_less_eq @ A) @ A2) @ C2) => ((((ord_less_eq @ A) @ B3) @ D2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ A2) @ B3)) @ (((sup_sup @ A) @ C2) @ D2)))))))))).
% 2.71/1.46 thf(fact_237_sup__least, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A,Z:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ Z) @ X) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ Y) @ Z)) @ X))))))))).
% 2.71/1.46 thf(fact_238_le__iff__sup, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X5:A,Y3:A]: (((((sup_sup @ A) @ X5) @ Y3) = Y3)))))))).
% 2.71/1.46 thf(fact_239_sup_OorderE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => (A2 = (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_240_sup_OorderI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((A2 = (((sup_sup @ A) @ A2) @ B3)) => (((ord_less_eq @ A) @ B3) @ A2)))))))).
% 2.71/1.46 thf(fact_241_sup__unique, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [F:(A > (A > A)),X:A,Y:A]: (((! [X2:A,Y4:A]: ((((ord_less_eq @ A) @ X2) @ ((F @ X2) @ Y4)))) => ((! [X2:A,Y4:A]: ((((ord_less_eq @ A) @ Y4) @ ((F @ X2) @ Y4)))) => ((! [X2:A,Y4:A,Z3:A]: (((((ord_less_eq @ A) @ Y4) @ X2) => ((((ord_less_eq @ A) @ Z3) @ X2) => (((ord_less_eq @ A) @ ((F @ Y4) @ Z3)) @ X2))))) => ((((sup_sup @ A) @ X) @ Y) = ((F @ X) @ Y))))))))))).
% 2.71/1.46 thf(fact_242_sup_Oabsorb1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((sup_sup @ A) @ A2) @ B3) = A2)))))))).
% 2.71/1.46 thf(fact_243_sup_Oabsorb2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: (((((ord_less_eq @ A) @ A2) @ B3) => ((((sup_sup @ A) @ A2) @ B3) = B3)))))))).
% 2.71/1.46 thf(fact_244_sup__absorb1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((sup_sup @ A) @ X) @ Y) = X)))))))).
% 2.71/1.46 thf(fact_245_sup__absorb2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((sup_sup @ A) @ X) @ Y) = Y)))))))).
% 2.71/1.46 thf(fact_246_sup_OboundedE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,C2:A,A2:A]: (((((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C2)) @ A2) => (~ (((((ord_less_eq @ A) @ B3) @ A2) => (~ ((((ord_less_eq @ A) @ C2) @ A2))))))))))))).
% 2.71/1.46 thf(fact_247_sup_OboundedI, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,A2:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A2) => ((((ord_less_eq @ A) @ C2) @ A2) => (((ord_less_eq @ A) @ (((sup_sup @ A) @ B3) @ C2)) @ A2))))))))).
% 2.71/1.46 thf(fact_248_sup_Oorder__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B6:A,A6:A]: ((A6 = (((sup_sup @ A) @ A6) @ B6))))))))).
% 2.71/1.46 thf(fact_249_sup_Ocobounded1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A2:A,B3:A]: ((((ord_less_eq @ A) @ A2) @ (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.71/1.46 thf(fact_250_sup_Ocobounded2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,A2:A]: ((((ord_less_eq @ A) @ B3) @ (((sup_sup @ A) @ A2) @ B3)))))))).
% 2.71/1.46 thf(fact_251_sup_Oabsorb__iff1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B6:A,A6:A]: (((((sup_sup @ A) @ A6) @ B6) = A6)))))))).
% 2.71/1.46 thf(fact_252_sup_Oabsorb__iff2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A6:A,B6:A]: (((((sup_sup @ A) @ A6) @ B6) = B6)))))))).
% 2.71/1.46 thf(fact_253_sup_OcoboundedI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,A2:A,B3:A]: (((((ord_less_eq @ A) @ C2) @ A2) => (((ord_less_eq @ A) @ C2) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 2.71/1.46 thf(fact_254_llexord__conv, axiom, (! [A:$tType]: (((coinductive_llexord @ A) = (^ [R2:(A > (A > $o)),Xs4:(coinductive_llist @ A),Ys5:(coinductive_llist @ A)]: (((Xs4 = Ys5) | (? [Zs3:(coinductive_llist @ A),Xs6:(coinductive_llist @ A),Y3:A,Ys4:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Zs3) & ((Xs4 = (((coinductive_lappend @ A) @ Zs3) @ Xs6)) & ((Ys5 = (((coinductive_lappend @ A) @ Zs3) @ (((coinductive_LCons @ A) @ Y3) @ Ys4))) & ((Xs6 = (coinductive_LNil @ A)) | ((R2 @ ((coinductive_lhd @ A) @ Xs6)) @ Y3)))))))))))))).
% 2.71/1.46 thf(fact_255_lstrict__prefix__lappend__conv, axiom, (! [A:$tType,Xs3:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs3) @ (((coinductive_lappend @ A) @ Xs3) @ Ys)) = (((coinductive_lfinite @ A) @ Xs3) & (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.71/1.46 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A7:$tType,A8:$tType]: ((((comple187826305attice @ A8) @ (type2 @ A8)) => ((comple187826305attice @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.46 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A7:$tType,A8:$tType]: ((((semilattice_sup @ A8) @ (type2 @ A8)) => ((semilattice_sup @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.46 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A8) @ (type2 @ A8)) => ((preorder @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.46 thf(tcon_fun___Lattices_Olattice, axiom, (! [A7:$tType,A8:$tType]: ((((lattice @ A8) @ (type2 @ A8)) => ((lattice @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.46 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.46 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.46 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1, axiom, (! [A7:$tType]: (((comple187826305attice @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_2, axiom, (! [A7:$tType]: (((semilattice_sup @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.46 thf(tcon_Set_Oset___Orderings_Opreorder_3, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.46 thf(tcon_Set_Oset___Lattices_Olattice_4, axiom, (! [A7:$tType]: (((lattice @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.46 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.46 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.46 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7, axiom, ((comple187826305attice @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_8, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(tcon_HOL_Obool___Orderings_Opreorder_9, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(tcon_HOL_Obool___Lattices_Olattice_10, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(tcon_HOL_Obool___Orderings_Oorder_11, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(tcon_HOL_Obool___Orderings_Oord_12, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.71/1.46 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.71/1.46 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.71/1.46 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.71/1.46 thf(conj_0, conjecture, (((member @ a) @ n2) @ ns)).
% 2.71/1.46 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2DTF21052.p
% 2.71/1.46 ------------------------
% 2.71/1.49 ---- Cleaned THF ---
% 2.71/1.49 thf(ty_t_Coinductive__List_Ollist,type,
% 2.71/1.49 coinductive_llist: $tType > $tType ).
% 2.71/1.49
% 2.71/1.49 thf(ty_t_Set_Oset,type,
% 2.71/1.49 set: $tType > $tType ).
% 2.71/1.49
% 2.71/1.49 thf(ty_t_itself,type,
% 2.71/1.49 itself: $tType > $tType ).
% 2.71/1.49
% 2.71/1.49 thf(ty_tf_a,type,
% 2.71/1.49 a: $tType ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_HOL_Otype,type,
% 2.71/1.49 type:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Orderings_Oord,type,
% 2.71/1.49 ord:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Orderings_Oorder,type,
% 2.71/1.49 order:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Lattices_Olattice,type,
% 2.71/1.49 lattice:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Orderings_Olinorder,type,
% 2.71/1.49 linorder:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Orderings_Opreorder,type,
% 2.71/1.49 preorder:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.71/1.49 semilattice_sup:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 2.71/1.49 comple187826305attice:
% 2.71/1.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.71/1.49 coindu328551480prefix:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 2.71/1.49 coinductive_gen_lset:
% 2.71/1.49 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Olappend,type,
% 2.71/1.49 coinductive_lappend:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Oldistinct,type,
% 2.71/1.49 coindu351974385stinct:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Olfilter,type,
% 2.71/1.49 coinductive_lfilter:
% 2.71/1.49 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.71/1.49 coinductive_lfinite:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollast,type,
% 2.71/1.49 coinductive_llast:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollexord,type,
% 2.71/1.49 coinductive_llexord:
% 2.71/1.49 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.71/1.49 coinductive_LCons:
% 2.71/1.49 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.71/1.49 coinductive_LNil:
% 2.71/1.49 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollist_Ocorec__llist,type,
% 2.71/1.49 coindu1259883913_llist:
% 2.71/1.49 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 2.71/1.49 coinductive_lhd:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 2.71/1.49 coinductive_lnull:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 2.71/1.49 coinductive_lset:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Olmember,type,
% 2.71/1.49 coinductive_lmember:
% 2.71/1.49 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.71/1.49 coindu1478340336prefix:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Oord__class_Olsorted,type,
% 2.71/1.49 coindu63249387sorted:
% 2.71/1.49 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Coinductive__List_Ounfold__llist,type,
% 2.71/1.49 coindu1441602521_llist:
% 2.71/1.49 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coinductive_llist @ B ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_If,type,
% 2.71/1.49 if:
% 2.71/1.49 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opaths,type,
% 2.71/1.49 koenig916195507_paths:
% 2.71/1.49 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ ( coinductive_llist @ Node ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opathsp,type,
% 2.71/1.49 koenig2031690877pathsp:
% 2.71/1.49 !>[Node: $tType] : ( ( Node > Node > $o ) > ( coinductive_llist @ Node ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oreachable__via,type,
% 2.71/1.49 koenig317145564le_via:
% 2.71/1.49 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ Node ) > Node > ( set @ Node ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oreachable__viap,type,
% 2.71/1.49 koenig1757754772e_viap:
% 2.71/1.49 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ Node ) > Node > Node > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.71/1.49 sup_sup:
% 2.71/1.49 !>[A: $tType] : ( A > A > A ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.71/1.49 ord_less_eq:
% 2.71/1.49 !>[A: $tType] : ( A > A > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Pure_Otype,type,
% 2.71/1.49 type2:
% 2.71/1.49 !>[A: $tType] : ( itself @ A ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_Set_OCollect,type,
% 2.71/1.49 collect:
% 2.71/1.49 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_c_member,type,
% 2.71/1.49 member:
% 2.71/1.49 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_graph,type,
% 2.71/1.49 graph: a > a > $o ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_n,type,
% 2.71/1.49 n: a ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_n_H____,type,
% 2.71/1.49 n2: a ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_ns,type,
% 2.71/1.49 ns: set @ a ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_x____,type,
% 2.71/1.49 x: a ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_xs_H____,type,
% 2.71/1.49 xs: coinductive_llist @ a ).
% 2.71/1.49
% 2.71/1.49 thf(sy_v_xs____,type,
% 2.71/1.49 xs2: coinductive_llist @ a ).
% 2.71/1.49
% 2.71/1.49 thf(fact_0__092_060open_062x_A_092_060in_062_Alset_Axs_092_060close_062,axiom,
% 2.71/1.49 member @ a @ x @ ( coinductive_lset @ a @ xs2 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.71/1.49 ~ ! [N: a,Xs: coinductive_llist @ a] :
% 2.71/1.49 ( xs2
% 2.71/1.49 != ( coinductive_LCons @ a @ N @ Xs ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_2_xs,axiom,
% 2.71/1.49 ( xs2
% 2.71/1.49 = ( coinductive_LCons @ a @ n2 @ xs ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_3__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062,axiom,
% 2.71/1.49 ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ xs2 ) @ ns ).
% 2.71/1.49
% 2.71/1.49 thf(fact_4_calculation,axiom,
% 2.71/1.49 graph @ n @ n2 ).
% 2.71/1.49
% 2.71/1.49 thf(fact_5__092_060open_062x_A_092_060in_062_Areachable__via_Agraph_Ans_An_092_060close_062,axiom,
% 2.71/1.49 member @ a @ x @ ( koenig317145564le_via @ a @ graph @ ns @ n ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_O_A_092_060lbrakk_062LCons_An_Axs_A_092_060in_062_Apaths_Agraph_059_Ax_A_092_060in_062_Alset_Axs_059_Alset_Axs_A_092_060subseteq_062_Ans_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.71/1.49 ~ ! [Xs2: coinductive_llist @ a] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ Xs2 ) @ ( koenig916195507_paths @ a @ graph ) )
% 2.71/1.49 => ( ( member @ a @ x @ ( coinductive_lset @ a @ Xs2 ) )
% 2.71/1.49 => ~ ( ord_less_eq @ ( set @ a ) @ ( coinductive_lset @ a @ Xs2 ) @ ns ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_7_path,axiom,
% 2.71/1.49 member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs2 ) @ ( koenig916195507_paths @ a @ graph ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_8_paths_OLCons,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,X: Node,Y: Node,Xs3: coinductive_llist @ Node] :
% 2.71/1.49 ( ( Graph @ X @ Y )
% 2.71/1.49 => ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y @ Xs3 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 => ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LCons @ Node @ Y @ Xs3 ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_9_paths__LConsD,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,Graph: A > A > $o] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.71/1.49 => ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_10_path__avoid__node,axiom,
% 2.71/1.49 ! [A: $tType,N2: A,Xs3: coinductive_llist @ A,Graph: A > A > $o,X: A] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ N2 @ Xs3 ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.71/1.49 => ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( ( N2 != X )
% 2.71/1.49 => ? [Xs: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ N2 @ Xs ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.71/1.49 & ( ord_less_eq @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 & ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.71/1.49 & ~ ( member @ A @ N2 @ ( coinductive_lset @ A @ Xs ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_11_reachable__via_Ocases,axiom,
% 2.71/1.49 ! [Node: $tType,A2: Node,Graph: Node > Node > $o,Ns: set @ Node,N2: Node] :
% 2.71/1.49 ( ( member @ Node @ A2 @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) )
% 2.71/1.49 => ~ ! [Xs2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 => ( ( member @ Node @ A2 @ ( coinductive_lset @ Node @ Xs2 ) )
% 2.71/1.49 => ~ ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_12_reachable__via_Osimps,axiom,
% 2.71/1.49 ! [Node: $tType,A2: Node,Graph: Node > Node > $o,Ns: set @ Node,N2: Node] :
% 2.71/1.49 ( ( member @ Node @ A2 @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) )
% 2.71/1.49 = ( ? [Xs4: coinductive_llist @ Node,N3: Node] :
% 2.71/1.49 ( ( A2 = N3 )
% 2.71/1.49 & ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs4 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 & ( member @ Node @ N3 @ ( coinductive_lset @ Node @ Xs4 ) )
% 2.71/1.49 & ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs4 ) @ Ns ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_13_reachable__via_Ointros,axiom,
% 2.71/1.49 ! [Node: $tType,N2: Node,Xs3: coinductive_llist @ Node,Graph: Node > Node > $o,N4: Node,Ns: set @ Node] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs3 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 => ( ( member @ Node @ N4 @ ( coinductive_lset @ Node @ Xs3 ) )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs3 ) @ Ns )
% 2.71/1.49 => ( member @ Node @ N4 @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_14_reachable__via_Oinducts,axiom,
% 2.71/1.49 ! [Node: $tType,X: Node,Graph: Node > Node > $o,Ns: set @ Node,N2: Node,P: Node > $o] :
% 2.71/1.49 ( ( member @ Node @ X @ ( koenig317145564le_via @ Node @ Graph @ Ns @ N2 ) )
% 2.71/1.49 => ( ! [Xs2: coinductive_llist @ Node,N: Node] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 => ( ( member @ Node @ N @ ( coinductive_lset @ Node @ Xs2 ) )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns )
% 2.71/1.49 => ( P @ N ) ) ) )
% 2.71/1.49 => ( P @ X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_15_llist_Oinject,axiom,
% 2.71/1.49 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 2.71/1.49 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.71/1.49 = ( ( X21 = Y21 )
% 2.71/1.49 & ( X22 = Y22 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_16_subsetI,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ! [X2: A] :
% 2.71/1.49 ( ( member @ A @ X2 @ A3 )
% 2.71/1.49 => ( member @ A @ X2 @ B2 ) )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ A3 @ B2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_17_subset__antisym,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A3 )
% 2.71/1.49 => ( A3 = B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_18_order__refl,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( preorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_19_lset__intros_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,X3: A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X3 @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_20_lset__intros_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_21_llist_Oset__intros_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 2.71/1.49 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_22_llist_Oset__intros_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_23_lset__cases,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( ! [Xs: coinductive_llist @ A] :
% 2.71/1.49 ( Xs3
% 2.71/1.49 != ( coinductive_LCons @ A @ X @ Xs ) )
% 2.71/1.49 => ~ ! [X4: A,Xs: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs3
% 2.71/1.49 = ( coinductive_LCons @ A @ X4 @ Xs ) )
% 2.71/1.49 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_24_lset__induct,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 2.71/1.49 => ( ! [X4: A,Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 2.71/1.49 => ( ( X != X4 )
% 2.71/1.49 => ( ( P @ Xs2 )
% 2.71/1.49 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs2 ) ) ) ) )
