%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT230^1 : 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 : n026.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 08:45:13 AM UTC 2026
% Result : Theorem 2.70s 1.62s
% Output : Refutation 2.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT230^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:12:25 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.50 ---- Original DTF file ---
% 0.29/0.50 thf(spec,logic,$$dhol).
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 % File : DAT230^1 : TPTP v9.2.1. Released v7.0.0.
% 0.29/0.50 % Domain : Data Structures
% 0.29/0.50 % Problem : Red-black trees 205
% 0.29/0.50 % Version : [Bla16] axioms : Especial.
% 0.29/0.50 % English :
% 0.29/0.50
% 0.29/0.50 % Refs : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.29/0.50 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.29/0.50 % Source : [Bla16]
% 0.29/0.50 % Names : rbt_impl__205.p [Bla16]
% 0.29/0.50
% 0.29/0.50 % Status : Theorem
% 0.29/0.50 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.29/0.50 % Syntax : Number of formulae : 326 ( 115 unt; 60 typ; 0 def)
% 0.29/0.50 % Number of atoms : 850 ( 338 equ; 0 cnn)
% 0.29/0.50 % Maximal formula atoms : 13 ( 3 avg)
% 0.29/0.50 % Number of connectives : 4324 ( 159 ~; 29 |; 106 &;3713 @)
% 0.29/0.50 % ( 0 <=>; 317 =>; 0 <=; 0 <~>)
% 0.29/0.50 % Maximal formula depth : 23 ( 8 avg)
% 0.29/0.50 % Number of types : 4 ( 3 usr)
% 0.29/0.50 % Number of type conns : 239 ( 239 >; 0 *; 0 +; 0 <<)
% 0.29/0.50 % Number of symbols : 60 ( 57 usr; 7 con; 0-7 aty)
% 0.29/0.50 % Number of variables : 1179 ( 22 ^; 988 !; 107 ?;1179 :)
% 0.29/0.50 % ( 62 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.50 % SPC : TH1_THM_EQU_NAR
% 0.29/0.50
% 0.29/0.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.50 % 2016-07-13 14:39:23.898
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 %----Could-be-implicit typings (9)
% 0.29/0.50 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 0.29/0.50 rBT_Im1923302023_color: $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 0.29/0.50 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_t_Product__Type_Oprod,type,
% 0.29/0.50 product_prod: $tType > $tType > $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_t_Option_Ooption,type,
% 0.29/0.50 option: $tType > $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_t_List_Olist,type,
% 0.29/0.50 list: $tType > $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_t_Set_Oset,type,
% 0.29/0.50 set: $tType > $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_t_itself,type,
% 0.29/0.50 itself: $tType > $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_tf_b,type,
% 0.29/0.50 b: $tType ).
% 0.29/0.50
% 0.29/0.50 thf(ty_tf_a,type,
% 0.29/0.50 a: $tType ).
% 0.29/0.50
% 0.29/0.50 %----Explicit typings (51)
% 0.29/0.50 thf(sy_cl_HOL_Otype,type,
% 0.29/0.50 type:
% 0.29/0.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_cl_Orderings_Oord,type,
% 0.29/0.50 ord:
% 0.29/0.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.50 order:
% 0.29/0.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.50 linorder:
% 0.29/0.50 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Fun_Oinj__on,type,
% 0.29/0.50 inj_on:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_If,type,
% 0.29/0.50 if:
% 0.29/0.50 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Oappend,type,
% 0.29/0.50 append:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Obind,type,
% 0.29/0.50 bind:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Obutlast,type,
% 0.29/0.50 butlast:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Odistinct,type,
% 0.29/0.50 distinct:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Oinsert,type,
% 0.29/0.50 insert:
% 0.29/0.50 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Olast,type,
% 0.29/0.50 last:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Olist_OCons,type,
% 0.29/0.50 cons:
% 0.29/0.50 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Olist_ONil,type,
% 0.29/0.50 nil:
% 0.29/0.50 !>[A: $tType] : ( list @ A ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Olist_Oset,type,
% 0.29/0.50 set2:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Omaps,type,
% 0.29/0.50 maps:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Oord_Olexordp,type,
% 0.29/0.50 lexordp:
% 0.29/0.50 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.29/0.50 lexordp_eq:
% 0.29/0.50 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Oproduct__lists,type,
% 0.29/0.50 product_lists:
% 0.29/0.50 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Orotate1,type,
% 0.29/0.50 rotate1:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Osublists,type,
% 0.29/0.50 sublists:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_List_Ounion,type,
% 0.29/0.50 union:
% 0.29/0.50 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Map_Odom,type,
% 0.29/0.50 dom:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Map_Omap__of,type,
% 0.29/0.50 map_of:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( list @ ( product_prod @ A @ B ) ) > A > ( option @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_ONone,type,
% 0.29/0.50 none:
% 0.29/0.50 !>[A: $tType] : ( option @ A ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Option_Ooption_OSome,type,
% 0.29/0.50 some:
% 0.29/0.50 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/0.50 ord_less:
% 0.29/0.50 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Orderings_Oorder_Ostrict__mono,type,
% 0.29/0.50 strict_mono:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Pure_Otype,type,
% 0.29/0.50 type2:
% 0.29/0.50 !>[A: $tType] : ( itself @ A ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries,type,
% 0.29/0.50 rBT_Im954575269ntries:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Okeys,type,
% 0.29/0.50 rBT_Im380146495e_keys:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 0.29/0.50 rBT_Im1259024060reater:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 0.29/0.50 rBT_Im2075124343t_less:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup,type,
% 0.29/0.50 rBT_Im35466040lookup:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > A > ( option @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 0.29/0.50 rBT_Im759614907sorted:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__greater,type,
% 0.29/0.50 rBT_Im1332541288reater:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__less,type,
% 0.29/0.50 rBT_Im903026891t_less:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__sorted,type,
% 0.29/0.50 rBT_Im1183586831sorted:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 0.29/0.50 rBT_Im480247531Branch:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 0.29/0.50 rBT_Im418718756_Empty:
% 0.29/0.50 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Set_OCollect,type,
% 0.29/0.50 collect:
% 0.29/0.50 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Set_Othe__elem,type,
% 0.29/0.50 the_elem:
% 0.29/0.50 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Set__Interval_Oord_OgreaterThan,type,
% 0.29/0.50 set_greaterThan:
% 0.29/0.50 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_Set__Interval_Oord_OlessThan,type,
% 0.29/0.50 set_lessThan:
% 0.29/0.50 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_c_member,type,
% 0.29/0.50 member:
% 0.29/0.50 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.50
% 0.29/0.50 thf(sy_v_c____,type,
% 0.29/0.50 c: rBT_Im1923302023_color ).