% 2.71/1.49 => ( P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_25_lset__induct_H,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 2.71/1.49 => ( ! [X4: A,Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 2.71/1.49 => ( ( P @ Xs2 )
% 2.71/1.49 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs2 ) ) ) )
% 2.71/1.49 => ( P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_26_dual__order_Oantisym,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( A2 = B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_27_dual__order_Otrans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,A2: A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 2.71/1.49 => ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_28_linorder__wlog,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [P: A > A > $o,A2: A,B3: A] :
% 2.71/1.49 ( ! [A4: A,B4: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A4 @ B4 )
% 2.71/1.49 => ( P @ A4 @ B4 ) )
% 2.71/1.49 => ( ! [A4: A,B4: A] :
% 2.71/1.49 ( ( P @ B4 @ A4 )
% 2.71/1.49 => ( P @ A4 @ B4 ) )
% 2.71/1.49 => ( P @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_29_dual__order_Orefl,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_30_order__trans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( preorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A,Z: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Y @ Z )
% 2.71/1.49 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_31_order__class_Oorder_Oantisym,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ( A2 = B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_32_ord__le__eq__trans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( ( B3 = C2 )
% 2.71/1.49 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_33_ord__eq__le__trans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A,C2: A] :
% 2.71/1.49 ( ( A2 = B3 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.71/1.49 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_34_antisym__conv,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 = ( X = Y ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_35_le__cases3,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A,Z: A] :
% 2.71/1.49 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 2.71/1.49 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 2.71/1.49 => ( ( ( ord_less_eq @ A @ X @ Z )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 2.71/1.49 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.71/1.49 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 2.71/1.49 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_36_order_Otrans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.71/1.49 => ( ord_less_eq @ A @ A2 @ C2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_37_le__cases,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] :
% 2.71/1.49 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_38_wlog__linorder__le,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [P: A > A > $o,B3: A,A2: A] :
% 2.71/1.49 ( ! [A4: A,B4: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A4 @ B4 )
% 2.71/1.49 => ( P @ A4 @ B4 ) )
% 2.71/1.49 => ( ( ( P @ B3 @ A2 )
% 2.71/1.49 => ( P @ A2 @ B3 ) )
% 2.71/1.49 => ( P @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_39_eq__refl,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( preorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] :
% 2.71/1.49 ( ( X = Y )
% 2.71/1.49 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_40_linear,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_41_antisym,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( X = Y ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_42_eq__iff,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 2.71/1.49 = ( ^ [X5: A,Y3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X5 @ Y3 )
% 2.71/1.49 & ( ord_less_eq @ A @ Y3 @ X5 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_43_ord__le__eq__subst,axiom,
% 2.71/1.49 ! [A: $tType,B: $tType] :
% 2.71/1.49 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.71/1.49 & ( ord @ A @ ( type2 @ A ) ) )
% 2.71/1.49 => ! [A2: A,B3: A,F: A > B,C2: B] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( ( ( F @ B3 )
% 2.71/1.49 = C2 )
% 2.71/1.49 => ( ! [X2: A,Y4: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.71/1.49 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.71/1.49 => ( ord_less_eq @ B @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_44_ord__eq__le__subst,axiom,
% 2.71/1.49 ! [A: $tType,B: $tType] :
% 2.71/1.49 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.71/1.49 & ( ord @ A @ ( type2 @ A ) ) )
% 2.71/1.49 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( F @ B3 ) )
% 2.71/1.49 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.71/1.49 => ( ! [X2: B,Y4: B] :
% 2.71/1.49 ( ( ord_less_eq @ B @ X2 @ Y4 )
% 2.71/1.49 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.71/1.49 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_45_mem__Collect__eq,axiom,
% 2.71/1.49 ! [A: $tType,A2: A,P: A > $o] :
% 2.71/1.49 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.71/1.49 = ( P @ A2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_46_Collect__mem__eq,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A] :
% 2.71/1.49 ( ( collect @ A
% 2.71/1.49 @ ^ [X5: A] : ( member @ A @ X5 @ A3 ) )
% 2.71/1.49 = A3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_47_Collect__cong,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.71/1.49 ( ! [X2: A] :
% 2.71/1.49 ( ( P @ X2 )
% 2.71/1.49 = ( Q @ X2 ) )
% 2.71/1.49 => ( ( collect @ A @ P )
% 2.71/1.49 = ( collect @ A @ Q ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_48_ext,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.71/1.49 ( ! [X2: A] :
% 2.71/1.49 ( ( F @ X2 )
% 2.71/1.49 = ( G @ X2 ) )
% 2.71/1.49 => ( F = G ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_49_order__subst2,axiom,
% 2.71/1.49 ! [A: $tType,C: $tType] :
% 2.71/1.49 ( ( ( order @ C @ ( type2 @ C ) )
% 2.71/1.49 & ( order @ A @ ( type2 @ A ) ) )
% 2.71/1.49 => ! [A2: A,B3: A,F: A > C,C2: C] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C2 )
% 2.71/1.49 => ( ! [X2: A,Y4: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.71/1.49 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.71/1.49 => ( ord_less_eq @ C @ ( F @ A2 ) @ C2 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_50_order__subst1,axiom,
% 2.71/1.49 ! [A: $tType,B: $tType] :
% 2.71/1.49 ( ( ( order @ B @ ( type2 @ B ) )
% 2.71/1.49 & ( order @ A @ ( type2 @ A ) ) )
% 2.71/1.49 => ! [A2: A,F: B > A,B3: B,C2: B] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ ( F @ B3 ) )
% 2.71/1.49 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.71/1.49 => ( ! [X2: B,Y4: B] :
% 2.71/1.49 ( ( ord_less_eq @ B @ X2 @ Y4 )
% 2.71/1.49 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 2.71/1.49 => ( ord_less_eq @ A @ A2 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_51_le__fun__def,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType] :
% 2.71/1.49 ( ( ord @ B @ ( type2 @ B ) )
% 2.71/1.49 => ( ( ord_less_eq @ ( A > B ) )
% 2.71/1.49 = ( ^ [F2: A > B,G2: A > B] :
% 2.71/1.49 ! [X5: A] : ( ord_less_eq @ B @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_52_le__funI,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType] :
% 2.71/1.49 ( ( ord @ B @ ( type2 @ B ) )
% 2.71/1.49 => ! [F: A > B,G: A > B] :
% 2.71/1.49 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 2.71/1.49 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_53_le__funE,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType] :
% 2.71/1.49 ( ( ord @ B @ ( type2 @ B ) )
% 2.71/1.49 => ! [F: A > B,G: A > B,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.71/1.49 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_54_le__funD,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType] :
% 2.71/1.49 ( ( ord @ B @ ( type2 @ B ) )
% 2.71/1.49 => ! [F: A > B,G: A > B,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.71/1.49 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_55_Collect__mono__iff,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.71/1.49 = ( ! [X5: A] :
% 2.71/1.49 ( ( P @ X5 )
% 2.71/1.49 => ( Q @ X5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_56_contra__subsetD,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ~ ( member @ A @ C2 @ B2 )
% 2.71/1.49 => ~ ( member @ A @ C2 @ A3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_57_set__eq__subset,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ^ [Y2: set @ A,Z2: set @ A] : ( Y2 = Z2 ) )
% 2.71/1.49 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B5 )
% 2.71/1.49 & ( ord_less_eq @ ( set @ A ) @ B5 @ A5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_58_subset__trans,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_59_Collect__mono,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.71/1.49 ( ! [X2: A] :
% 2.71/1.49 ( ( P @ X2 )
% 2.71/1.49 => ( Q @ X2 ) )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_60_subset__refl,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_61_rev__subsetD,axiom,
% 2.71/1.49 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( member @ A @ C2 @ A3 )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_62_subset__iff,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) )
% 2.71/1.49 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.71/1.49 ! [T: A] :
% 2.71/1.49 ( ( member @ A @ T @ A5 )
% 2.71/1.49 => ( member @ A @ T @ B5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_63_set__rev__mp,axiom,
% 2.71/1.49 ! [A: $tType,X: A,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( member @ A @ X @ A3 )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( member @ A @ X @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_64_equalityD2,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( A3 = B2 )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ B2 @ A3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_65_equalityD1,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( A3 = B2 )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ A3 @ B2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_66_subset__eq,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) )
% 2.71/1.49 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.71/1.49 ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ A5 )
% 2.71/1.49 => ( member @ A @ X5 @ B5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_67_equalityE,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( A3 = B2 )
% 2.71/1.49 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ~ ( ord_less_eq @ ( set @ A ) @ B2 @ A3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_68_subsetCE,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( member @ A @ C2 @ A3 )
% 2.71/1.49 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_69_subsetD,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( member @ A @ C2 @ A3 )
% 2.71/1.49 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_70_in__mono,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( member @ A @ X @ A3 )
% 2.71/1.49 => ( member @ A @ X @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_71_set__mp,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( member @ A @ X @ A3 )
% 2.71/1.49 => ( member @ A @ X @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_72_llist_Oset__induct,axiom,
% 2.71/1.49 ! [A: $tType,X: A,A2: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ A2 ) )
% 2.71/1.49 => ( ! [Z1: A,Z22: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 2.71/1.49 => ( ! [Z1: A,Z22: coinductive_llist @ A,Xa: A] :
% 2.71/1.49 ( ( member @ A @ Xa @ ( coinductive_lset @ A @ Z22 ) )
% 2.71/1.49 => ( ( P @ Xa @ Z22 )
% 2.71/1.49 => ( P @ Xa @ ( coinductive_LCons @ A @ Z1 @ Z22 ) ) ) )
% 2.71/1.49 => ( P @ X @ A2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_73_llist_Oset__cases,axiom,
% 2.71/1.49 ! [A: $tType,E: A,A2: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ E @ ( coinductive_lset @ A @ A2 ) )
% 2.71/1.49 => ( ! [Z22: coinductive_llist @ A] :
% 2.71/1.49 ( A2
% 2.71/1.49 != ( coinductive_LCons @ A @ E @ Z22 ) )
% 2.71/1.49 => ~ ! [Z1: A,Z22: coinductive_llist @ A] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 2.71/1.49 => ~ ( member @ A @ E @ ( coinductive_lset @ A @ Z22 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_74_reachable__viap__reachable__via__eq,axiom,
% 2.71/1.49 ! [Node: $tType] :
% 2.71/1.49 ( ( koenig1757754772e_viap @ Node )
% 2.71/1.49 = ( ^ [Graph2: Node > Node > $o,Ns2: set @ Node,N5: Node,X5: Node] : ( member @ Node @ X5 @ ( koenig317145564le_via @ Node @ Graph2 @ Ns2 @ N5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_75_lset__lmember,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 = ( coinductive_lmember @ A @ X @ Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_76_lsorted__LCons,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( preorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( ( coindu63249387sorted @ A @ Xs3 )
% 2.71/1.49 & ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( ord_less_eq @ A @ X @ X5 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_77_lmember__code_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Y: A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lmember @ A @ X @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.71/1.49 = ( ( X = Y )
% 2.71/1.49 | ( coinductive_lmember @ A @ X @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_78_lfp_Oleq__antisym,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( X = Y ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_79_gfp_Oleq__antisym,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( X = Y ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_80_lfp_Oleq__trans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A,Z: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Y @ Z )
% 2.71/1.49 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_81_gfp_Oleq__trans,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A,Z: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Z @ Y )
% 2.71/1.49 => ( ord_less_eq @ A @ Z @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_82_lfp_Oleq__refl,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_83_lsorted__LCons__LCons,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) )
% 2.71/1.49 = ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 & ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_84_LCons__LCons,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y @ Xs3 ) )
% 2.71/1.49 => ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_85_reachable__viap_Ocases,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,Ns: set @ Node,N2: Node,A2: Node] :
% 2.71/1.49 ( ( koenig1757754772e_viap @ Node @ Graph @ Ns @ N2 @ A2 )
% 2.71/1.49 => ~ ! [Xs2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) )
% 2.71/1.49 => ( ( member @ Node @ A2 @ ( coinductive_lset @ Node @ Xs2 ) )
% 2.71/1.49 => ~ ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_86_reachable__viap_Osimps,axiom,
% 2.71/1.49 ! [Node: $tType] :
% 2.71/1.49 ( ( koenig1757754772e_viap @ Node )
% 2.71/1.49 = ( ^ [Graph2: Node > Node > $o,Ns2: set @ Node,N5: Node,A6: Node] :
% 2.71/1.49 ? [Xs4: coinductive_llist @ Node,N3: Node] :
% 2.71/1.49 ( ( A6 = N3 )
% 2.71/1.49 & ( koenig2031690877pathsp @ Node @ Graph2 @ ( coinductive_LCons @ Node @ N5 @ Xs4 ) )
% 2.71/1.49 & ( member @ Node @ N3 @ ( coinductive_lset @ Node @ Xs4 ) )
% 2.71/1.49 & ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs4 ) @ Ns2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_87_reachable__viap_Ointros,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,N2: Node,Xs3: coinductive_llist @ Node,N4: Node,Ns: set @ Node] :
% 2.71/1.49 ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ N2 @ Xs3 ) )
% 2.71/1.49 => ( ( member @ Node @ N4 @ ( coinductive_lset @ Node @ Xs3 ) )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs3 ) @ Ns )
% 2.71/1.49 => ( koenig1757754772e_viap @ Node @ Graph @ Ns @ N2 @ N4 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_88_reachable__viap_Oinducts,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,Ns: set @ Node,N2: Node,X: Node,P: Node > $o] :
% 2.71/1.49 ( ( koenig1757754772e_viap @ Node @ Graph @ Ns @ N2 @ X )
% 2.71/1.49 => ( ! [Xs2: coinductive_llist @ Node,N: Node] :
% 2.71/1.49 ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ N2 @ Xs2 ) )
% 2.71/1.49 => ( ( member @ Node @ N @ ( coinductive_lset @ Node @ Xs2 ) )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ Node ) @ ( coinductive_lset @ Node @ Xs2 ) @ Ns )
% 2.71/1.49 => ( P @ N ) ) ) )
% 2.71/1.49 => ( P @ X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_89_lsorted_Ocases,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu63249387sorted @ A @ A2 )
% 2.71/1.49 => ( ( A2
% 2.71/1.49 != ( coinductive_LNil @ A ) )
% 2.71/1.49 => ( ! [X2: A] :
% 2.71/1.49 ( A2
% 2.71/1.49 != ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) )
% 2.71/1.49 => ~ ! [X2: A,Y4: A,Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( coinductive_LCons @ A @ X2 @ ( coinductive_LCons @ A @ Y4 @ Xs2 ) ) )
% 2.71/1.49 => ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.71/1.49 => ~ ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_90_lsorted_Osimps,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( ( coindu63249387sorted @ A )
% 2.71/1.49 = ( ^ [A6: coinductive_llist @ A] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ? [X5: A] :
% 2.71/1.49 ( A6
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ ( coinductive_LNil @ A ) ) )
% 2.71/1.49 | ? [X5: A,Y3: A,Xs4: coinductive_llist @ A] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ ( coinductive_LCons @ A @ Y3 @ Xs4 ) ) )
% 2.71/1.49 & ( ord_less_eq @ A @ X5 @ Y3 )
% 2.71/1.49 & ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y3 @ Xs4 ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_91_lsorted__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( coindu63249387sorted @ A @ ( coinductive_LNil @ A ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_92_lsorted__code_I2_J,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A] : ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_93_pathsp_Ocases,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,A2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( koenig2031690877pathsp @ Node @ Graph @ A2 )
% 2.71/1.49 => ( ( A2
% 2.71/1.49 != ( coinductive_LNil @ Node ) )
% 2.71/1.49 => ( ! [X2: Node] :
% 2.71/1.49 ( A2
% 2.71/1.49 != ( coinductive_LCons @ Node @ X2 @ ( coinductive_LNil @ Node ) ) )