% 0.29/0.50
% 0.29/0.50 thf(sy_v_k____,type,
% 0.29/0.50 k: a ).
% 0.29/0.50
% 0.29/0.50 thf(sy_v_less,type,
% 0.29/0.50 less: a > a > $o ).
% 0.29/0.50
% 0.29/0.50 thf(sy_v_t1____,type,
% 0.29/0.50 t1: rBT_Im246033960le_rbt @ a @ b ).
% 0.29/0.50
% 0.29/0.50 thf(sy_v_t2____,type,
% 0.29/0.50 t2: rBT_Im246033960le_rbt @ a @ b ).
% 0.29/0.50
% 0.29/0.50 thf(sy_v_v____,type,
% 0.29/0.50 v: b ).
% 0.29/0.50
% 0.29/0.50 %----Relevant facts (255)
% 0.29/0.50 thf(fact_0_local_Oantisym__conv3,axiom,
% 0.29/0.50 ! [Y: a,X: a] :
% 0.29/0.50 ( ~ ( less @ Y @ X )
% 0.29/0.50 => ( ( ~ ( less @ X @ Y ) )
% 0.29/0.50 = ( X = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.antisym_conv3
% 0.29/0.50 thf(fact_1_local_Odual__order_Oasym,axiom,
% 0.29/0.50 ! [B2: a,A2: a] :
% 0.29/0.50 ( ( less @ B2 @ A2 )
% 0.29/0.50 => ~ ( less @ A2 @ B2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.dual_order.asym
% 0.29/0.50 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.50 ! [B2: a,A2: a] :
% 0.29/0.50 ( ( less @ B2 @ A2 )
% 0.29/0.50 => ( A2 != B2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.dual_order.strict_implies_not_eq
% 0.29/0.50 thf(fact_3_local_Odual__order_Ostrict__trans,axiom,
% 0.29/0.50 ! [B2: a,A2: a,C: a] :
% 0.29/0.50 ( ( less @ B2 @ A2 )
% 0.29/0.50 => ( ( less @ C @ B2 )
% 0.29/0.50 => ( less @ C @ A2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.dual_order.strict_trans
% 0.29/0.50 thf(fact_4_local_Oless__asym,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ~ ( less @ Y @ X ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_asym
% 0.29/0.50 thf(fact_5_local_Oless__asym_H,axiom,
% 0.29/0.50 ! [A2: a,B2: a] :
% 0.29/0.50 ( ( less @ A2 @ B2 )
% 0.29/0.50 => ~ ( less @ B2 @ A2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_asym'
% 0.29/0.50 thf(fact_6_local_Oless__imp__neq,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( X != Y ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_imp_neq
% 0.29/0.50 thf(fact_7_local_Oless__imp__not__eq,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( X != Y ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_imp_not_eq
% 0.29/0.50 thf(fact_8_local_Oless__imp__not__eq2,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( Y != X ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_imp_not_eq2
% 0.29/0.50 thf(fact_9_local_Oless__imp__not__less,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ~ ( less @ Y @ X ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_imp_not_less
% 0.29/0.50 thf(fact_10_local_Oless__imp__triv,axiom,
% 0.29/0.50 ! [X: a,Y: a,P: $o] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( ( less @ Y @ X )
% 0.29/0.50 => P ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_imp_triv
% 0.29/0.50 thf(fact_11_local_Oless__irrefl,axiom,
% 0.29/0.50 ! [X: a] :
% 0.29/0.50 ~ ( less @ X @ X ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_irrefl
% 0.29/0.50 thf(fact_12_local_Oless__linear,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 | ( X = Y )
% 0.29/0.50 | ( less @ Y @ X ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_linear
% 0.29/0.50 thf(fact_13_local_Oless__not__sym,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ~ ( less @ Y @ X ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_not_sym
% 0.29/0.50 thf(fact_14_local_Oless__trans,axiom,
% 0.29/0.50 ! [X: a,Y: a,Z: a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( ( less @ Y @ Z )