% 2.71/1.49 => ~ ! [X2: Node,Y4: Node,Xs2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( coinductive_LCons @ Node @ X2 @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) ) )
% 2.71/1.49 => ( ( Graph @ X2 @ Y4 )
% 2.71/1.49 => ~ ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_94_pathsp_Osimps,axiom,
% 2.71/1.49 ! [Node: $tType] :
% 2.71/1.49 ( ( koenig2031690877pathsp @ Node )
% 2.71/1.49 = ( ^ [Graph2: Node > Node > $o,A6: coinductive_llist @ Node] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LNil @ Node ) )
% 2.71/1.49 | ? [X5: Node] :
% 2.71/1.49 ( A6
% 2.71/1.49 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LNil @ Node ) ) )
% 2.71/1.49 | ? [X5: Node,Y3: Node,Xs4: coinductive_llist @ Node] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) ) )
% 2.71/1.49 & ( Graph2 @ X5 @ Y3 )
% 2.71/1.49 & ( koenig2031690877pathsp @ Node @ Graph2 @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_95_pathsp_OSingle,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,X: Node] : ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ X @ ( coinductive_LNil @ Node ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_96_pathsp_Ocoinduct,axiom,
% 2.71/1.49 ! [Node: $tType,X6: ( coinductive_llist @ Node ) > $o,X: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.71/1.49 ( ( X6 @ X )
% 2.71/1.49 => ( ! [X2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( X6 @ X2 )
% 2.71/1.49 => ( ( X2
% 2.71/1.49 = ( coinductive_LNil @ Node ) )
% 2.71/1.49 | ? [Xa2: Node] :
% 2.71/1.49 ( X2
% 2.71/1.49 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LNil @ Node ) ) )
% 2.71/1.49 | ? [Xa2: Node,Y5: Node,Xs5: coinductive_llist @ Node] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) ) )
% 2.71/1.49 & ( Graph @ Xa2 @ Y5 )
% 2.71/1.49 & ( ( X6 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) )
% 2.71/1.49 | ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) ) ) ) ) )
% 2.71/1.49 => ( koenig2031690877pathsp @ Node @ Graph @ X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_97_pathsp_OEmpty,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o] : ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LNil @ Node ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_98_neq__LNil__conv,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs3
% 2.71/1.49 != ( coinductive_LNil @ A ) )
% 2.71/1.49 = ( ? [X5: A,Xs6: coinductive_llist @ A] :
% 2.71/1.49 ( Xs3
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ Xs6 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_99_llist_Oexhaust,axiom,
% 2.71/1.49 ! [A: $tType,Y: coinductive_llist @ A] :
% 2.71/1.49 ( ( Y
% 2.71/1.49 != ( coinductive_LNil @ A ) )
% 2.71/1.49 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 2.71/1.49 ( Y
% 2.71/1.49 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_100_llist_Odistinct_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_LNil @ A )
% 2.71/1.49 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_101_LNil,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( coindu63249387sorted @ A @ ( coinductive_LNil @ A ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_102_paths_OEmpty,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LNil @ Node ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_103_pathsp_OLCons,axiom,
% 2.71/1.49 ! [Node: $tType,Graph: Node > Node > $o,X: Node,Y: Node,Xs3: coinductive_llist @ Node] :
% 2.71/1.49 ( ( Graph @ X @ Y )
% 2.71/1.49 => ( ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ Y @ Xs3 ) )
% 2.71/1.49 => ( koenig2031690877pathsp @ Node @ Graph @ ( coinductive_LCons @ Node @ X @ ( coinductive_LCons @ Node @ Y @ Xs3 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_104_lmember__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,X: A] :
% 2.71/1.49 ~ ( coinductive_lmember @ A @ X @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_105_pathsp__paths__eq,axiom,
% 2.71/1.49 ! [Node: $tType] :
% 2.71/1.49 ( ( koenig2031690877pathsp @ Node )
% 2.71/1.49 = ( ^ [Graph2: Node > Node > $o,X5: coinductive_llist @ Node] : ( member @ ( coinductive_llist @ Node ) @ X5 @ ( koenig916195507_paths @ Node @ Graph2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_106_Singleton,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A] : ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_107_paths_Ocoinduct,axiom,
% 2.71/1.49 ! [Node: $tType,X6: ( coinductive_llist @ Node ) > $o,X: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.71/1.49 ( ( X6 @ X )
% 2.71/1.49 => ( ! [X2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( X6 @ X2 )
% 2.71/1.49 => ( ( X2
% 2.71/1.49 = ( coinductive_LNil @ Node ) )
% 2.71/1.49 | ? [Xa2: Node] :
% 2.71/1.49 ( X2
% 2.71/1.49 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LNil @ Node ) ) )
% 2.71/1.49 | ? [Xa2: Node,Y5: Node,Xs5: coinductive_llist @ Node] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LCons @ Node @ Xa2 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) ) )
% 2.71/1.49 & ( Graph @ Xa2 @ Y5 )
% 2.71/1.49 & ( ( X6 @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) )
% 2.71/1.49 | ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y5 @ Xs5 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) )
% 2.71/1.49 => ( member @ ( coinductive_llist @ Node ) @ X @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_108_paths_OSingle,axiom,
% 2.71/1.49 ! [Node: $tType,X: Node,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LNil @ Node ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_109_paths_Osimps,axiom,
% 2.71/1.49 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 = ( ( A2
% 2.71/1.49 = ( coinductive_LNil @ Node ) )
% 2.71/1.49 | ? [X5: Node] :
% 2.71/1.49 ( A2
% 2.71/1.49 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LNil @ Node ) ) )
% 2.71/1.49 | ? [X5: Node,Y3: Node,Xs4: coinductive_llist @ Node] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( coinductive_LCons @ Node @ X5 @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) ) )
% 2.71/1.49 & ( Graph @ X5 @ Y3 )
% 2.71/1.49 & ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y3 @ Xs4 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_110_paths_Ocases,axiom,
% 2.71/1.49 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.71/1.49 => ( ( A2
% 2.71/1.49 != ( coinductive_LNil @ Node ) )
% 2.71/1.49 => ( ! [X2: Node] :
% 2.71/1.49 ( A2
% 2.71/1.49 != ( coinductive_LCons @ Node @ X2 @ ( coinductive_LNil @ Node ) ) )
% 2.71/1.49 => ~ ! [X2: Node,Y4: Node,Xs2: coinductive_llist @ Node] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( coinductive_LCons @ Node @ X2 @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) ) )
% 2.71/1.49 => ( ( Graph @ X2 @ Y4 )
% 2.71/1.49 => ~ ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y4 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_111_lsorted_Ocoinduct,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X6: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A] :
% 2.71/1.49 ( ( X6 @ X )
% 2.71/1.49 => ( ! [X2: coinductive_llist @ A] :
% 2.71/1.49 ( ( X6 @ X2 )
% 2.71/1.49 => ( ( X2
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ? [Xa2: A] :
% 2.71/1.49 ( X2
% 2.71/1.49 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_LNil @ A ) ) )
% 2.71/1.49 | ? [Xa2: A,Y5: A,Xs5: coinductive_llist @ A] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_LCons @ A @ Y5 @ Xs5 ) ) )
% 2.71/1.49 & ( ord_less_eq @ A @ Xa2 @ Y5 )
% 2.71/1.49 & ( ( X6 @ ( coinductive_LCons @ A @ Y5 @ Xs5 ) )
% 2.71/1.49 | ( coindu63249387sorted @ A @ ( coinductive_LCons @ A @ Y5 @ Xs5 ) ) ) ) ) )
% 2.71/1.49 => ( coindu63249387sorted @ A @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_112_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu328551480prefix @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.71/1.49 = ( ( Xs3
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ? [Xs6: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs3
% 2.71/1.49 = ( coinductive_LCons @ A @ Y @ Xs6 ) )
% 2.71/1.49 & ( coindu328551480prefix @ A @ Xs6 @ Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_113_lstrict__prefix__code_I2_J,axiom,
% 2.71/1.49 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_114_lstrict__prefix__code_I3_J,axiom,
% 2.71/1.49 ! [B: $tType,X: B,Xs3: coinductive_llist @ B] :
% 2.71/1.49 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs3 ) @ ( coinductive_LNil @ B ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_115_llast__singleton,axiom,
% 2.71/1.49 ! [A: $tType,X: A] :
% 2.71/1.49 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 2.71/1.49 = X ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_116_ldistinct_Ocoinduct,axiom,
% 2.71/1.49 ! [A: $tType,X6: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A] :
% 2.71/1.49 ( ( X6 @ X )
% 2.71/1.49 => ( ! [X2: coinductive_llist @ A] :
% 2.71/1.49 ( ( X6 @ X2 )
% 2.71/1.49 => ( ( X2
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ? [Xa2: A,Xs5: coinductive_llist @ A] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LCons @ A @ Xa2 @ Xs5 ) )
% 2.71/1.49 & ~ ( member @ A @ Xa2 @ ( coinductive_lset @ A @ Xs5 ) )
% 2.71/1.49 & ( ( X6 @ Xs5 )
% 2.71/1.49 | ( coindu351974385stinct @ A @ Xs5 ) ) ) ) )
% 2.71/1.49 => ( coindu351974385stinct @ A @ X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_117_ldistinct_Osimps,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( coindu351974385stinct @ A )
% 2.71/1.49 = ( ^ [A6: coinductive_llist @ A] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ? [X5: A,Xs4: coinductive_llist @ A] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 2.71/1.49 & ~ ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs4 ) )
% 2.71/1.49 & ( coindu351974385stinct @ A @ Xs4 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_118_ldistinct__LNil__code,axiom,
% 2.71/1.49 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_119_llast__LCons2,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Y: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) )
% 2.71/1.49 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_120_lstrict__prefix__code_I4_J,axiom,
% 2.71/1.49 ! [B: $tType,X: B,Xs3: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 2.71/1.49 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs3 ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 2.71/1.49 = ( ( X = Y )
% 2.71/1.49 & ( coindu1478340336prefix @ B @ Xs3 @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_121_lstrict__prefix__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_122_ldistinct__LCons,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 & ( coindu351974385stinct @ A @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_123_llist__less__induct,axiom,
% 2.71/1.49 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ! [Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ! [Ys2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs2 )
% 2.71/1.49 => ( P @ Ys2 ) )
% 2.71/1.49 => ( P @ Xs2 ) )
% 2.71/1.49 => ( P @ Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_124_ldistinct_OLNil,axiom,
% 2.71/1.49 ! [A: $tType] : ( coindu351974385stinct @ A @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_125_ldistinct_OLCons,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( ( coindu351974385stinct @ A @ Xs3 )
% 2.71/1.49 => ( coindu351974385stinct @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_126_lsorted__ldistinct__lset__unique,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu63249387sorted @ A @ Xs3 )
% 2.71/1.49 => ( ( coindu351974385stinct @ A @ Xs3 )
% 2.71/1.49 => ( ( coindu63249387sorted @ A @ Ys )
% 2.71/1.49 => ( ( coindu351974385stinct @ A @ Ys )
% 2.71/1.49 => ( ( ( coinductive_lset @ A @ Xs3 )
% 2.71/1.49 = ( coinductive_lset @ A @ Ys ) )
% 2.71/1.49 => ( Xs3 = Ys ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_127_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu328551480prefix @ A @ Xs3 @ ( coinductive_LNil @ A ) )
% 2.71/1.49 = ( Xs3
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_128_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_129_ldistinct_Ocases,axiom,
% 2.71/1.49 ! [A: $tType,A2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu351974385stinct @ A @ A2 )
% 2.71/1.49 => ( ( A2
% 2.71/1.49 != ( coinductive_LNil @ A ) )
% 2.71/1.49 => ~ ! [X2: A,Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 2.71/1.49 => ( ~ ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs2 ) )
% 2.71/1.49 => ~ ( coindu351974385stinct @ A @ Xs2 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_130_llimit__induct,axiom,
% 2.71/1.49 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( P @ ( coinductive_LNil @ A ) )
% 2.71/1.49 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs2 )
% 2.71/1.49 => ( ( P @ Xs2 )
% 2.71/1.49 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.71/1.49 => ( ( ! [Ys2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.71/1.49 => ( P @ Ys2 ) )
% 2.71/1.49 => ( P @ Xs3 ) )
% 2.71/1.49 => ( P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_131_gen__lset__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A] :
% 2.71/1.49 ( ( coinductive_gen_lset @ A @ A3 @ ( coinductive_LNil @ A ) )
% 2.71/1.49 = A3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_132_llist_Ocorec__code,axiom,
% 2.71/1.49 ! [A: $tType,C: $tType] :
% 2.71/1.49 ( ( coindu1259883913_llist @ C @ A )
% 2.71/1.49 = ( ^ [P2: C > $o,G21: C > A,Q22: C > $o,G221: C > ( coinductive_llist @ A ),G222: C > C,A6: C] : ( if @ ( coinductive_llist @ A ) @ ( P2 @ A6 ) @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ A @ ( G21 @ A6 ) @ ( if @ ( coinductive_llist @ A ) @ ( Q22 @ A6 ) @ ( G221 @ A6 ) @ ( coindu1259883913_llist @ C @ A @ P2 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A6 ) ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_133_unfold__llist_Ocode,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType] :
% 2.71/1.49 ( ( coindu1441602521_llist @ A @ B )
% 2.71/1.49 = ( ^ [P2: A > $o,G21: A > B,G22: A > A,A6: A] : ( if @ ( coinductive_llist @ B ) @ ( P2 @ A6 ) @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ ( G21 @ A6 ) @ ( coindu1441602521_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A6 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_134_lfinite__code_I2_J,axiom,
% 2.71/1.49 ! [B: $tType,X: B,Xs3: coinductive_llist @ B] :
% 2.71/1.49 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs3 ) )
% 2.71/1.49 = ( coinductive_lfinite @ B @ Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_135_lfinite__LCons,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( coinductive_lfinite @ A @ Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_136_lfinite__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_137_unfold__llist__eq__LCons,axiom,
% 2.71/1.49 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B3 )
% 2.71/1.49 = ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( ~ ( IS_LNIL @ B3 )
% 2.71/1.49 & ( X
% 2.71/1.49 = ( LHD @ B3 ) )
% 2.71/1.49 & ( Xs3
% 2.71/1.49 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_138_lfinite__LConsI,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,X: A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_139_lfinite__LNil,axiom,
% 2.71/1.49 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_140_lstrict__prefix__lfinite1,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu1478340336prefix @ A @ Xs3 @ Ys )
% 2.71/1.49 => ( coinductive_lfinite @ A @ Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_141_unfold__llist_Octr_I2_J,axiom,
% 2.71/1.49 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.71/1.49 ( ~ ( P3 @ A2 )
% 2.71/1.49 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 2.71/1.49 = ( coinductive_LCons @ B @ ( G212 @ A2 ) @ ( coindu1441602521_llist @ A @ B @ P3 @ G212 @ G223 @ ( G223 @ A2 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_142_unfold__llist_Octr_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G212: A > B,G223: A > A] :
% 2.71/1.49 ( ( P3 @ A2 )
% 2.71/1.49 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G212 @ G223 @ A2 )
% 2.71/1.49 = ( coinductive_LNil @ B ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_143_llist_Ocorec_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,C: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coinductive_llist @ A ),G2222: C > C] :
% 2.71/1.49 ( ~ ( P3 @ A2 )
% 2.71/1.49 => ( ( coindu1259883913_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.71/1.49 = ( coinductive_LCons @ A @ ( G212 @ A2 ) @ ( if @ ( coinductive_llist @ A ) @ ( Q222 @ A2 ) @ ( G2212 @ A2 ) @ ( coindu1259883913_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ ( G2222 @ A2 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_144_llist_Ocorec_I1_J,axiom,
% 2.71/1.49 ! [C: $tType,A: $tType,P3: C > $o,A2: C,G212: C > A,Q222: C > $o,G2212: C > ( coinductive_llist @ A ),G2222: C > C] :
% 2.71/1.49 ( ( P3 @ A2 )
% 2.71/1.49 => ( ( coindu1259883913_llist @ C @ A @ P3 @ G212 @ Q222 @ G2212 @ G2222 @ A2 )
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_145_lfinite_Oinducts,axiom,
% 2.71/1.49 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ X )
% 2.71/1.49 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.71/1.49 => ( ! [Xs2: coinductive_llist @ A,X2: A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs2 )
% 2.71/1.49 => ( ( P @ Xs2 )
% 2.71/1.49 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.71/1.49 => ( P @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_146_lfinite_Osimps,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( coinductive_lfinite @ A )
% 2.71/1.49 = ( ^ [A6: coinductive_llist @ A] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ? [Xs4: coinductive_llist @ A,X5: A] :
% 2.71/1.49 ( ( A6
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 2.71/1.49 & ( coinductive_lfinite @ A @ Xs4 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_147_lfinite_Ocases,axiom,
% 2.71/1.49 ! [A: $tType,A2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ A2 )
% 2.71/1.49 => ( ( A2
% 2.71/1.49 != ( coinductive_LNil @ A ) )
% 2.71/1.49 => ~ ! [Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ? [X2: A] :
% 2.71/1.49 ( A2
% 2.71/1.49 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 2.71/1.49 => ~ ( coinductive_lfinite @ A @ Xs2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_148_llast__lappend__LCons,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 2.71/1.49 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_149_split__llist,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ? [Ys3: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs3
% 2.71/1.49 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 2.71/1.49 & ( coinductive_lfinite @ A @ Ys3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_150_split__llist__first,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ? [Ys3: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs3
% 2.71/1.49 = ( coinductive_lappend @ A @ Ys3 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 2.71/1.49 & ( coinductive_lfinite @ A @ Ys3 )
% 2.71/1.49 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_151_lfinite__rev__induct,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.71/1.49 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs2 )
% 2.71/1.49 => ( ( P @ Xs2 )
% 2.71/1.49 => ( P @ ( coinductive_lappend @ A @ Xs2 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 2.71/1.49 => ( P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_152_lappend__code_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,Xa3: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa3 @ X ) @ Ys )
% 2.71/1.49 = ( coinductive_LCons @ A @ Xa3 @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_153_lappend__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.71/1.49 = Ys ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_154_lappend__LNil2,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LNil @ A ) )
% 2.71/1.49 = Xs3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_155_lfinite__lappend,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_156_lappend__inf,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( coinductive_lappend @ A @ Xs3 @ Ys )
% 2.71/1.49 = Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_157_lappend__assoc,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ Zs2 )
% 2.71/1.49 = ( coinductive_lappend @ A @ Xs3 @ ( coinductive_lappend @ A @ Ys @ Zs2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_158_paths__lappendD1,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 2.71/1.49 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.71/1.49 => ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_159_lappend__LNil__LNil,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_160_LNil__eq__lappend__iff,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_LNil @ A )
% 2.71/1.49 = ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( ( Xs3
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 & ( Ys
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_161_lappend__eq__LNil__iff,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_lappend @ A @ Xs3 @ Ys )
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 = ( ( Xs3
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 & ( Ys
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_162_lset__lappend1,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_163_lappend__snocL1__conv__LCons2,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.71/1.49 = ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_164_in__lset__lappend__iff,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) )
% 2.71/1.49 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 | ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_165_paths__lappendD2,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.71/1.49 => ( member @ ( coinductive_llist @ A ) @ Ys @ ( koenig916195507_paths @ A @ Graph ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_166_lfilter__eq__LConsD,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Ys: coinductive_llist @ A,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_lfilter @ A @ P @ Ys )
% 2.71/1.49 = ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 2.71/1.49 ( ( Ys
% 2.71/1.49 = ( coinductive_lappend @ A @ Us @ ( coinductive_LCons @ A @ X @ Vs ) ) )
% 2.71/1.49 & ( coinductive_lfinite @ A @ Us )
% 2.71/1.49 & ! [X7: A] :
% 2.71/1.49 ( ( member @ A @ X7 @ ( coinductive_lset @ A @ Us ) )
% 2.71/1.49 => ~ ( P @ X7 ) )
% 2.71/1.49 & ( P @ X )
% 2.71/1.49 & ( Xs3
% 2.71/1.49 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_167_lset__lappend__lfinite,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_168_llexord__lappend__leftD,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( coinductive_lappend @ A @ Xs3 @ Zs2 ) )
% 2.71/1.49 => ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ! [X2: A] :
% 2.71/1.49 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ~ ( R @ X2 @ X2 ) )
% 2.71/1.49 => ( coinductive_llexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_169_UnCI,axiom,
% 2.71/1.49 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 2.71/1.49 ( ( ~ ( member @ A @ C2 @ B2 )
% 2.71/1.49 => ( member @ A @ C2 @ A3 ) )
% 2.71/1.49 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_170_Un__iff,axiom,
% 2.71/1.49 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 2.71/1.49 = ( ( member @ A @ C2 @ A3 )
% 2.71/1.49 | ( member @ A @ C2 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_171_lfilter__idem,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs3 ) )
% 2.71/1.49 = ( coinductive_lfilter @ A @ P @ Xs3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_172_llexord__refl,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs3 @ Xs3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_173_Un__subset__iff,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C3 )
% 2.71/1.49 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C3 )
% 2.71/1.49 & ( ord_less_eq @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_174_lfilter__LCons,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( P @ X )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) )
% 2.71/1.49 & ( ~ ( P @ X )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_175_lfilter__LNil,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o] :
% 2.71/1.49 ( ( coinductive_lfilter @ A @ P @ ( coinductive_LNil @ A ) )
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_176_llexord__LCons__LCons,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.71/1.49 = ( ( ( X = Y )
% 2.71/1.49 & ( coinductive_llexord @ A @ R @ Xs3 @ Ys ) )
% 2.71/1.49 | ( R @ X @ Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_177_llexord__code_I1_J,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_178_diverge__lfilter__LNil,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o] :
% 2.71/1.49 ( ! [X2: A] :
% 2.71/1.49 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ~ ( P @ X2 ) )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 2.71/1.49 = ( coinductive_LNil @ A ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_179_lfilter__lappend__lfinite,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( coinductive_lappend @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_180_llexord__lappend__leftI,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ Ys @ Zs2 )
% 2.71/1.49 => ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( coinductive_lappend @ A @ Xs3 @ Zs2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_181_llexord__append__right,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ Xs3 @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_182_ldistinct__lfilterI,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o] :
% 2.71/1.49 ( ( coindu351974385stinct @ A @ Xs3 )
% 2.71/1.49 => ( coindu351974385stinct @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_183_lfilter__LCons__seek,axiom,
% 2.71/1.49 ! [A: $tType,P3: A > $o,X: A,L: coinductive_llist @ A] :
% 2.71/1.49 ( ~ ( P3 @ X )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P3 @ ( coinductive_LCons @ A @ X @ L ) )
% 2.71/1.49 = ( coinductive_lfilter @ A @ P3 @ L ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_184_lfilter__LCons__found,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( P @ X )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs3 ) )
% 2.71/1.49 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_185_lfilter__cong,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o,Q: A > $o] :
% 2.71/1.49 ( ( Xs3 = Ys )
% 2.71/1.49 => ( ! [X2: A] :
% 2.71/1.49 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Ys ) )
% 2.71/1.49 => ( ( P @ X2 )
% 2.71/1.49 = ( Q @ X2 ) ) )
% 2.71/1.49 => ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 2.71/1.49 = ( coinductive_lfilter @ A @ Q @ Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_186_lfilter__id__conv,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 2.71/1.49 = Xs3 )
% 2.71/1.49 = ( ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ( P @ X5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_187_Un__mono,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,C3: set @ A,B2: set @ A,D: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C3 )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C3 @ D ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_188_Un__least,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,C3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C3 )
% 2.71/1.49 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C3 )
% 2.71/1.49 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_189_Un__upper1,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_190_Un__upper2,axiom,
% 2.71/1.49 ! [A: $tType,B2: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_191_Un__absorb1,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 => ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 = B2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_192_Un__absorb2,axiom,
% 2.71/1.49 ! [A: $tType,B2: set @ A,A3: set @ A] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A3 )
% 2.71/1.49 => ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 2.71/1.49 = A3 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_193_subset__Un__eq,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( ord_less_eq @ ( set @ A ) )
% 2.71/1.49 = ( ^ [A5: set @ A,B5: set @ A] :
% 2.71/1.49 ( ( sup_sup @ ( set @ A ) @ A5 @ B5 )
% 2.71/1.49 = B5 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_194_lsorted__lfilterI,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( preorder @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Xs3: coinductive_llist @ A,P: A > $o] :
% 2.71/1.49 ( ( coindu63249387sorted @ A @ Xs3 )
% 2.71/1.49 => ( coindu63249387sorted @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_195_llexord__code_I3_J,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.71/1.49 = ( ( R @ X @ Y )
% 2.71/1.49 | ( ( X = Y )
% 2.71/1.49 & ( coinductive_llexord @ A @ R @ Xs3 @ Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_196_llexord__LCons__left,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ Ys )
% 2.71/1.49 = ( ? [Y3: A,Ys4: coinductive_llist @ A] :
% 2.71/1.49 ( ( Ys
% 2.71/1.49 = ( coinductive_LCons @ A @ Y3 @ Ys4 ) )
% 2.71/1.49 & ( ( ( X = Y3 )
% 2.71/1.49 & ( coinductive_llexord @ A @ R @ Xs3 @ Ys4 ) )
% 2.71/1.49 | ( R @ X @ Y3 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_197_llexord__LCons__eq,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 2.71/1.49 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_198_llexord__LCons__less,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( R @ X @ Y )
% 2.71/1.49 => ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_199_llexord__LNil,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R @ ( coinductive_LNil @ A ) @ Ys ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_200_UnE,axiom,
% 2.71/1.49 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 2.71/1.49 => ( ~ ( member @ A @ C2 @ A3 )
% 2.71/1.49 => ( member @ A @ C2 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_201_UnI1,axiom,
% 2.71/1.49 ! [A: $tType,C2: A,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( member @ A @ C2 @ A3 )
% 2.71/1.49 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_202_UnI2,axiom,
% 2.71/1.49 ! [A: $tType,C2: A,B2: set @ A,A3: set @ A] :
% 2.71/1.49 ( ( member @ A @ C2 @ B2 )
% 2.71/1.49 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_203_bex__Un,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 2.71/1.49 ( ( ? [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 2.71/1.49 & ( P @ X5 ) ) )
% 2.71/1.49 = ( ? [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ A3 )
% 2.71/1.49 & ( P @ X5 ) )
% 2.71/1.49 | ? [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ B2 )
% 2.71/1.49 & ( P @ X5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_204_ball__Un,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 2.71/1.49 ( ( ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 2.71/1.49 => ( P @ X5 ) ) )
% 2.71/1.49 = ( ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ A3 )
% 2.71/1.49 => ( P @ X5 ) )
% 2.71/1.49 & ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ B2 )
% 2.71/1.49 => ( P @ X5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_205_Un__assoc,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 2.71/1.49 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C3 )
% 2.71/1.49 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_206_Un__absorb,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A] :
% 2.71/1.49 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 2.71/1.49 = A3 ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_207_Un__commute,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( sup_sup @ ( set @ A ) )
% 2.71/1.49 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_208_Un__left__absorb,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 2.71/1.49 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 2.71/1.49 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_209_Un__left__commute,axiom,
% 2.71/1.49 ! [A: $tType,A3: set @ A,B2: set @ A,C3: set @ A] :
% 2.71/1.49 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C3 ) )
% 2.71/1.49 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ C3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_210_llexord__trans,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 2.71/1.49 => ( ( coinductive_llexord @ A @ R @ Ys @ Zs2 )
% 2.71/1.49 => ( ! [A4: A,B4: A,C4: A] :
% 2.71/1.49 ( ( R @ A4 @ B4 )
% 2.71/1.49 => ( ( R @ B4 @ C4 )
% 2.71/1.49 => ( R @ A4 @ C4 ) ) )
% 2.71/1.49 => ( coinductive_llexord @ A @ R @ Xs3 @ Zs2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_211_llexord__linear,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ! [X2: A,Y4: A] :
% 2.71/1.49 ( ( R @ X2 @ Y4 )
% 2.71/1.49 | ( X2 = Y4 )
% 2.71/1.49 | ( R @ Y4 @ X2 ) )
% 2.71/1.49 => ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 2.71/1.49 | ( coinductive_llexord @ A @ R @ Ys @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_212_llexord__antisym,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ Xs3 @ Ys )
% 2.71/1.49 => ( ( coinductive_llexord @ A @ R @ Ys @ Xs3 )
% 2.71/1.49 => ( ! [A4: A,B4: A] :
% 2.71/1.49 ( ( R @ A4 @ B4 )
% 2.71/1.49 => ~ ( R @ B4 @ A4 ) )
% 2.71/1.49 => ( Xs3 = Ys ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_213_lfinite__lfilterI,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,P: A > $o] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( coinductive_lfinite @ A @ ( coinductive_lfilter @ A @ P @ Xs3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_214_lfilter__empty__conv,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 = ( ! [X5: A] :
% 2.71/1.49 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ~ ( P @ X5 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_215_lfilter__eq__lappend__lfiniteD,axiom,
% 2.71/1.49 ! [A: $tType,P: A > $o,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_lfilter @ A @ P @ Xs3 )
% 2.71/1.49 = ( coinductive_lappend @ A @ Ys @ Zs2 ) )
% 2.71/1.49 => ( ( coinductive_lfinite @ A @ Ys )
% 2.71/1.49 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs3
% 2.71/1.49 = ( coinductive_lappend @ A @ Us @ Vs ) )
% 2.71/1.49 & ( coinductive_lfinite @ A @ Us )
% 2.71/1.49 & ( Ys
% 2.71/1.49 = ( coinductive_lfilter @ A @ P @ Us ) )
% 2.71/1.49 & ( Zs2
% 2.71/1.49 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_216_llexord_Ocoinduct,axiom,
% 2.71/1.49 ! [A: $tType,X6: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa3: coinductive_llist @ A,R: A > A > $o] :
% 2.71/1.49 ( ( X6 @ X @ Xa3 )
% 2.71/1.49 => ( ! [X2: coinductive_llist @ A,Xa: coinductive_llist @ A] :
% 2.71/1.49 ( ( X6 @ X2 @ Xa )
% 2.71/1.49 => ( ? [Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A,Xb: A] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 2.71/1.49 & ( Xa
% 2.71/1.49 = ( coinductive_LCons @ A @ Xb @ Ys2 ) )
% 2.71/1.49 & ( ( X6 @ Xs5 @ Ys2 )
% 2.71/1.49 | ( coinductive_llexord @ A @ R @ Xs5 @ Ys2 ) ) )
% 2.71/1.49 | ? [Xb: A,Y5: A,Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 2.71/1.49 & ( Xa
% 2.71/1.49 = ( coinductive_LCons @ A @ Y5 @ Ys2 ) )
% 2.71/1.49 & ( R @ Xb @ Y5 ) )
% 2.71/1.49 | ? [Ys2: coinductive_llist @ A] :
% 2.71/1.49 ( ( X2
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 & ( Xa = Ys2 ) ) ) )
% 2.71/1.49 => ( coinductive_llexord @ A @ R @ X @ Xa3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_217_llexord_Osimps,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( coinductive_llexord @ A )
% 2.71/1.49 = ( ^ [R2: A > A > $o,A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 2.71/1.49 ( ? [Xs4: coinductive_llist @ A,Ys5: coinductive_llist @ A,X5: A] :
% 2.71/1.49 ( ( A12
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 2.71/1.49 & ( A23
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ Ys5 ) )
% 2.71/1.49 & ( coinductive_llexord @ A @ R2 @ Xs4 @ Ys5 ) )
% 2.71/1.49 | ? [X5: A,Y3: A,Xs4: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 2.71/1.49 ( ( A12
% 2.71/1.49 = ( coinductive_LCons @ A @ X5 @ Xs4 ) )
% 2.71/1.49 & ( A23
% 2.71/1.49 = ( coinductive_LCons @ A @ Y3 @ Ys5 ) )
% 2.71/1.49 & ( R2 @ X5 @ Y3 ) )
% 2.71/1.49 | ? [Ys5: coinductive_llist @ A] :
% 2.71/1.49 ( ( A12
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 & ( A23 = Ys5 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_218_llexord_Ocases,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_llexord @ A @ R @ A1 @ A22 )
% 2.71/1.49 => ( ! [Xs2: coinductive_llist @ A,Ys3: coinductive_llist @ A,X2: A] :
% 2.71/1.49 ( ( A1
% 2.71/1.49 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 2.71/1.49 => ( ( A22
% 2.71/1.49 = ( coinductive_LCons @ A @ X2 @ Ys3 ) )
% 2.71/1.49 => ~ ( coinductive_llexord @ A @ R @ Xs2 @ Ys3 ) ) )
% 2.71/1.49 => ( ! [X2: A] :
% 2.71/1.49 ( ? [Xs2: coinductive_llist @ A] :
% 2.71/1.49 ( A1
% 2.71/1.49 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 2.71/1.49 => ! [Y4: A] :
% 2.71/1.49 ( ? [Ys3: coinductive_llist @ A] :
% 2.71/1.49 ( A22
% 2.71/1.49 = ( coinductive_LCons @ A @ Y4 @ Ys3 ) )
% 2.71/1.49 => ~ ( R @ X2 @ Y4 ) ) )
% 2.71/1.49 => ~ ( ( A1
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 => ! [Ys3: coinductive_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_219_llexord__code_I2_J,axiom,
% 2.71/1.49 ! [A: $tType,R: A > A > $o,X: A,Xs3: coinductive_llist @ A] :