% 0.29/0.50 => ( less @ X @ Z ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.less_trans
% 0.29/0.50 thf(fact_15_local_Olinorder__cases,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ~ ( less @ X @ Y )
% 0.29/0.50 => ( ( X != Y )
% 0.29/0.50 => ( less @ Y @ X ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.linorder_cases
% 0.29/0.50 thf(fact_16_local_OneqE,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( X != Y )
% 0.29/0.50 => ( ~ ( less @ X @ Y )
% 0.29/0.50 => ( less @ Y @ X ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.neqE
% 0.29/0.50 thf(fact_17_local_Oneq__iff,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( X != Y )
% 0.29/0.50 = ( ( less @ X @ Y )
% 0.29/0.50 | ( less @ Y @ X ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.neq_iff
% 0.29/0.50 thf(fact_18_local_Onot__less__iff__gr__or__eq,axiom,
% 0.29/0.50 ! [X: a,Y: a] :
% 0.29/0.50 ( ( ~ ( less @ X @ Y ) )
% 0.29/0.50 = ( ( less @ Y @ X )
% 0.29/0.50 | ( X = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.not_less_iff_gr_or_eq
% 0.29/0.50 thf(fact_19_local_Oord__eq__less__trans,axiom,
% 0.29/0.50 ! [A2: a,B2: a,C: a] :
% 0.29/0.50 ( ( A2 = B2 )
% 0.29/0.50 => ( ( less @ B2 @ C )
% 0.29/0.50 => ( less @ A2 @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.ord_eq_less_trans
% 0.29/0.50 thf(fact_20_local_Oord__less__eq__trans,axiom,
% 0.29/0.50 ! [A2: a,B2: a,C: a] :
% 0.29/0.50 ( ( less @ A2 @ B2 )
% 0.29/0.50 => ( ( B2 = C )
% 0.29/0.50 => ( less @ A2 @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.ord_less_eq_trans
% 0.29/0.50 thf(fact_21_local_Oorder_Oasym,axiom,
% 0.29/0.50 ! [A2: a,B2: a] :
% 0.29/0.50 ( ( less @ A2 @ B2 )
% 0.29/0.50 => ~ ( less @ B2 @ A2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.order.asym
% 0.29/0.50 thf(fact_22_local_Oorder_Oirrefl,axiom,
% 0.29/0.50 ! [A2: a] :
% 0.29/0.50 ~ ( less @ A2 @ A2 ) ).
% 0.29/0.50
% 0.29/0.50 % local.order.irrefl
% 0.29/0.50 thf(fact_23_local_Oorder_Ostrict__implies__not__eq,axiom,
% 0.29/0.50 ! [A2: a,B2: a] :
% 0.29/0.50 ( ( less @ A2 @ B2 )
% 0.29/0.50 => ( A2 != B2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.order.strict_implies_not_eq
% 0.29/0.50 thf(fact_24_local_Oorder_Ostrict__trans,axiom,
% 0.29/0.50 ! [A2: a,B2: a,C: a] :
% 0.29/0.50 ( ( less @ A2 @ B2 )
% 0.29/0.50 => ( ( less @ B2 @ C )
% 0.29/0.50 => ( less @ A2 @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.order.strict_trans
% 0.29/0.50 thf(fact_25_local_Orbt__greater__prop,axiom,
% 0.29/0.50 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.50 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 0.29/0.50 = ( ! [X2: a] :
% 0.29/0.50 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 0.29/0.50 => ( less @ K @ X2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.rbt_greater_prop
% 0.29/0.50 thf(fact_26_local_Orbt__greater__trans,axiom,
% 0.29/0.50 ! [C2: $tType,X: a,Y: a,T: rBT_Im246033960le_rbt @ a @ C2] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( ( rBT_Im1259024060reater @ a @ C2 @ less @ Y @ T )
% 0.29/0.50 => ( rBT_Im1259024060reater @ a @ C2 @ less @ X @ T ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.rbt_greater_trans
% 0.29/0.50 thf(fact_27__092_060open_062k_A_092_060guillemotleft_062_124_At2_092_060close_062,axiom,
% 0.29/0.50 rBT_Im1259024060reater @ a @ b @ less @ k @ t2 ).
% 0.29/0.50
% 0.29/0.50 % \<open>k \<guillemotleft>| t2\<close>
% 0.29/0.50 thf(fact_28_local_Ostrict__mono__eq,axiom,
% 0.29/0.50 ! [B: $tType] :
% 0.29/0.50 ( ( order @ B @ ( type2 @ B ) )
% 0.29/0.50 => ! [F: a > B,X: a,Y: a] :
% 0.29/0.50 ( ( strict_mono @ a @ B @ less @ F )
% 0.29/0.50 => ( ( ( F @ X )
% 0.29/0.50 = ( F @ Y ) )
% 0.29/0.50 = ( X = Y ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.strict_mono_eq
% 0.29/0.50 thf(fact_29_local_Orbt__less__prop,axiom,
% 0.29/0.50 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.50 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 0.29/0.50 = ( ! [X2: a] :
% 0.29/0.50 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 0.29/0.50 => ( less @ X2 @ K ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.rbt_less_prop
% 0.29/0.50 thf(fact_30_ord_Orbt__greater__prop,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType] :
% 0.29/0.50 ( ( rBT_Im1259024060reater @ A @ B )
% 0.29/0.50 = ( ^ [Less: A > A > $o,K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.50 ! [X2: A] :
% 0.29/0.50 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 0.29/0.50 => ( Less @ K2 @ X2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.rbt_greater_prop
% 0.29/0.50 thf(fact_31_local_Orbt__less__trans,axiom,
% 0.29/0.50 ! [C2: $tType,X: a,T: rBT_Im246033960le_rbt @ a @ C2,Y: a] :
% 0.29/0.50 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ X @ T )
% 0.29/0.50 => ( ( less @ X @ Y )
% 0.29/0.50 => ( rBT_Im2075124343t_less @ a @ C2 @ less @ Y @ T ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.rbt_less_trans
% 0.29/0.50 thf(fact_32_local_Olexordp__eq__antisym,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( ( lexordp_eq @ a @ less @ Ys @ Xs )
% 0.29/0.50 => ( Xs = Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_antisym
% 0.29/0.50 thf(fact_33_local_Olexordp__eq__linear,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.29/0.50 | ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_linear
% 0.29/0.50 thf(fact_34_local_Olexordp__eq__refl,axiom,
% 0.29/0.50 ! [Xs: list @ a] : ( lexordp_eq @ a @ less @ Xs @ Xs ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_refl
% 0.29/0.50 thf(fact_35_local_Olexordp__eq__trans,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( ( lexordp_eq @ a @ less @ Ys @ Zs )
% 0.29/0.50 => ( lexordp_eq @ a @ less @ Xs @ Zs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_trans
% 0.29/0.50 thf(fact_36_ord_Orbt__less__prop,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType] :
% 0.29/0.50 ( ( rBT_Im2075124343t_less @ A @ B )
% 0.29/0.50 = ( ^ [Less: A > A > $o,K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.50 ! [X2: A] :
% 0.29/0.50 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 0.29/0.50 => ( Less @ X2 @ K2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.rbt_less_prop
% 0.29/0.50 thf(fact_37_local_Olexordp__antisym,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ~ ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_antisym
% 0.29/0.50 thf(fact_38_local_Olexordp__irreflexive,axiom,
% 0.29/0.50 ! [Xs: list @ a] :
% 0.29/0.50 ( ! [X3: a] :
% 0.29/0.50 ~ ( less @ X3 @ X3 )
% 0.29/0.50 => ~ ( lexordp @ a @ less @ Xs @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_irreflexive
% 0.29/0.50 thf(fact_39_local_Olexordp__irreflexive_H,axiom,
% 0.29/0.50 ! [Xs: list @ a] :
% 0.29/0.50 ~ ( lexordp @ a @ less @ Xs @ Xs ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_irreflexive'
% 0.29/0.50 thf(fact_40_local_Olexordp__linear,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 | ( Xs = Ys )
% 0.29/0.50 | ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_linear
% 0.29/0.50 thf(fact_41_local_Olexordp__trans,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( ( lexordp @ a @ less @ Ys @ Zs )
% 0.29/0.50 => ( lexordp @ a @ less @ Xs @ Zs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_trans
% 0.29/0.50 thf(fact_42_local_Olexordp__into__lexordp__eq,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_into_lexordp_eq
% 0.29/0.50 thf(fact_43_local_Olexordp__eq__conv__lexord,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.29/0.50 = ( ( Xs = Ys )
% 0.29/0.50 | ( lexordp @ a @ less @ Xs @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_conv_lexord
% 0.29/0.50 thf(fact_44_local_Olexordp__conv__lexordp__eq,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 = ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.29/0.50 & ~ ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_conv_lexordp_eq
% 0.29/0.50 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.50 ! [A: $tType,A2: A,P: A > $o] :
% 0.29/0.50 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/0.50 = ( P @ A2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % mem_Collect_eq
% 0.29/0.50 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.50 ! [A: $tType,A3: set @ A] :
% 0.29/0.50 ( ( collect @ A
% 0.29/0.50 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.29/0.50 = A3 ) ).
% 0.29/0.50
% 0.29/0.50 % Collect_mem_eq
% 0.29/0.50 thf(fact_47_Collect__cong,axiom,
% 0.29/0.50 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.50 ( ! [X3: A] :
% 0.29/0.50 ( ( P @ X3 )
% 0.29/0.50 = ( Q @ X3 ) )
% 0.29/0.50 => ( ( collect @ A @ P )
% 0.29/0.50 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Collect_cong
% 0.29/0.50 thf(fact_48_ext,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.50 ( ! [X3: A] :
% 0.29/0.50 ( ( F @ X3 )
% 0.29/0.50 = ( G @ X3 ) )
% 0.29/0.50 => ( F = G ) ) ).