% 2.71/1.49 ~ ( coinductive_llexord @ A @ R @ ( coinductive_LCons @ A @ X @ Xs3 ) @ ( coinductive_LNil @ A ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_220_gen__lset__def,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( coinductive_gen_lset @ A )
% 2.71/1.49 = ( ^ [A5: set @ A,Xs4: coinductive_llist @ A] : ( sup_sup @ ( set @ A ) @ A5 @ ( coinductive_lset @ A @ Xs4 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_221_lset__lappend,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( ord_less_eq @ ( set @ A ) @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) ) @ ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_222_lset__lappend__conv,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs3 ) @ ( coinductive_lset @ A @ Ys ) ) ) )
% 2.71/1.49 & ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( coinductive_lset @ A @ Xs3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_223_llexord__lappend__left,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,R: A > A > $o,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 => ( ! [X2: A] :
% 2.71/1.49 ( ( member @ A @ X2 @ ( coinductive_lset @ A @ Xs3 ) )
% 2.71/1.49 => ~ ( R @ X2 @ X2 ) )
% 2.71/1.49 => ( ( coinductive_llexord @ A @ R @ ( coinductive_lappend @ A @ Xs3 @ Ys ) @ ( coinductive_lappend @ A @ Xs3 @ Zs2 ) )
% 2.71/1.49 = ( coinductive_llexord @ A @ R @ Ys @ Zs2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_224_le__sup__iff,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A,Z: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.71/1.49 = ( ( ord_less_eq @ A @ X @ Z )
% 2.71/1.49 & ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_225_sup_Obounded__iff,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,C2: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 )
% 2.71/1.49 = ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 & ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_226_sup_OcoboundedI2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [C2: A,B3: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ C2 @ B3 )
% 2.71/1.49 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_227_inf__sup__ord_I4_J,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( lattice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_228_inf__sup__ord_I3_J,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( lattice @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_229_le__supE,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X )
% 2.71/1.49 => ~ ( ( ord_less_eq @ A @ A2 @ X )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ B3 @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_230_le__supI,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,X: A,B3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ X )
% 2.71/1.49 => ( ( ord_less_eq @ A @ B3 @ X )
% 2.71/1.49 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_231_sup__ge1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] : ( ord_less_eq @ A @ X @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_232_sup__ge2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A] : ( ord_less_eq @ A @ Y @ ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_233_le__supI1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,A2: A,B3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ A2 )
% 2.71/1.49 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_234_le__supI2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,B3: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ B3 )
% 2.71/1.49 => ( ord_less_eq @ A @ X @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_235_sup_Omono,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [C2: A,A2: A,D2: A,B3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ C2 @ A2 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ D2 @ B3 )
% 2.71/1.49 => ( ord_less_eq @ A @ ( sup_sup @ A @ C2 @ D2 ) @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_236_sup__mono,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,C2: A,B3: A,D2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ C2 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ B3 @ D2 )
% 2.71/1.49 => ( ord_less_eq @ A @ ( sup_sup @ A @ A2 @ B3 ) @ ( sup_sup @ A @ C2 @ D2 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_237_sup__least,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A,Z: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Z @ X )
% 2.71/1.49 => ( ord_less_eq @ A @ ( sup_sup @ A @ Y @ Z ) @ X ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_238_le__iff__sup,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( ( ord_less_eq @ A )
% 2.71/1.49 = ( ^ [X5: A,Y3: A] :
% 2.71/1.49 ( ( sup_sup @ A @ X5 @ Y3 )
% 2.71/1.49 = Y3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_239_sup_OorderE,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ( A2
% 2.71/1.49 = ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_240_sup_OorderI,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A] :
% 2.71/1.49 ( ( A2
% 2.71/1.49 = ( sup_sup @ A @ A2 @ B3 ) )
% 2.71/1.49 => ( ord_less_eq @ A @ B3 @ A2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_241_sup__unique,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [F: A > A > A,X: A,Y: A] :
% 2.71/1.49 ( ! [X2: A,Y4: A] : ( ord_less_eq @ A @ X2 @ ( F @ X2 @ Y4 ) )
% 2.71/1.49 => ( ! [X2: A,Y4: A] : ( ord_less_eq @ A @ Y4 @ ( F @ X2 @ Y4 ) )
% 2.71/1.49 => ( ! [X2: A,Y4: A,Z3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ Y4 @ X2 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ Z3 @ X2 )
% 2.71/1.49 => ( ord_less_eq @ A @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 2.71/1.49 => ( ( sup_sup @ A @ X @ Y )
% 2.71/1.49 = ( F @ X @ Y ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_242_sup_Oabsorb1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ( ( sup_sup @ A @ A2 @ B3 )
% 2.71/1.49 = A2 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_243_sup_Oabsorb2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ A2 @ B3 )
% 2.71/1.49 => ( ( sup_sup @ A @ A2 @ B3 )
% 2.71/1.49 = B3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_244_sup__absorb1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [Y: A,X: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ Y @ X )
% 2.71/1.49 => ( ( sup_sup @ A @ X @ Y )
% 2.71/1.49 = X ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_245_sup__absorb2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [X: A,Y: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ X @ Y )
% 2.71/1.49 => ( ( sup_sup @ A @ X @ Y )
% 2.71/1.49 = Y ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_246_sup_OboundedE,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,C2: A,A2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 )
% 2.71/1.49 => ~ ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ~ ( ord_less_eq @ A @ C2 @ A2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_247_sup_OboundedI,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,A2: A,C2: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ B3 @ A2 )
% 2.71/1.49 => ( ( ord_less_eq @ A @ C2 @ A2 )
% 2.71/1.49 => ( ord_less_eq @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A2 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_248_sup_Oorder__iff,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( ( ord_less_eq @ A )
% 2.71/1.49 = ( ^ [B6: A,A6: A] :
% 2.71/1.49 ( A6
% 2.71/1.49 = ( sup_sup @ A @ A6 @ B6 ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_249_sup_Ocobounded1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [A2: A,B3: A] : ( ord_less_eq @ A @ A2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_250_sup_Ocobounded2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [B3: A,A2: A] : ( ord_less_eq @ A @ B3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_251_sup_Oabsorb__iff1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( ( ord_less_eq @ A )
% 2.71/1.49 = ( ^ [B6: A,A6: A] :
% 2.71/1.49 ( ( sup_sup @ A @ A6 @ B6 )
% 2.71/1.49 = A6 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_252_sup_Oabsorb__iff2,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ( ( ord_less_eq @ A )
% 2.71/1.49 = ( ^ [A6: A,B6: A] :
% 2.71/1.49 ( ( sup_sup @ A @ A6 @ B6 )
% 2.71/1.49 = B6 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_253_sup_OcoboundedI1,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.71/1.49 => ! [C2: A,A2: A,B3: A] :
% 2.71/1.49 ( ( ord_less_eq @ A @ C2 @ A2 )
% 2.71/1.49 => ( ord_less_eq @ A @ C2 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_254_llexord__conv,axiom,
% 2.71/1.49 ! [A: $tType] :
% 2.71/1.49 ( ( coinductive_llexord @ A )
% 2.71/1.49 = ( ^ [R2: A > A > $o,Xs4: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 2.71/1.49 ( ( Xs4 = Ys5 )
% 2.71/1.49 | ? [Zs3: coinductive_llist @ A,Xs6: coinductive_llist @ A,Y3: A,Ys4: coinductive_llist @ A] :
% 2.71/1.49 ( ( coinductive_lfinite @ A @ Zs3 )
% 2.71/1.49 & ( Xs4
% 2.71/1.49 = ( coinductive_lappend @ A @ Zs3 @ Xs6 ) )
% 2.71/1.49 & ( Ys5
% 2.71/1.49 = ( coinductive_lappend @ A @ Zs3 @ ( coinductive_LCons @ A @ Y3 @ Ys4 ) ) )
% 2.71/1.49 & ( ( Xs6
% 2.71/1.49 = ( coinductive_LNil @ A ) )
% 2.71/1.49 | ( R2 @ ( coinductive_lhd @ A @ Xs6 ) @ Y3 ) ) ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(fact_255_lstrict__prefix__lappend__conv,axiom,
% 2.71/1.49 ! [A: $tType,Xs3: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.71/1.49 ( ( coindu1478340336prefix @ A @ Xs3 @ ( coinductive_lappend @ A @ Xs3 @ Ys ) )
% 2.71/1.49 = ( ( coinductive_lfinite @ A @ Xs3 )
% 2.71/1.49 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 2.71/1.49 ! [A7: $tType,A8: $tType] :
% 2.71/1.49 ( ( comple187826305attice @ A8 @ ( type2 @ A8 ) )
% 2.71/1.49 => ( comple187826305attice @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.71/1.49 ! [A7: $tType,A8: $tType] :
% 2.71/1.49 ( ( semilattice_sup @ A8 @ ( type2 @ A8 ) )
% 2.71/1.49 => ( semilattice_sup @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.71/1.49 ! [A7: $tType,A8: $tType] :
% 2.71/1.49 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 2.71/1.49 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.71/1.49 ! [A7: $tType,A8: $tType] :
% 2.71/1.49 ( ( lattice @ A8 @ ( type2 @ A8 ) )
% 2.71/1.49 => ( lattice @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.71/1.49 ! [A7: $tType,A8: $tType] :
% 2.71/1.49 ( ( order @ A8 @ ( type2 @ A8 ) )
% 2.71/1.49 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_fun___Orderings_Oord,axiom,
% 2.71/1.49 ! [A7: $tType,A8: $tType] :
% 2.71/1.49 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 2.71/1.49 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_1,axiom,
% 2.71/1.49 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_2,axiom,
% 2.71/1.49 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_Set_Oset___Orderings_Opreorder_3,axiom,
% 2.71/1.49 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_Set_Oset___Lattices_Olattice_4,axiom,
% 2.71/1.49 ! [A7: $tType] : ( lattice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.71/1.49 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 2.71/1.49 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_7,axiom,
% 2.71/1.49 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_8,axiom,
% 2.71/1.49 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Orderings_Opreorder_9,axiom,
% 2.71/1.49 preorder @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.71/1.49 linorder @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Lattices_Olattice_10,axiom,
% 2.71/1.49 lattice @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 2.71/1.49 order @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 2.71/1.49 ord @ $o @ ( type2 @ $o ) ).
% 2.71/1.49
% 2.71/1.49 thf(help_If_3_1_T,axiom,
% 2.71/1.49 ! [P: $o] :
% 2.71/1.49 ( ( P = $true )
% 2.71/1.49 | ( P = $false ) ) ).
% 2.71/1.49
% 2.71/1.49 thf(help_If_2_1_T,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Y: A] :
% 2.71/1.49 ( ( if @ A @ $false @ X @ Y )
% 2.71/1.49 = Y ) ).
% 2.71/1.49
% 2.71/1.49 thf(help_If_1_1_T,axiom,
% 2.71/1.49 ! [A: $tType,X: A,Y: A] :
% 2.71/1.49 ( ( if @ A @ $true @ X @ Y )
% 2.71/1.49 = X ) ).
% 2.71/1.49
% 2.71/1.49 thf(conj_0,conjecture,
% 2.71/1.49 member @ a @ n2 @ ns ).
% 2.71/1.49 ------------------------
% 2.91/1.52 % (21152)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/183Mi)
% 2.91/1.53 % (21154)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_21052 for (2999ds/27Mi)
% 2.91/1.53 % (21155)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/2Mi)
% 2.91/1.53 % (21157)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_21052 for (2999ds/275Mi)
% 2.91/1.53 % (21158)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/18Mi)
% 2.91/1.53 % (21156)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_21052 for (2999ds/2Mi)
% 2.91/1.53 % (21155)Instruction limit reached!
% 2.91/1.53 % (21155)------------------------------
% 2.91/1.53 % (21155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.53 % (21155)Termination reason: Unknown
% 2.91/1.53 % (21155)Termination phase: shuffling
% 2.91/1.53 % (21156)Instruction limit reached!
% 2.91/1.53 % (21156)------------------------------
% 2.91/1.53 % (21156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.53
% 2.91/1.53 % (21155)Memory used [KB]: 1407
% 2.91/1.53 % (21155)Time elapsed: 0.003 s
% 2.91/1.53 % (21155)Instructions burned: 3 (million)
% 2.91/1.53 % (21155)------------------------------
% 2.91/1.53 % (21155)------------------------------
% 2.91/1.53 % (21156)Termination reason: Unknown
% 2.91/1.53 % (21156)Termination phase: shuffling
% 2.91/1.53
% 2.91/1.53 % (21156)Memory used [KB]: 1407
% 2.91/1.53 % (21156)Time elapsed: 0.003 s
% 2.91/1.53 % (21156)Instructions burned: 3 (million)
% 2.91/1.53 % (21156)------------------------------
% 2.91/1.53 % (21156)------------------------------
% 2.91/1.53 % (21153)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_21052 for (2999ds/4Mi)
% 2.91/1.54 % (21153)Instruction limit reached!
% 2.91/1.54 % (21153)------------------------------
% 2.91/1.54 % (21153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.54 % (21153)Termination reason: Unknown
% 2.91/1.54 % (21153)Termination phase: shuffling
% 2.91/1.54
% 2.91/1.54 % (21153)Memory used [KB]: 1407
% 2.91/1.54 % (21153)Time elapsed: 0.004 s
% 2.91/1.54 % (21153)Instructions burned: 5 (million)
% 2.91/1.54 % (21153)------------------------------
% 2.91/1.54 % (21153)------------------------------
% 2.91/1.54 % (21158)Instruction limit reached!
% 2.91/1.54 % (21158)------------------------------
% 2.91/1.54 % (21158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.54 % (21158)Termination reason: Unknown
% 2.91/1.54 % (21158)Termination phase: shuffling
% 2.91/1.54
% 2.91/1.54 % (21158)Memory used [KB]: 1791
% 2.91/1.54 % (21158)Time elapsed: 0.011 s
% 2.91/1.54 % (21158)Instructions burned: 19 (million)
% 2.91/1.54 % (21158)------------------------------
% 2.91/1.54 % (21158)------------------------------
% 2.91/1.54 % (21154)Instruction limit reached!
% 2.91/1.54 % (21154)------------------------------
% 2.91/1.54 % (21154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.54 % (21154)Termination reason: Unknown
% 2.91/1.54 % (21154)Termination phase: shuffling
% 2.91/1.54
% 2.91/1.54 % (21154)Memory used [KB]: 1918
% 2.91/1.54 % (21154)Time elapsed: 0.015 s
% 2.91/1.54 % (21154)Instructions burned: 27 (million)
% 2.91/1.54 % (21154)------------------------------
% 2.91/1.54 % (21154)------------------------------
% 2.91/1.55 % (21159)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/3Mi)
% 2.91/1.55 % (21160)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_21052 for (2999ds/37Mi)
% 2.91/1.55 % (21159)Instruction limit reached!
% 2.91/1.55 % (21159)------------------------------
% 2.91/1.55 % (21159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.55 % (21159)Termination reason: Unknown
% 2.91/1.55 % (21159)Termination phase: shuffling
% 2.91/1.55
% 2.91/1.55 % (21159)Memory used [KB]: 1407
% 2.91/1.55 % (21159)Time elapsed: 0.003 s
% 2.91/1.55 % (21159)Instructions burned: 4 (million)
% 2.91/1.55 % (21159)------------------------------
% 2.91/1.55 % (21159)------------------------------
% 2.91/1.55 % (21161)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_21052 for (2999ds/15Mi)
% 2.91/1.55 % (21162)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_21052 for (2999ds/3Mi)
% 2.91/1.56 % (21157)Refutation not found, incomplete strategy
% 2.91/1.56 % (21157)------------------------------
% 2.91/1.56 % (21157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.56 % (21157)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.56
% 2.91/1.56
% 2.91/1.56 % (21157)Memory used [KB]: 6524
% 2.91/1.56 % (21157)Time elapsed: 0.028 s
% 2.91/1.56 % (21157)Instructions burned: 55 (million)
% 2.91/1.56 % (21157)------------------------------
% 2.91/1.56 % (21157)------------------------------
% 2.91/1.56 % (21162)Instruction limit reached!
% 2.91/1.56 % (21162)------------------------------
% 2.91/1.56 % (21162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.56 % (21162)Termination reason: Unknown
% 2.91/1.56 % (21162)Termination phase: shuffling
% 2.91/1.56
% 2.91/1.56 % (21162)Memory used [KB]: 1407
% 2.91/1.56 % (21162)Time elapsed: 0.003 s
% 2.91/1.56 % (21162)Instructions burned: 3 (million)
% 2.91/1.56 % (21162)------------------------------
% 2.91/1.56 % (21162)------------------------------
% 2.91/1.56 % (21163)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_21052 for (2999ds/1041Mi)
% 2.91/1.56 % (21161)Instruction limit reached!
% 2.91/1.56 % (21161)------------------------------
% 2.91/1.56 % (21161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.56 % (21161)Termination reason: Unknown
% 2.91/1.56 % (21161)Termination phase: shuffling
% 2.91/1.56
% 2.91/1.56 % (21161)Memory used [KB]: 1663
% 2.91/1.56 % (21161)Time elapsed: 0.009 s
% 2.91/1.56 % (21161)Instructions burned: 15 (million)
% 2.91/1.56 % (21161)------------------------------
% 2.91/1.56 % (21161)------------------------------
% 2.91/1.57 % (21160)Instruction limit reached!
% 2.91/1.57 % (21160)------------------------------
% 2.91/1.57 % (21160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (21160)Termination reason: Unknown
% 2.91/1.57 % (21160)Termination phase: shuffling
% 2.91/1.57
% 2.91/1.57 % (21160)Memory used [KB]: 2174
% 2.91/1.57 % (21160)Time elapsed: 0.019 s
% 2.91/1.57 % (21160)Instructions burned: 38 (million)
% 2.91/1.57 % (21160)------------------------------
% 2.91/1.57 % (21160)------------------------------
% 2.91/1.57 % (21164)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/7Mi)
% 2.91/1.57 % (21164)Instruction limit reached!