% 0.29/0.50
% 0.29/0.50 % ext
% 0.29/0.50 thf(fact_49_local_Ostrict__mono__less,axiom,
% 0.29/0.50 ! [B: $tType] :
% 0.29/0.50 ( ( order @ B @ ( type2 @ B ) )
% 0.29/0.50 => ! [F: a > B,X: a,Y: a] :
% 0.29/0.50 ( ( strict_mono @ a @ B @ less @ F )
% 0.29/0.50 => ( ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) )
% 0.29/0.50 = ( less @ X @ Y ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.strict_mono_less
% 0.29/0.50 thf(fact_50_local_Ostrict__mono__def,axiom,
% 0.29/0.50 ! [B: $tType] :
% 0.29/0.50 ( ( order @ B @ ( type2 @ B ) )
% 0.29/0.50 => ! [F: a > B] :
% 0.29/0.50 ( ( strict_mono @ a @ B @ less @ F )
% 0.29/0.50 = ( ! [X2: a,Y2: a] :
% 0.29/0.50 ( ( less @ X2 @ Y2 )
% 0.29/0.50 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.strict_mono_def
% 0.29/0.50 thf(fact_51_local_Ostrict__monoI,axiom,
% 0.29/0.50 ! [B: $tType] :
% 0.29/0.50 ( ( order @ B @ ( type2 @ B ) )
% 0.29/0.50 => ! [F: a > B] :
% 0.29/0.50 ( ! [X3: a,Y3: a] :
% 0.29/0.50 ( ( less @ X3 @ Y3 )
% 0.29/0.50 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.50 => ( strict_mono @ a @ B @ less @ F ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.strict_monoI
% 0.29/0.50 thf(fact_52_local_Ostrict__monoD,axiom,
% 0.29/0.50 ! [B: $tType] :
% 0.29/0.50 ( ( order @ B @ ( type2 @ B ) )
% 0.29/0.50 => ! [F: a > B,X: a,Y: a] :
% 0.29/0.50 ( ( strict_mono @ a @ B @ less @ F )
% 0.29/0.50 => ( ( less @ X @ Y )
% 0.29/0.50 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.strict_monoD
% 0.29/0.50 thf(fact_53_local_Olexordp__eq_ONil,axiom,
% 0.29/0.50 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq.Nil
% 0.29/0.50 thf(fact_54_ord_Olexordp__into__lexordp__eq,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ Xs @ Ys )
% 0.29/0.50 => ( lexordp_eq @ A @ Less2 @ Xs @ Ys ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_into_lexordp_eq
% 0.29/0.50 thf(fact_55_local_Olexordp__eq_OCons__eq,axiom,
% 0.29/0.50 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ~ ( less @ X @ Y )
% 0.29/0.50 => ( ~ ( less @ Y @ X )
% 0.29/0.50 => ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq.Cons_eq
% 0.29/0.50 thf(fact_56_local_Olexordp__eq_OCons,axiom,
% 0.29/0.50 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq.Cons
% 0.29/0.50 thf(fact_57_local_Olexordp_OCons,axiom,
% 0.29/0.50 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp.Cons
% 0.29/0.50 thf(fact_58_local_Olexordp_OCons__eq,axiom,
% 0.29/0.50 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ~ ( less @ X @ Y )
% 0.29/0.50 => ( ~ ( less @ Y @ X )
% 0.29/0.50 => ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp.Cons_eq
% 0.29/0.50 thf(fact_59_list_Oinject,axiom,
% 0.29/0.50 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.29/0.50 ( ( ( cons @ A @ X21 @ X22 )
% 0.29/0.50 = ( cons @ A @ Y21 @ Y22 ) )
% 0.29/0.50 = ( ( X21 = Y21 )
% 0.29/0.50 & ( X22 = Y22 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.inject
% 0.29/0.50 thf(fact_60_local_Olexordp_ONil,axiom,
% 0.29/0.50 ! [Y: a,Ys: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ Y @ Ys ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp.Nil
% 0.29/0.50 thf(fact_61_local_Olexordp_Ocases,axiom,
% 0.29/0.50 ! [A1: list @ a,A22: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ A1 @ A22 )
% 0.29/0.50 => ( ( ( A1
% 0.29/0.50 = ( nil @ a ) )
% 0.29/0.50 => ! [Y3: a,Ys2: list @ a] :
% 0.29/0.50 ( A22
% 0.29/0.50 != ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: a] :
% 0.29/0.50 ( ? [Xs2: list @ a] :
% 0.29/0.50 ( A1
% 0.29/0.50 = ( cons @ a @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Y3: a] :
% 0.29/0.50 ( ? [Ys2: list @ a] :
% 0.29/0.50 ( A22
% 0.29/0.50 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.29/0.50 => ~ ( less @ X3 @ Y3 ) ) )
% 0.29/0.50 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ a @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Ys2: list @ a] :
% 0.29/0.50 ( ( A22
% 0.29/0.50 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ~ ( less @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( less @ Y3 @ X3 )
% 0.29/0.50 => ~ ( lexordp @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp.cases
% 0.29/0.50 thf(fact_62_local_Olexordp_Oinducts,axiom,
% 0.29/0.50 ! [X1: list @ a,X23: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.29/0.50 ( ( lexordp @ a @ less @ X1 @ X23 )
% 0.29/0.50 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.29/0.50 ( ( less @ X3 @ Y3 )
% 0.29/0.50 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.29/0.50 ( ~ ( less @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( less @ Y3 @ X3 )