% 2.91/1.57 % (21164)------------------------------
% 2.91/1.57 % (21164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (21164)Termination reason: Unknown
% 2.91/1.57 % (21164)Termination phase: shuffling
% 2.91/1.57
% 2.91/1.57 % (21164)Memory used [KB]: 1535
% 2.91/1.57 % (21164)Time elapsed: 0.005 s
% 2.91/1.57 % (21164)Instructions burned: 8 (million)
% 2.91/1.57 % (21164)------------------------------
% 2.91/1.57 % (21164)------------------------------
% 2.91/1.57 % (21165)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/16Mi)
% 2.91/1.57 % (21166)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_21052 for (2999ds/3Mi)
% 2.91/1.57 % (21166)Instruction limit reached!
% 2.91/1.57 % (21166)------------------------------
% 2.91/1.57 % (21166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (21166)Termination reason: Unknown
% 2.91/1.57 % (21152)Instruction limit reached!
% 2.91/1.57 % (21152)------------------------------
% 2.91/1.57 % (21152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.57 % (21152)Termination reason: Unknown
% 2.91/1.57 % (21152)Termination phase: Saturation
% 2.91/1.57
% 2.91/1.57 % (21152)Memory used [KB]: 7291
% 2.91/1.57 % (21152)Time elapsed: 0.053 s
% 2.91/1.57 % (21152)Instructions burned: 185 (million)
% 2.91/1.57 % (21152)------------------------------
% 2.91/1.57 % (21152)------------------------------
% 2.91/1.57 % (21166)Termination phase: shuffling
% 2.91/1.57
% 2.91/1.57 % (21166)Memory used [KB]: 1407
% 2.91/1.57 % (21166)Time elapsed: 0.003 s
% 2.91/1.57 % (21166)Instructions burned: 4 (million)
% 2.91/1.57 % (21166)------------------------------
% 2.91/1.57 % (21166)------------------------------
% 2.91/1.58 % (21167)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_21052 for (2999ds/3Mi)
% 2.91/1.58 % (21167)Instruction limit reached!
% 2.91/1.58 % (21167)------------------------------
% 2.91/1.58 % (21167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.58 % (21167)Termination reason: Unknown
% 2.91/1.58 % (21167)Termination phase: shuffling
% 2.91/1.58
% 2.91/1.58 % (21167)Memory used [KB]: 1407
% 2.91/1.58 % (21167)Time elapsed: 0.003 s
% 2.91/1.58 % (21167)Instructions burned: 3 (million)
% 2.91/1.58 % (21167)------------------------------
% 2.91/1.58 % (21167)------------------------------
% 2.91/1.58 % (21165)Instruction limit reached!
% 2.91/1.58 % (21165)------------------------------
% 2.91/1.58 % (21165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.58 % (21165)Termination reason: Unknown
% 2.91/1.58 % (21165)Termination phase: shuffling
% 2.91/1.58
% 2.91/1.58 % (21165)Memory used [KB]: 1791
% 2.91/1.58 % (21165)Time elapsed: 0.010 s
% 2.91/1.58 % (21165)Instructions burned: 17 (million)
% 2.91/1.58 % (21165)------------------------------
% 2.91/1.58 % (21165)------------------------------
% 2.91/1.58 % (21169)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/3Mi)
% 2.91/1.58 % (21168)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/7Mi)
% 2.91/1.58 % (21169)Instruction limit reached!
% 2.91/1.58 % (21169)------------------------------
% 2.91/1.58 % (21169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.58 % (21169)Termination reason: Unknown
% 2.91/1.58 % (21169)Termination phase: shuffling
% 2.91/1.58
% 2.91/1.58 % (21169)Memory used [KB]: 1407
% 2.91/1.58 % (21169)Time elapsed: 0.002 s
% 2.91/1.58 % (21169)Instructions burned: 3 (million)
% 2.91/1.58 % (21169)------------------------------
% 2.91/1.58 % (21169)------------------------------
% 2.91/1.59 % (21168)Instruction limit reached!
% 2.91/1.59 % (21168)------------------------------
% 2.91/1.59 % (21168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.59 % (21168)Termination reason: Unknown
% 2.91/1.59 % (21168)Termination phase: shuffling
% 2.91/1.59
% 2.91/1.59 % (21168)Memory used [KB]: 1535
% 2.91/1.59 % (21168)Time elapsed: 0.005 s
% 2.91/1.59 % (21168)Instructions burned: 7 (million)
% 2.91/1.59 % (21168)------------------------------
% 2.91/1.59 % (21168)------------------------------
% 2.91/1.59 % (21170)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/4Mi)
% 2.91/1.59 % (21171)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/18Mi)
% 2.91/1.59 % (21170)Instruction limit reached!
% 2.91/1.59 % (21170)------------------------------
% 2.91/1.59 % (21170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.59 % (21170)Termination reason: Unknown
% 2.91/1.59 % (21170)Termination phase: shuffling
% 2.91/1.59
% 2.91/1.59 % (21170)Memory used [KB]: 1407
% 2.91/1.59 % (21170)Time elapsed: 0.003 s
% 2.91/1.59 % (21170)Instructions burned: 4 (million)
% 2.91/1.59 % (21170)------------------------------
% 2.91/1.59 % (21170)------------------------------
% 2.91/1.59 % (21172)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/710Mi)
% 2.91/1.59 % (21174)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_21052 for (2999ds/902Mi)
% 2.91/1.60 % (21173)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/6Mi)
% 2.91/1.60 % (21173)Instruction limit reached!
% 2.91/1.60 % (21173)------------------------------
% 2.91/1.60 % (21173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (21173)Termination reason: Unknown
% 2.91/1.60 % (21173)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (21173)Memory used [KB]: 1535
% 2.91/1.60 % (21173)Time elapsed: 0.004 s
% 2.91/1.60 % (21173)Instructions burned: 6 (million)
% 2.91/1.60 % (21173)------------------------------
% 2.91/1.60 % (21173)------------------------------
% 2.91/1.60 % (21171)Instruction limit reached!
% 2.91/1.60 % (21171)------------------------------
% 2.91/1.60 % (21171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (21171)Termination reason: Unknown
% 2.91/1.60 % (21171)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (21171)Memory used [KB]: 1791
% 2.91/1.60 % (21171)Time elapsed: 0.011 s
% 2.91/1.60 % (21171)Instructions burned: 19 (million)
% 2.91/1.60 % (21171)------------------------------
% 2.91/1.60 % (21171)------------------------------
% 2.91/1.60 % (21175)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_21052 for (2999ds/21Mi)
% 2.91/1.61 % (21176)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21052 for (2999ds/5Mi)
% 2.91/1.61 % (21176)Instruction limit reached!
% 2.91/1.61 % (21176)------------------------------
% 2.91/1.61 % (21176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.61 % (21176)Termination reason: Unknown
% 2.91/1.61 % (21176)Termination phase: shuffling
% 2.91/1.61
% 2.91/1.61 % (21176)Memory used [KB]: 1407
% 2.91/1.61 % (21176)Time elapsed: 0.004 s
% 2.91/1.61 % (21176)Instructions burned: 6 (million)
% 2.91/1.61 % (21176)------------------------------
% 2.91/1.61 % (21176)------------------------------
% 2.91/1.61 % (21175)Instruction limit reached!
% 2.91/1.61 % (21175)------------------------------
% 2.91/1.61 % (21175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.61 % (21175)Termination reason: Unknown
% 2.91/1.61 % (21175)Termination phase: shuffling
% 2.91/1.61
% 2.91/1.61 % (21175)Memory used [KB]: 1791
% 2.91/1.61 % (21175)Time elapsed: 0.012 s
% 2.91/1.61 % (21175)Instructions burned: 21 (million)
% 2.91/1.61 % (21175)------------------------------
% 2.91/1.61 % (21175)------------------------------
% 2.91/1.62 % (21177)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_21052 for (2998ds/6Mi)
% 2.91/1.62 % (21178)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/377Mi)
% 2.91/1.62 % (21177)Instruction limit reached!
% 2.91/1.62 % (21177)------------------------------
% 2.91/1.62 % (21177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.62 % (21177)Termination reason: Unknown
% 2.91/1.62 % (21177)Termination phase: shuffling
% 2.91/1.62
% 2.91/1.62 % (21177)Memory used [KB]: 1407
% 2.91/1.62 % (21177)Time elapsed: 0.004 s
% 2.91/1.62 % (21177)Instructions burned: 6 (million)
% 2.91/1.62 % (21177)------------------------------
% 2.91/1.62 % (21177)------------------------------
% 2.91/1.63 % (21179)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_21052 for (2998ds/779Mi)
% 2.91/1.63 % (21180)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_21052 for (2998ds/19Mi)
% 2.91/1.63 % (21181)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/879Mi)
% 2.91/1.64 % (21180)Instruction limit reached!
% 2.91/1.64 % (21180)------------------------------
% 2.91/1.64 % (21180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (21180)Termination reason: Unknown
% 2.91/1.64 % (21180)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (21180)Memory used [KB]: 1663
% 2.91/1.64 % (21180)Time elapsed: 0.010 s
% 2.91/1.64 % (21180)Instructions burned: 19 (million)
% 2.91/1.64 % (21180)------------------------------
% 2.91/1.64 % (21180)------------------------------
% 2.91/1.65 % (21182)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/17Mi)
% 2.91/1.66 % (21174)Refutation not found, incomplete strategy
% 2.91/1.66 % (21174)------------------------------
% 2.91/1.66 % (21174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (21174)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.66
% 2.91/1.66
% 2.91/1.66 % (21174)Memory used [KB]: 7419
% 2.91/1.66 % (21174)Time elapsed: 0.070 s
% 2.91/1.66 % (21174)Instructions burned: 154 (million)
% 2.91/1.66 % (21174)------------------------------
% 2.91/1.66 % (21174)------------------------------
% 2.91/1.66 % (21182)Instruction limit reached!
% 2.91/1.66 % (21182)------------------------------
% 2.91/1.66 % (21182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (21182)Termination reason: Unknown
% 2.91/1.66 % (21182)Termination phase: shuffling
% 2.91/1.66
% 2.91/1.66 % (21182)Memory used [KB]: 1791
% 2.91/1.66 % (21182)Time elapsed: 0.010 s
% 2.91/1.66 % (21182)Instructions burned: 18 (million)
% 2.91/1.66 % (21182)------------------------------
% 2.91/1.66 % (21182)------------------------------
% 2.91/1.68 % (21183)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/3Mi)
% 2.91/1.68 % (21184)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/30Mi)
% 2.91/1.68 % (21183)Instruction limit reached!
% 2.91/1.68 % (21183)------------------------------
% 2.91/1.68 % (21183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.68 % (21183)Termination reason: Unknown
% 2.91/1.68 % (21183)Termination phase: shuffling
% 2.91/1.68
% 2.91/1.68 % (21183)Memory used [KB]: 1407
% 2.91/1.68 % (21183)Time elapsed: 0.003 s
% 2.91/1.68 % (21183)Instructions burned: 3 (million)
% 2.91/1.68 % (21183)------------------------------
% 2.91/1.68 % (21183)------------------------------
% 2.91/1.70 % (21184)Instruction limit reached!
% 2.91/1.70 % (21184)------------------------------
% 2.91/1.70 % (21184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.70 % (21184)Termination reason: Unknown
% 2.91/1.70 % (21184)Termination phase: Property scanning
% 2.91/1.70
% 2.91/1.70 % (21184)Memory used [KB]: 1918
% 2.91/1.70 % (21184)Time elapsed: 0.017 s
% 2.91/1.70 % (21184)Instructions burned: 30 (million)
% 2.91/1.70 % (21184)------------------------------
% 2.91/1.70 % (21184)------------------------------
% 2.91/1.70 % (21185)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/127Mi)
% 2.91/1.71 % (21186)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21052 for (2998ds/100Mi)
% 2.91/1.74 % (21186)Instruction limit reached!
% 2.91/1.74 % (21186)------------------------------
% 2.91/1.74 % (21186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.74 % (21186)Termination reason: Unknown
% 2.91/1.74 % (21186)Termination phase: Property scanning
% 2.91/1.74
% 2.91/1.74 % (21186)Memory used [KB]: 2302
% 2.91/1.74 % (21186)Time elapsed: 0.029 s
% 2.91/1.74 % (21186)Instructions burned: 103 (million)
% 2.91/1.74 % (21186)------------------------------
% 2.91/1.74 % (21186)------------------------------
% 2.91/1.75 % (21187)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_21052 for (2997ds/3Mi)
% 2.91/1.75 % (21187)Instruction limit reached!
% 2.91/1.75 % (21187)------------------------------
% 2.91/1.75 % (21187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.75 % (21187)Termination reason: Unknown
% 2.91/1.75 % (21187)Termination phase: shuffling
% 2.91/1.75
% 2.91/1.75 % (21187)Memory used [KB]: 1407
% 2.91/1.75 % (21187)Time elapsed: 0.003 s
% 2.91/1.75 % (21187)Instructions burned: 6 (million)
% 2.91/1.75 % (21187)------------------------------
% 2.91/1.75 % (21187)------------------------------
% 2.91/1.76 % (21185)Instruction limit reached!
% 2.91/1.76 % (21185)------------------------------
% 2.91/1.76 % (21185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.76 % (21185)Termination reason: Unknown
% 2.91/1.76 % (21185)Termination phase: Property scanning
% 2.91/1.76
% 2.91/1.76 % (21185)Memory used [KB]: 2430
% 2.91/1.76 % (21185)Time elapsed: 0.060 s
% 2.91/1.76 % (21185)Instructions burned: 127 (million)
% 2.91/1.76 % (21185)------------------------------
% 2.91/1.76 % (21185)------------------------------
% 2.91/1.76 % (21188)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_21052 for (2997ds/20Mi)
% 2.91/1.77 % (21188)Instruction limit reached!
% 2.91/1.77 % (21188)------------------------------
% 2.91/1.77 % (21188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.77 % (21188)Termination reason: Unknown
% 2.91/1.77 % (21188)Termination phase: shuffling
% 2.91/1.77
% 2.91/1.77 % (21188)Memory used [KB]: 1791
% 2.91/1.77 % (21188)Time elapsed: 0.008 s
% 2.91/1.77 % (21188)Instructions burned: 21 (million)
% 2.91/1.77 % (21188)------------------------------
% 2.91/1.77 % (21188)------------------------------
% 2.91/1.77 % (21189)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_21052 for (2997ds/86Mi)
% 2.91/1.78 % (21190)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_21052 for (2997ds/107Mi)
% 2.91/1.78 % (21178)Instruction limit reached!
% 2.91/1.78 % (21178)------------------------------
% 2.91/1.78 % (21178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.78 % (21178)Termination reason: Unknown
% 2.91/1.78 % (21178)Termination phase: Saturation
% 2.91/1.78
% 2.91/1.78 % (21178)Memory used [KB]: 7931
% 2.91/1.78 % (21178)Time elapsed: 0.170 s
% 2.91/1.78 % (21178)Instructions burned: 377 (million)
% 2.91/1.78 % (21178)------------------------------
% 2.91/1.78 % (21178)------------------------------
% 2.91/1.80 % (21191)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_21052 for (2997ds/39Mi)
% 2.91/1.81 % (21190)Instruction limit reached!
% 2.91/1.81 % (21190)------------------------------
% 2.91/1.81 % (21190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.81 % (21190)Termination reason: Unknown
% 2.91/1.81 % (21190)Termination phase: Saturation
% 2.91/1.81
% 2.91/1.81 % (21190)Memory used [KB]: 6780
% 2.91/1.81 % (21190)Time elapsed: 0.032 s
% 2.91/1.81 % (21190)Instructions burned: 107 (million)
% 2.91/1.81 % (21190)------------------------------
% 2.91/1.81 % (21190)------------------------------
% 2.91/1.81 % (21189)Instruction limit reached!
% 2.91/1.81 % (21189)------------------------------
% 2.91/1.81 % (21189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.81 % (21189)Termination reason: Unknown
% 2.91/1.81 % (21189)Termination phase: Function definition elimination
% 2.91/1.81
% 2.91/1.81 % (21189)Memory used [KB]: 2302
% 2.91/1.81 % (21189)Time elapsed: 0.043 s
% 2.91/1.81 % (21189)Instructions burned: 87 (million)
% 2.91/1.81 % (21189)------------------------------
% 2.91/1.81 % (21189)------------------------------
% 2.91/1.82 % (21192)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_21052 for (2996ds/448Mi)
% 2.91/1.82 % (21191)Instruction limit reached!
% 2.91/1.82 % (21191)------------------------------
% 2.91/1.82 % (21191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.82 % (21191)Termination reason: Unknown
% 2.91/1.82 % (21191)Termination phase: shuffling
% 2.91/1.82
% 2.91/1.82 % (21191)Memory used [KB]: 2174
% 2.91/1.82 % (21191)Time elapsed: 0.019 s
% 2.91/1.82 % (21191)Instructions burned: 39 (million)
% 2.91/1.82 % (21191)------------------------------
% 2.91/1.82 % (21191)------------------------------
% 2.91/1.83 % (21193)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_21052 for (2996ds/46Mi)
% 2.91/1.83 % (21194)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_21052 for (2996ds/98Mi)
% 2.91/1.85 % (21193)Instruction limit reached!
% 2.91/1.85 % (21193)------------------------------
% 2.91/1.85 % (21193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.85 % (21193)Termination reason: Unknown
% 2.91/1.85 % (21193)Termination phase: SInE selection
% 2.91/1.85
% 2.91/1.85 % (21193)Memory used [KB]: 2046
% 2.91/1.85 % (21193)Time elapsed: 0.024 s
% 2.91/1.85 % (21193)Instructions burned: 47 (million)
% 2.91/1.85 % (21193)------------------------------
% 2.91/1.85 % (21193)------------------------------
% 2.91/1.88 % (21195)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_21052 for (2996ds/507Mi)
% 2.91/1.88 % (21194)Instruction limit reached!
% 2.91/1.88 % (21194)------------------------------
% 2.91/1.88 % (21194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.88 % (21194)Termination reason: Unknown
% 2.91/1.88 % (21194)Termination phase: Property scanning
% 2.91/1.88
% 2.91/1.88 % (21194)Memory used [KB]: 2302
% 2.91/1.88 % (21194)Time elapsed: 0.045 s
% 2.91/1.88 % (21194)Instructions burned: 99 (million)
% 2.91/1.88 % (21194)------------------------------
% 2.91/1.88 % (21194)------------------------------
% 2.91/1.89 % (21196)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_21052 for (2996ds/149Mi)
% 2.91/1.94 % (21172)Instruction limit reached!
% 2.91/1.94 % (21172)------------------------------
% 2.91/1.94 % (21172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.94 % (21172)Termination reason: Unknown
% 2.91/1.94 % (21172)Termination phase: Saturation
% 2.91/1.94
% 2.91/1.94 % (21172)Memory used [KB]: 8187
% 2.91/1.94 % (21172)Time elapsed: 0.345 s
% 2.91/1.94 % (21172)Instructions burned: 710 (million)
% 2.91/1.94 % (21172)------------------------------
% 2.91/1.94 % (21172)------------------------------
% 2.91/1.95 % (21198)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21052 for (2995ds/39Mi)
% 2.91/1.96 % (21196)Instruction limit reached!
% 2.91/1.96 % (21196)------------------------------
% 2.91/1.96 % (21196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.96 % (21196)Termination reason: Unknown
% 2.91/1.96 % (21196)Termination phase: Saturation
% 2.91/1.96
% 2.91/1.96 % (21196)Memory used [KB]: 7036
% 2.91/1.96 % (21196)Time elapsed: 0.069 s
% 2.91/1.96 % (21196)Instructions burned: 149 (million)
% 2.91/1.96 % (21196)------------------------------
% 2.91/1.96 % (21196)------------------------------
% 2.91/1.97 % (21198)Instruction limit reached!
% 2.91/1.97 % (21198)------------------------------
% 2.91/1.97 % (21198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.97 % (21198)Termination reason: Unknown
% 2.91/1.97 % (21198)Termination phase: Property scanning
% 2.91/1.97
% 2.91/1.97 % (21198)Memory used [KB]: 1918
% 2.91/1.97 % (21198)Time elapsed: 0.021 s
% 2.91/1.97 % (21198)Instructions burned: 39 (million)
% 2.91/1.97 % (21198)------------------------------
% 2.91/1.97 % (21198)------------------------------
% 2.91/1.98 % (21199)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_21052 for (2995ds/6Mi)
% 2.91/1.98 % (21199)Instruction limit reached!
% 2.91/1.98 % (21199)------------------------------
% 2.91/1.98 % (21199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.98 % (21199)Termination reason: Unknown
% 2.91/1.98 % (21199)Termination phase: shuffling
% 2.91/1.98
% 2.91/1.98 % (21199)Memory used [KB]: 1407
% 2.91/1.98 % (21199)Time elapsed: 0.004 s
% 2.91/1.98 % (21199)Instructions burned: 6 (million)
% 2.91/1.98 % (21199)------------------------------
% 2.91/1.98 % (21199)------------------------------
% 2.91/1.99 % (21163)Instruction limit reached!
% 2.91/1.99 % (21163)------------------------------
% 2.91/1.99 % (21163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.99 % (21163)Termination reason: Unknown
% 2.91/1.99 % (21163)Termination phase: Saturation
% 2.91/1.99
% 2.91/1.99 % (21163)Memory used [KB]: 9594
% 2.91/1.99 % (21163)Time elapsed: 0.430 s
% 2.91/1.99 % (21163)Instructions burned: 1043 (million)
% 2.91/1.99 % (21163)------------------------------
% 2.91/1.99 % (21163)------------------------------
% 2.91/1.99 % (21200)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_21052 for (2995ds/1087Mi)
% 2.91/2.00 % (21201)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_21052 for (2995ds/47Mi)
% 2.91/2.00 % (21179)Instruction limit reached!
% 2.91/2.00 % (21179)------------------------------
% 2.91/2.00 % (21179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/2.00 % (21179)Termination reason: Unknown
% 2.91/2.00 % (21179)Termination phase: Saturation
% 2.91/2.00
% 2.91/2.00 % (21179)Memory used [KB]: 8187
% 2.91/2.00 % (21179)Time elapsed: 0.375 s
% 2.91/2.00 % (21179)Instructions burned: 779 (million)
% 2.91/2.00 % (21179)------------------------------
% 2.91/2.00 % (21179)------------------------------
% 2.91/2.00 % (21202)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_21052 for (2995ds/44Mi)
% 2.91/2.02 % (21201)Instruction limit reached!
% 2.91/2.02 % (21201)------------------------------
% 2.91/2.02 % (21201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/2.02 % (21201)Termination reason: Unknown
% 2.91/2.02 % (21201)Termination phase: Naming
% 2.91/2.02
% 2.91/2.02 % (21201)Memory used [KB]: 2174
% 2.91/2.02 % (21201)Time elapsed: 0.025 s
% 2.91/2.02 % (21201)Instructions burned: 47 (million)
% 2.91/2.02 % (21201)------------------------------
% 2.91/2.02 % (21201)------------------------------
% 2.91/2.02 % (21192)Instruction limit reached!
% 2.91/2.02 % (21192)------------------------------
% 2.91/2.02 % (21192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/2.02 % (21192)Termination reason: Unknown
% 2.91/2.02 % (21192)Termination phase: Saturation
% 2.91/2.02
% 2.91/2.02 % (21192)Memory used [KB]: 7931
% 2.91/2.02 % (21192)Time elapsed: 0.218 s
% 2.91/2.02 % (21192)Instructions burned: 448 (million)
% 2.91/2.02 % (21192)------------------------------
% 2.91/2.02 % (21192)------------------------------
% 2.91/2.02 % (21203)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/432Mi)
% 6.29/2.02 % (21202)Instruction limit reached!
% 6.29/2.02 % (21202)------------------------------
% 6.29/2.02 % (21202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.02 % (21202)Termination reason: Unknown
% 6.29/2.02 % (21202)Termination phase: shuffling
% 6.29/2.02
% 6.29/2.02 % (21202)Memory used [KB]: 2174
% 6.29/2.02 % (21202)Time elapsed: 0.022 s
% 6.29/2.02 % (21202)Instructions burned: 44 (million)
% 6.29/2.02 % (21202)------------------------------
% 6.29/2.02 % (21202)------------------------------
% 6.29/2.04 % (21204)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/62Mi)
% 6.29/2.04 % (21205)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/31Mi)
% 6.29/2.04 % (21206)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/96Mi)
% 6.29/2.05 % (21181)Instruction limit reached!
% 6.29/2.05 % (21181)------------------------------
% 6.29/2.05 % (21181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.05 % (21181)Termination reason: Unknown
% 6.29/2.05 % (21181)Termination phase: Saturation
% 6.29/2.05
% 6.29/2.05 % (21181)Memory used [KB]: 7803
% 6.29/2.05 % (21181)Time elapsed: 0.415 s
% 6.29/2.05 % (21181)Instructions burned: 879 (million)
% 6.29/2.05 % (21181)------------------------------
% 6.29/2.05 % (21181)------------------------------
% 6.29/2.05 % (21205)Instruction limit reached!
% 6.29/2.05 % (21205)------------------------------
% 6.29/2.05 % (21205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.05 % (21205)Termination reason: Unknown
% 6.29/2.05 % (21205)Termination phase: Property scanning
% 6.29/2.05
% 6.29/2.05 % (21205)Memory used [KB]: 2046
% 6.29/2.05 % (21205)Time elapsed: 0.018 s
% 6.29/2.05 % (21205)Instructions burned: 32 (million)
% 6.29/2.05 % (21205)------------------------------
% 6.29/2.05 % (21205)------------------------------
% 6.29/2.06 % (21204)Instruction limit reached!
% 6.29/2.06 % (21204)------------------------------
% 6.29/2.06 % (21204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.06 % (21204)Termination reason: Unknown
% 6.29/2.06 % (21207)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/453Mi)
% 6.29/2.06 % (21204)Termination phase: Property scanning
% 6.29/2.06
% 6.29/2.06 % (21204)Memory used [KB]: 2174
% 6.29/2.06 % (21204)Time elapsed: 0.030 s
% 6.29/2.06 % (21204)Instructions burned: 62 (million)
% 6.29/2.06 % (21204)------------------------------
% 6.29/2.06 % (21204)------------------------------
% 6.29/2.07 % (21208)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/71Mi)
% 6.29/2.08 % (21206)Instruction limit reached!
% 6.29/2.08 % (21206)------------------------------
% 6.29/2.08 % (21206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.08 % (21206)Termination reason: Unknown
% 6.29/2.08 % (21206)Termination phase: Property scanning
% 6.29/2.08
% 6.29/2.08 % (21206)Memory used [KB]: 2430
% 6.29/2.08 % (21206)Time elapsed: 0.037 s
% 6.29/2.08 % (21206)Instructions burned: 96 (million)
% 6.29/2.08 % (21206)------------------------------
% 6.29/2.08 % (21206)------------------------------
% 6.29/2.08 % (21209)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/83Mi)
% 6.29/2.09 % (21210)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/11Mi)
% 6.29/2.09 % (21195)Instruction limit reached!
% 6.29/2.09 % (21195)------------------------------
% 6.29/2.09 % (21195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.09 % (21195)Termination reason: Unknown
% 6.29/2.09 % (21195)Termination phase: Saturation
% 6.29/2.09
% 6.29/2.09 % (21195)Memory used [KB]: 8699
% 6.29/2.09 % (21195)Time elapsed: 0.238 s
% 6.29/2.09 % (21195)Instructions burned: 507 (million)
% 6.29/2.09 % (21195)------------------------------
% 6.29/2.09 % (21195)------------------------------
% 6.29/2.09 % (21210)Instruction limit reached!
% 6.29/2.09 % (21210)------------------------------
% 6.29/2.09 % (21210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.09 % (21210)Termination reason: Unknown
% 6.29/2.09 % (21210)Termination phase: shuffling
% 6.29/2.09
% 6.29/2.09 % (21210)Memory used [KB]: 1535
% 6.29/2.09 % (21210)Time elapsed: 0.004 s
% 6.29/2.09 % (21210)Instructions burned: 11 (million)
% 6.29/2.09 % (21210)------------------------------
% 6.29/2.09 % (21210)------------------------------
% 6.29/2.10 % (21212)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/6Mi)
% 6.29/2.10 % (21212)Instruction limit reached!
% 6.29/2.10 % (21212)------------------------------
% 6.29/2.10 % (21212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.10 % (21212)Termination reason: Unknown
% 6.29/2.10 % (21212)Termination phase: shuffling
% 6.29/2.10
% 6.29/2.10 % (21212)Memory used [KB]: 1535
% 6.29/2.10 % (21212)Time elapsed: 0.003 s
% 6.29/2.10 % (21212)Instructions burned: 7 (million)
% 6.29/2.10 % (21212)------------------------------
% 6.29/2.10 % (21212)------------------------------
% 6.29/2.10 % (21211)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_21052 for (2994ds/41Mi)
% 6.29/2.10 % (21208)Instruction limit reached!
% 6.29/2.10 % (21208)------------------------------
% 6.29/2.10 % (21208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.10 % (21208)Termination reason: Unknown
% 6.29/2.10 % (21208)Termination phase: Property scanning
% 6.29/2.10
% 6.29/2.10 % (21208)Memory used [KB]: 2302
% 6.29/2.10 % (21208)Time elapsed: 0.036 s
% 6.29/2.10 % (21208)Instructions burned: 71 (million)
% 6.29/2.10 % (21208)------------------------------
% 6.29/2.10 % (21208)------------------------------
% 6.29/2.11 % (21213)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_21052 for (2993ds/150Mi)
% 6.29/2.12 % (21214)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_21052 for (2993ds/343Mi)
% 6.29/2.12 % (21211)Instruction limit reached!
% 6.29/2.12 % (21211)------------------------------
% 6.29/2.12 % (21211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.12 % (21211)Termination reason: Unknown
% 6.29/2.12 % (21211)Termination phase: shuffling
% 6.29/2.12
% 6.29/2.12 % (21211)Memory used [KB]: 2174
% 6.29/2.12 % (21211)Time elapsed: 0.020 s
% 6.29/2.12 % (21211)Instructions burned: 41 (million)
% 6.29/2.12 % (21211)------------------------------
% 6.29/2.12 % (21211)------------------------------
% 6.29/2.12 % (21209)Instruction limit reached!
% 6.29/2.12 % (21209)------------------------------
% 6.29/2.12 % (21209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.12 % (21209)Termination reason: Unknown
% 6.29/2.12 % (21209)Termination phase: Saturation
% 6.29/2.12
% 6.29/2.12 % (21209)Memory used [KB]: 6652
% 6.29/2.12 % (21209)Time elapsed: 0.042 s
% 6.29/2.12 % (21209)Instructions burned: 83 (million)
% 6.29/2.12 % (21209)------------------------------
% 6.29/2.12 % (21209)------------------------------
% 6.78/2.12 % (21200)First to succeed.
% 6.78/2.13 % (21200)Refutation found. Thanks to Tanya!
% 6.78/2.13 % SZS status Theorem for DTF2THF_21052
% 6.78/2.13 % SZS output start Proof for DTF2THF_21052
% 6.78/2.13 thf(type_def_5, type, itself: ($tType) > $tType).
% 6.78/2.13 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 6.78/2.13 thf(type_def_8, type, set: ($tType) > $tType).
% 6.78/2.13 thf(type_def_9, type, a: $tType).
% 6.78/2.13 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 6.78/2.13 thf(func_def_1, type, set: ($tType) > $tType).
% 6.78/2.13 thf(func_def_2, type, itself: ($tType) > $tType).
% 6.78/2.13 thf(func_def_3, type, a: $tType).
% 6.78/2.13 thf(func_def_4, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_5, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_6, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_7, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_8, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_9, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_10, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_11, type, comple187826305attice: !>[X0: $tType]:(itself @ X0 > $o)).
% 6.78/2.13 thf(func_def_12, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_13, type, coinductive_gen_lset: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ X0)).
% 6.78/2.13 thf(func_def_14, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_15, type, coindu351974385stinct: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_16, type, coinductive_lfilter: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_17, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_18, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 6.78/2.13 thf(func_def_19, type, coinductive_llexord: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_20, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_21, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_22, type, coindu1259883913_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coinductive_llist @ X1) > (X0 > X0) > X0 > coinductive_llist @ X1)).
% 6.78/2.13 thf(func_def_23, type, coinductive_lhd: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 6.78/2.13 thf(func_def_24, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_25, type, coinductive_lset: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0)).
% 6.78/2.13 thf(func_def_26, type, coinductive_lmember: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_27, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_28, type, coindu63249387sorted: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_29, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1)).
% 6.78/2.13 thf(func_def_30, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 6.78/2.13 thf(func_def_31, type, koenig916195507_paths: !>[X0: $tType]:((X0 > X0 > $o) > set @ coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_32, type, koenig2031690877pathsp: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_33, type, koenig317145564le_via: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > X0 > set @ X0)).
% 6.78/2.13 thf(func_def_34, type, koenig1757754772e_viap: !>[X0: $tType]:((X0 > X0 > $o) > set @ X0 > X0 > X0 > $o)).
% 6.78/2.13 thf(func_def_35, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 6.78/2.13 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 6.78/2.13 thf(func_def_37, type, type2: !>[X0: $tType]:(itself @ X0)).
% 6.78/2.13 thf(func_def_38, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 6.78/2.13 thf(func_def_39, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 6.78/2.13 thf(func_def_40, type, graph: a > a > $o).
% 6.78/2.13 thf(func_def_41, type, n: a).
% 6.78/2.13 thf(func_def_42, type, n2: a).