% 0.29/0.50 => ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 0.29/0.50 => ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 0.29/0.50 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp.inducts
% 0.29/0.50 thf(fact_63_local_Olexordp_Osimps,axiom,
% 0.29/0.50 ! [A1: list @ a,A22: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ A1 @ A22 )
% 0.29/0.50 = ( ? [Y2: a,Ys3: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( nil @ a ) )
% 0.29/0.50 & ( A22
% 0.29/0.50 = ( cons @ a @ Y2 @ Ys3 ) ) )
% 0.29/0.50 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ a @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A22
% 0.29/0.50 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.29/0.50 & ( less @ X2 @ Y2 ) )
% 0.29/0.50 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ a @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A22
% 0.29/0.50 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.29/0.50 & ~ ( less @ X2 @ Y2 )
% 0.29/0.50 & ~ ( less @ Y2 @ X2 )
% 0.29/0.50 & ( lexordp @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp.simps
% 0.29/0.50 thf(fact_64_local_Olexordp__cases,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( ( ( Xs
% 0.29/0.50 = ( nil @ a ) )
% 0.29/0.50 => ! [Y3: a,Ys4: list @ a] :
% 0.29/0.50 ( Ys
% 0.29/0.50 != ( cons @ a @ Y3 @ Ys4 ) ) )
% 0.29/0.50 => ( ! [X3: a] :
% 0.29/0.50 ( ? [Xs4: list @ a] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( cons @ a @ X3 @ Xs4 ) )
% 0.29/0.50 => ! [Y3: a] :
% 0.29/0.50 ( ? [Ys4: list @ a] :
% 0.29/0.50 ( Ys
% 0.29/0.50 = ( cons @ a @ Y3 @ Ys4 ) )
% 0.29/0.50 => ~ ( less @ X3 @ Y3 ) ) )
% 0.29/0.50 => ~ ! [X3: a,Xs4: list @ a] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( cons @ a @ X3 @ Xs4 ) )
% 0.29/0.50 => ! [Ys4: list @ a] :
% 0.29/0.50 ( ( Ys
% 0.29/0.50 = ( cons @ a @ X3 @ Ys4 ) )
% 0.29/0.50 => ~ ( lexordp @ a @ less @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_cases
% 0.29/0.50 thf(fact_65_local_Olexordp__induct,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ! [X3: a,Xs2: list @ a,Y3: a,Ys2: list @ a] :
% 0.29/0.50 ( ( less @ X3 @ Y3 )
% 0.29/0.50 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 0.29/0.50 => ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ X3 @ Ys2 ) ) ) )
% 0.29/0.50 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_induct
% 0.29/0.50 thf(fact_66_local_Olexordp__eq_Ocases,axiom,
% 0.29/0.50 ! [A1: list @ a,A22: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 0.29/0.50 => ( ( ( A1
% 0.29/0.50 = ( nil @ a ) )
% 0.29/0.50 => ! [Ys2: list @ a] : ( A22 != Ys2 ) )
% 0.29/0.50 => ( ! [X3: a] :
% 0.29/0.50 ( ? [Xs2: list @ a] :
% 0.29/0.50 ( A1
% 0.29/0.50 = ( cons @ a @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Y3: a] :
% 0.29/0.50 ( ? [Ys2: list @ a] :
% 0.29/0.50 ( A22
% 0.29/0.50 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.29/0.50 => ~ ( less @ X3 @ Y3 ) ) )
% 0.29/0.50 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ a @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Ys2: list @ a] :
% 0.29/0.50 ( ( A22
% 0.29/0.50 = ( cons @ a @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ~ ( less @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( less @ Y3 @ X3 )
% 0.29/0.50 => ~ ( lexordp_eq @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq.cases
% 0.29/0.50 thf(fact_67_local_Olexordp__eq_Oinducts,axiom,
% 0.29/0.50 ! [X1: list @ a,X23: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ X1 @ X23 )
% 0.29/0.50 => ( ! [X12: list @ a] : ( P @ ( nil @ a ) @ X12 )
% 0.29/0.50 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.29/0.50 ( ( less @ X3 @ Y3 )
% 0.29/0.50 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.29/0.50 ( ~ ( less @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( less @ Y3 @ X3 )
% 0.29/0.50 => ( ( lexordp_eq @ a @ less @ Xs2 @ Ys2 )
% 0.29/0.50 => ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 0.29/0.50 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq.inducts
% 0.29/0.50 thf(fact_68_local_Olexordp__eq_Osimps,axiom,
% 0.29/0.50 ! [A1: list @ a,A22: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 0.29/0.50 = ( ? [Ys3: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( nil @ a ) )
% 0.29/0.50 & ( A22 = Ys3 ) )
% 0.29/0.50 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ a @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A22
% 0.29/0.50 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.29/0.50 & ( less @ X2 @ Y2 ) )
% 0.29/0.50 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ a @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A22
% 0.29/0.50 = ( cons @ a @ Y2 @ Ys3 ) )
% 0.29/0.50 & ~ ( less @ X2 @ Y2 )
% 0.29/0.50 & ~ ( less @ Y2 @ X2 )
% 0.29/0.50 & ( lexordp_eq @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq.simps
% 0.29/0.50 thf(fact_69_ord_Olexordp__simps_I3_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.29/0.50 = ( ( Less2 @ X @ Y )
% 0.29/0.50 | ( ~ ( Less2 @ Y @ X )
% 0.29/0.50 & ( lexordp @ A @ Less2 @ Xs @ Ys ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_simps(3)
% 0.29/0.50 thf(fact_70_ord_Olexordp__simps_I1_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Ys: list @ A] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ ( nil @ A ) @ Ys )
% 0.29/0.50 = ( Ys
% 0.29/0.50 != ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_simps(1)
% 0.29/0.50 thf(fact_71_ord_Olexordp__simps_I2_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] :
% 0.29/0.50 ~ ( lexordp @ A @ Less2 @ Xs @ ( nil @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_simps(2)
% 0.29/0.50 thf(fact_72_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.29/0.50 ( ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.29/0.50 = ( ( Less2 @ X @ Y )
% 0.29/0.50 | ( ~ ( Less2 @ Y @ X )
% 0.29/0.50 & ( lexordp_eq @ A @ Less2 @ Xs @ Ys ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq_simps(4)
% 0.29/0.50 thf(fact_73_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less2 @ ( nil @ A ) @ Ys ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq_simps(1)
% 0.29/0.50 thf(fact_74_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] :
% 0.29/0.50 ( ( lexordp_eq @ A @ Less2 @ Xs @ ( nil @ A ) )
% 0.29/0.50 = ( Xs
% 0.29/0.50 = ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq_simps(2)
% 0.29/0.50 thf(fact_75_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Xs: list @ A] :
% 0.29/0.50 ~ ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq_simps(3)
% 0.29/0.50 thf(fact_76_local_Olexordp__simps_I3_J,axiom,
% 0.29/0.50 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 0.29/0.50 = ( ( less @ X @ Y )
% 0.29/0.50 | ( ~ ( less @ Y @ X )
% 0.29/0.50 & ( lexordp @ a @ less @ Xs @ Ys ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_simps(3)
% 0.29/0.50 thf(fact_77_local_Olexordp__eq__simps_I4_J,axiom,
% 0.29/0.50 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 0.29/0.50 = ( ( less @ X @ Y )
% 0.29/0.50 | ( ~ ( less @ Y @ X )
% 0.29/0.50 & ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_simps(4)
% 0.29/0.50 thf(fact_78_local_Olexordp__simps_I2_J,axiom,
% 0.29/0.50 ! [Xs: list @ a] :
% 0.29/0.50 ~ ( lexordp @ a @ less @ Xs @ ( nil @ a ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_simps(2)
% 0.29/0.50 thf(fact_79_local_Olexordp__simps_I1_J,axiom,
% 0.29/0.50 ! [Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ ( nil @ a ) @ Ys )
% 0.29/0.50 = ( Ys
% 0.29/0.50 != ( nil @ a ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_simps(1)
% 0.29/0.50 thf(fact_80_local_Olexordp__eq__simps_I2_J,axiom,
% 0.29/0.50 ! [Xs: list @ a] :
% 0.29/0.50 ( ( lexordp_eq @ a @ less @ Xs @ ( nil @ a ) )
% 0.29/0.50 = ( Xs
% 0.29/0.50 = ( nil @ a ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_simps(2)
% 0.29/0.50 thf(fact_81_local_Olexordp__eq__simps_I1_J,axiom,
% 0.29/0.50 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_simps(1)
% 0.29/0.50 thf(fact_82_local_Olexordp__eq__simps_I3_J,axiom,
% 0.29/0.50 ! [X: a,Xs: list @ a] :
% 0.29/0.50 ~ ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( nil @ a ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_eq_simps(3)
% 0.29/0.50 thf(fact_83_ord_Olexordp_ONil,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Y: A,Ys: list @ A] : ( lexordp @ A @ Less2 @ ( nil @ A ) @ ( cons @ A @ Y @ Ys ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp.Nil
% 0.29/0.50 thf(fact_84_ord_Olexordp_Ocases,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ A1 @ A22 )
% 0.29/0.50 => ( ( ( A1
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 => ! [Y3: A,Ys2: list @ A] :
% 0.29/0.50 ( A22
% 0.29/0.50 != ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: A] :
% 0.29/0.50 ( ? [Xs2: list @ A] :
% 0.29/0.50 ( A1
% 0.29/0.50 = ( cons @ A @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Y3: A] :
% 0.29/0.50 ( ? [Ys2: list @ A] :
% 0.29/0.50 ( A22
% 0.29/0.50 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.29/0.50 => ~ ( Less2 @ X3 @ Y3 ) ) )
% 0.29/0.50 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ A @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Ys2: list @ A] :
% 0.29/0.50 ( ( A22
% 0.29/0.50 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ~ ( Less2 @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( Less2 @ Y3 @ X3 )
% 0.29/0.50 => ~ ( lexordp @ A @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp.cases
% 0.29/0.50 thf(fact_85_ord_Olexordp_Osimps,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( lexordp @ A )