% 6.78/2.13 thf(func_def_43, type, ns: set @ a).
% 6.78/2.13 thf(func_def_44, type, x: a).
% 6.78/2.13 thf(func_def_45, type, xs: coinductive_llist @ a).
% 6.78/2.13 thf(func_def_46, type, xs2: coinductive_llist @ a).
% 6.78/2.13 thf(func_def_65, type, sP0: !>[X0: $tType]:(X0 > (coinductive_llist @ X0 > $o) > $o)).
% 6.78/2.13 thf(func_def_66, type, sP1: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 6.78/2.13 thf(func_def_67, type, sP2: !>[X0: $tType]:(set @ X0 > set @ X0 > (X0 > $o) > $o)).
% 6.78/2.13 thf(func_def_68, type, sP3: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > $o)).
% 6.78/2.13 thf(func_def_69, type, sP4: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > $o)).
% 6.78/2.13 thf(func_def_70, type, sP5: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > $o)).
% 6.78/2.13 thf(func_def_71, type, sP6: !>[X0: $tType]:(X0 > (coinductive_llist @ X0 > $o) > $o)).
% 6.78/2.13 thf(func_def_72, type, sP7: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > $o)).
% 6.78/2.13 thf(func_def_73, type, sP8: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 6.78/2.13 thf(func_def_74, type, sP9: !>[X0: $tType]:(set @ X0 > set @ X0 > (X0 > $o) > $o)).
% 6.78/2.13 thf(func_def_75, type, sP10: !>[X0: $tType]:(set @ X0 > set @ X0 > (X0 > $o) > $o)).
% 6.78/2.13 thf(func_def_76, type, sK11: !>[X0: $tType]:(X0 > (coinductive_llist @ X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_77, type, sK12: !>[X0: $tType]:(X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_78, type, sK13: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_79, type, sK14: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_80, type, sK15: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_81, type, sK16: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_82, type, sK17: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > X0)).
% 6.78/2.13 thf(func_def_83, type, sK18: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_84, type, sK19: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 6.78/2.13 thf(func_def_85, type, sK20: !>[X0: $tType]:(set @ X0 > set @ X0 > (X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_86, type, sK21: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 6.78/2.13 thf(func_def_87, type, sK22: a).
% 6.78/2.13 thf(func_def_88, type, sK23: coinductive_llist @ a).
% 6.78/2.13 thf(func_def_89, type, sK24: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_90, type, sK25: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_91, type, sK26: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_92, type, sK27: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_93, type, sK28: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_94, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 6.78/2.13 thf(func_def_95, type, sK30: coinductive_llist @ a).
% 6.78/2.13 thf(func_def_96, type, sK31: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > X0)).
% 6.78/2.13 thf(func_def_97, type, sK32: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_98, type, sK33: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_99, type, sK34: !>[X0: $tType]:(X0 > (coinductive_llist @ X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_100, type, sK35: !>[X0: $tType]:(X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_101, type, sK36: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_102, type, sK37: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 6.78/2.13 thf(func_def_103, type, sK38: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_104, type, sK39: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 6.78/2.13 thf(func_def_105, type, sK40: !>[X0: $tType]:(set @ X0 > set @ X0 > (X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_106, type, sK41: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 6.78/2.13 thf(func_def_107, type, sK42: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 6.78/2.13 thf(func_def_109, type, ph44: !>[X0: $tType]:(X0)).
% 6.78/2.13 thf(f1459,plain,(
% 6.78/2.13 $false),
% 6.78/2.13 inference(subsumption_resolution,[status(thm)],[f1455,f1008])).
% 6.78/2.13 thf(f1008,plain,(
% 6.78/2.13 ((member @ a @ n2 @ ns) != $true)),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f790])).
% 6.78/2.13 thf(f790,plain,(
% 6.78/2.13 ((member @ a @ n2 @ ns) != $true)),
% 6.78/2.13 inference(flattening,[status(thm)],[f705])).
% 6.78/2.13 thf(f705,plain,(
% 6.78/2.13 ~((member @ a @ n2 @ ns) = $true)),
% 6.78/2.13 inference(fool_elimination,[status(thm)],[f704])).
% 6.78/2.13 thf(f704,plain,(
% 6.78/2.13 ~(member @ a @ n2 @ ns)),
% 6.78/2.13 inference(rectify,[status(thm)],[f280])).
% 6.78/2.13 thf(f280,negated_conjecture,(
% 6.78/2.13 ~(member @ a @ n2 @ ns)),
% 6.78/2.13 inference(negated_conjecture,[status(cth)],[f279])).
% 6.78/2.13 thf(f279,conjecture,(
% 6.78/2.13 (member @ a @ n2 @ ns)),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',conj_0)).
% 6.78/2.13 thf(f1455,plain,(
% 6.78/2.13 ((member @ a @ n2 @ ns) = $true)),
% 6.78/2.13 inference(trivial_inequality_removal,[status(thm)],[f1448])).
% 6.78/2.13 thf(f1448,plain,(
% 6.78/2.13 ($true != $true) | ((member @ a @ n2 @ ns) = $true)),
% 6.78/2.13 inference(superposition,[status(thm)],[f1252,f1002])).
% 6.78/2.13 thf(f1002,plain,(
% 6.78/2.13 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : X0] : (((member @ X0 @ X1 @ (coinductive_lset @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2))) = $true)) )),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f371])).
% 6.78/2.13 thf(f371,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0] : ((member @ X0 @ X1 @ (coinductive_lset @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2))) = $true)),
% 6.78/2.13 inference(fool_elimination,[status(thm)],[f370])).
% 6.78/2.13 thf(f370,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0] : (member @ X0 @ X1 @ (coinductive_lset @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2)))),
% 6.78/2.13 inference(rectify,[status(thm)],[f21])).
% 6.78/2.13 thf(f21,axiom,(
% 6.78/2.13 ! [X0 : $tType,X8 : X0,X10 : coinductive_llist @ X0] : (member @ X0 @ X8 @ (coinductive_lset @ X0 @ (coinductive_LCons @ X0 @ X8 @ X10)))),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',fact_20_lset__intros_I1_J)).
% 6.78/2.13 thf(f1252,plain,(
% 6.78/2.13 ( ! [X0 : a] : (((member @ a @ X0 @ (coinductive_lset @ a @ (coinductive_LCons @ a @ n2 @ xs))) != $true) | ($true = (member @ a @ X0 @ ns))) )),
% 6.78/2.13 inference(trivial_inequality_removal,[status(thm)],[f1250])).
% 6.78/2.13 thf(f1250,plain,(
% 6.78/2.13 ( ! [X0 : a] : (($true = (member @ a @ X0 @ ns)) | ($true != $true) | ((member @ a @ X0 @ (coinductive_lset @ a @ (coinductive_LCons @ a @ n2 @ xs))) != $true)) )),
% 6.78/2.13 inference(superposition,[status(thm)],[f998,f1158])).
% 6.78/2.13 thf(f1158,plain,(
% 6.78/2.13 ($true = (ord_less_eq @ set @ a @ (coinductive_lset @ a @ (coinductive_LCons @ a @ n2 @ xs)) @ ns))),
% 6.78/2.13 inference(forward_demodulation,[status(thm)],[f1157,f1101])).
% 6.78/2.13 thf(f1101,plain,(
% 6.78/2.13 ((coinductive_LCons @ a @ n2 @ xs) = (coinductive_LCons @ a @ n2 @ sK23))),
% 6.78/2.13 inference(backward_demodulation,[status(thm)],[f1065,f1094])).
% 6.78/2.13 thf(f1094,plain,(
% 6.78/2.13 (n2 = sK22)),
% 6.78/2.13 inference(equality_resolution,[status(thm)],[f1076])).
% 6.78/2.13 thf(f1076,plain,(
% 6.78/2.13 ( ! [X0 : a,X1 : coinductive_llist @ a] : (((coinductive_LCons @ a @ n2 @ xs) != (coinductive_LCons @ a @ X0 @ X1)) | (sK22 = X0)) )),
% 6.78/2.13 inference(superposition,[status(thm)],[f965,f1065])).
% 6.78/2.13 thf(f965,plain,(
% 6.78/2.13 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : X0,X1 : X0,X4 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X1 @ X2) != (coinductive_LCons @ X0 @ X3 @ X4)) | (X1 = X3)) )),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f891])).
% 6.78/2.13 thf(f891,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0,X3 : X0,X4 : coinductive_llist @ X0] : ((((coinductive_LCons @ X0 @ X1 @ X2) = (coinductive_LCons @ X0 @ X3 @ X4)) | (X2 != X4) | (X1 != X3)) & (((X2 = X4) & (X1 = X3)) | ((coinductive_LCons @ X0 @ X1 @ X2) != (coinductive_LCons @ X0 @ X3 @ X4))))),
% 6.78/2.13 inference(flattening,[status(thm)],[f890])).
% 6.78/2.13 thf(f890,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0,X3 : X0,X4 : coinductive_llist @ X0] : ((((coinductive_LCons @ X0 @ X1 @ X2) = (coinductive_LCons @ X0 @ X3 @ X4)) | ((X2 != X4) | (X1 != X3))) & (((X2 = X4) & (X1 = X3)) | ((coinductive_LCons @ X0 @ X1 @ X2) != (coinductive_LCons @ X0 @ X3 @ X4))))),
% 6.78/2.13 inference(nnf_transformation,[status(thm)],[f653])).
% 6.78/2.13 thf(f653,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0,X3 : X0,X4 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X1 @ X2) = (coinductive_LCons @ X0 @ X3 @ X4)) <=> ((X2 = X4) & (X1 = X3)))),
% 6.78/2.13 inference(fool_elimination,[status(thm)],[f652])).
% 6.78/2.13 thf(f652,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0,X3 : X0,X4 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X1 @ X2) = (coinductive_LCons @ X0 @ X3 @ X4)) = (X2 = X4) & (X1 = X3))),
% 6.78/2.13 inference(rectify,[status(thm)],[f16])).
% 6.78/2.13 thf(f16,axiom,(
% 6.78/2.13 ! [X0 : $tType,X18 : X0,X19 : coinductive_llist @ X0,X20 : X0,X21 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X18 @ X19) = (coinductive_LCons @ X0 @ X20 @ X21)) = (X19 = X21) & (X18 = X20))),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',fact_15_llist_Oinject)).
% 6.78/2.13 thf(f1065,plain,(
% 6.78/2.13 ((coinductive_LCons @ a @ n2 @ xs) = (coinductive_LCons @ a @ sK22 @ sK23))),
% 6.78/2.13 inference(definition_unfolding,[status(thm)],[f1032,f989])).
% 6.78/2.13 thf(f989,plain,(
% 6.78/2.13 (xs2 = (coinductive_LCons @ a @ sK22 @ sK23))),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f909])).
% 6.78/2.13 thf(f909,plain,(
% 6.78/2.13 (xs2 = (coinductive_LCons @ a @ sK22 @ sK23))),
% 6.78/2.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f828,f908])).
% 6.78/2.13 thf(f908,plain,(
% 6.78/2.13 ? [X0 : a,X1 : coinductive_llist @ a] : (xs2 = (coinductive_LCons @ a @ X0 @ X1)) => (xs2 = (coinductive_LCons @ a @ sK22 @ sK23))),
% 6.78/2.13 introduced(definition,[],[choice_axiom])).
% 6.78/2.13 thf(f828,plain,(
% 6.78/2.13 ? [X0 : a,X1 : coinductive_llist @ a] : (xs2 = (coinductive_LCons @ a @ X0 @ X1))),
% 6.78/2.13 inference(ennf_transformation,[status(thm)],[f805])).
% 6.78/2.13 thf(f805,plain,(
% 6.78/2.13 ~! [X0 : a,X1 : coinductive_llist @ a] : (xs2 != (coinductive_LCons @ a @ X0 @ X1))),
% 6.78/2.13 inference(rectify,[status(thm)],[f2])).
% 6.78/2.13 thf(f2,axiom,(
% 6.78/2.13 ~! [X4 : a,X5 : coinductive_llist @ a] : (xs2 != (coinductive_LCons @ a @ X4 @ X5))),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_H_Axs_H_O_Axs_A_061_ALCons_An_H_Axs_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 6.78/2.13 thf(f1032,plain,(
% 6.78/2.13 (xs2 = (coinductive_LCons @ a @ n2 @ xs))),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f3])).
% 6.78/2.13 thf(f3,axiom,(
% 6.78/2.13 (xs2 = (coinductive_LCons @ a @ n2 @ xs))),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',fact_2_xs)).
% 6.78/2.13 thf(f1157,plain,(
% 6.78/2.13 ((ord_less_eq @ set @ a @ (coinductive_lset @ a @ (coinductive_LCons @ a @ n2 @ sK23)) @ ns) = $true)),
% 6.78/2.13 inference(forward_demodulation,[status(thm)],[f1064,f1094])).
% 6.78/2.13 thf(f1064,plain,(
% 6.78/2.13 ((ord_less_eq @ set @ a @ (coinductive_lset @ a @ (coinductive_LCons @ a @ sK22 @ sK23)) @ ns) = $true)),
% 6.78/2.13 inference(definition_unfolding,[status(thm)],[f1009,f989])).
% 6.78/2.13 thf(f1009,plain,(
% 6.78/2.13 ((ord_less_eq @ set @ a @ (coinductive_lset @ a @ xs2) @ ns) = $true)),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f335])).
% 6.78/2.13 thf(f335,plain,(
% 6.78/2.13 ((ord_less_eq @ set @ a @ (coinductive_lset @ a @ xs2) @ ns) = $true)),
% 6.78/2.13 inference(fool_elimination,[status(thm)],[f334])).
% 6.78/2.13 thf(f334,plain,(
% 6.78/2.13 (ord_less_eq @ set @ a @ (coinductive_lset @ a @ xs2) @ ns)),
% 6.78/2.13 inference(rectify,[status(thm)],[f4])).
% 6.78/2.13 thf(f4,axiom,(
% 6.78/2.13 (ord_less_eq @ set @ a @ (coinductive_lset @ a @ xs2) @ ns)),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',fact_3__092_060open_062lset_Axs_A_092_060subseteq_062_Ans_092_060close_062)).
% 6.78/2.13 thf(f998,plain,(
% 6.78/2.13 ( ! [X0 : $tType,X2 : set @ X0,X3 : X0,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) != $true) | ((member @ X0 @ X3 @ X2) = $true) | ((member @ X0 @ X3 @ X1) != $true)) )),
% 6.78/2.13 inference(cnf_transformation,[status(thm)],[f844])).
% 6.78/2.13 thf(f844,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : (((member @ X0 @ X3 @ X1) != $true) | ((member @ X0 @ X3 @ X2) = $true) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true))),
% 6.78/2.13 inference(flattening,[status(thm)],[f843])).
% 6.78/2.13 thf(f843,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((((member @ X0 @ X3 @ X2) = $true) | ((member @ X0 @ X3 @ X1) != $true)) | ((ord_less_eq @ set @ X0 @ X1 @ X2) != $true))),
% 6.78/2.13 inference(ennf_transformation,[status(thm)],[f525])).
% 6.78/2.13 thf(f525,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : (((ord_less_eq @ set @ X0 @ X1 @ X2) = $true) => (((member @ X0 @ X3 @ X1) = $true) => ((member @ X0 @ X3 @ X2) = $true)))),
% 6.78/2.13 inference(fool_elimination,[status(thm)],[f524])).
% 6.78/2.13 thf(f524,plain,(
% 6.78/2.13 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0,X3 : X0] : ((ord_less_eq @ set @ X0 @ X1 @ X2) => ((member @ X0 @ X3 @ X1) => (member @ X0 @ X3 @ X2)))),
% 6.78/2.13 inference(rectify,[status(thm)],[f70])).
% 6.78/2.13 thf(f70,axiom,(
% 6.78/2.13 ! [X0 : $tType,X22 : set @ X0,X23 : set @ X0,X30 : X0] : ((ord_less_eq @ set @ X0 @ X22 @ X23) => ((member @ X0 @ X30 @ X22) => (member @ X0 @ X30 @ X23)))),
% 6.78/2.13 file('/export/starexec/sandbox/tmp/tmp.G4Ayo7VUgj/DTF2THF_21052.p',fact_69_subsetD)).
% 6.78/2.13 % SZS output end Proof for DTF2THF_21052
% 6.78/2.13 % (21200)------------------------------
% 6.78/2.13 % (21200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.13 % (21200)Termination reason: Refutation
% 6.78/2.13
% 6.78/2.13 % (21200)Memory used [KB]: 7164
% 6.78/2.13 % (21200)Time elapsed: 0.163 s
% 6.78/2.13 % (21200)Instructions burned: 271 (million)
% 6.78/2.13 % (21200)------------------------------
% 6.78/2.13 % (21200)------------------------------
% 6.78/2.13 % (21151)Success in time 0.632 s
%------------------------------------------------------------------------------