% 0.29/0.50 = ( ^ [Less: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.29/0.50 ( ? [Y2: A,Ys3: list @ A] :
% 0.29/0.50 ( ( A12
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 & ( A23
% 0.29/0.50 = ( cons @ A @ Y2 @ Ys3 ) ) )
% 0.29/0.50 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.50 ( ( A12
% 0.29/0.50 = ( cons @ A @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A23
% 0.29/0.50 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.29/0.50 & ( Less @ X2 @ Y2 ) )
% 0.29/0.50 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.50 ( ( A12
% 0.29/0.50 = ( cons @ A @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A23
% 0.29/0.50 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.29/0.50 & ~ ( Less @ X2 @ Y2 )
% 0.29/0.50 & ~ ( Less @ Y2 @ X2 )
% 0.29/0.50 & ( lexordp @ A @ Less @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp.simps
% 0.29/0.50 thf(fact_86_ord_Olexordp_Oinducts,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ X1 @ X23 )
% 0.29/0.50 => ( ! [Y3: A,Ys2: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.50 ( ( Less2 @ X3 @ Y3 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.50 ( ~ ( Less2 @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( Less2 @ Y3 @ X3 )
% 0.29/0.50 => ( ( lexordp @ A @ Less2 @ Xs2 @ Ys2 )
% 0.29/0.50 => ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 0.29/0.50 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp.inducts
% 0.29/0.50 thf(fact_87_ord_Olexordp__eq_Ocases,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.29/0.50 ( ( lexordp_eq @ A @ Less2 @ A1 @ A22 )
% 0.29/0.50 => ( ( ( A1
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 => ! [Ys2: list @ A] : ( A22 != Ys2 ) )
% 0.29/0.50 => ( ! [X3: A] :
% 0.29/0.50 ( ? [Xs2: list @ A] :
% 0.29/0.50 ( A1
% 0.29/0.50 = ( cons @ A @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Y3: A] :
% 0.29/0.50 ( ? [Ys2: list @ A] :
% 0.29/0.50 ( A22
% 0.29/0.50 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.29/0.50 => ~ ( Less2 @ X3 @ Y3 ) ) )
% 0.29/0.50 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.29/0.50 ( ( A1
% 0.29/0.50 = ( cons @ A @ X3 @ Xs2 ) )
% 0.29/0.50 => ! [Ys2: list @ A] :
% 0.29/0.50 ( ( A22
% 0.29/0.50 = ( cons @ A @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ~ ( Less2 @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( Less2 @ Y3 @ X3 )
% 0.29/0.50 => ~ ( lexordp_eq @ A @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq.cases
% 0.29/0.50 thf(fact_88_ord_Olexordp__eq_Osimps,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( lexordp_eq @ A )
% 0.29/0.50 = ( ^ [Less: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.29/0.50 ( ? [Ys3: list @ A] :
% 0.29/0.50 ( ( A12
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 & ( A23 = Ys3 ) )
% 0.29/0.50 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.50 ( ( A12
% 0.29/0.50 = ( cons @ A @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A23
% 0.29/0.50 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.29/0.50 & ( Less @ X2 @ Y2 ) )
% 0.29/0.50 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.50 ( ( A12
% 0.29/0.50 = ( cons @ A @ X2 @ Xs3 ) )
% 0.29/0.50 & ( A23
% 0.29/0.50 = ( cons @ A @ Y2 @ Ys3 ) )
% 0.29/0.50 & ~ ( Less @ X2 @ Y2 )
% 0.29/0.50 & ~ ( Less @ Y2 @ X2 )
% 0.29/0.50 & ( lexordp_eq @ A @ Less @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq.simps
% 0.29/0.50 thf(fact_89_ord_Olexordp__eq_Oinducts,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.29/0.50 ( ( lexordp_eq @ A @ Less2 @ X1 @ X23 )
% 0.29/0.50 => ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.29/0.50 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.50 ( ( Less2 @ X3 @ Y3 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.50 ( ~ ( Less2 @ X3 @ Y3 )
% 0.29/0.50 => ( ~ ( Less2 @ Y3 @ X3 )
% 0.29/0.50 => ( ( lexordp_eq @ A @ Less2 @ Xs2 @ Ys2 )
% 0.29/0.50 => ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 0.29/0.50 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq.inducts
% 0.29/0.50 thf(fact_90_list_Oset__cases,axiom,
% 0.29/0.50 ! [A: $tType,E: A,A2: list @ A] :
% 0.29/0.50 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 0.29/0.50 => ( ! [Z2: list @ A] :
% 0.29/0.50 ( A2
% 0.29/0.50 != ( cons @ A @ E @ Z2 ) )
% 0.29/0.50 => ~ ! [Z1: A,Z2: list @ A] :
% 0.29/0.50 ( ( A2
% 0.29/0.50 = ( cons @ A @ Z1 @ Z2 ) )
% 0.29/0.50 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.set_cases
% 0.29/0.50 thf(fact_91_set__ConsD,axiom,
% 0.29/0.50 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 0.29/0.50 => ( ( Y = X )
% 0.29/0.50 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % set_ConsD
% 0.29/0.50 thf(fact_92_list_Oset__intros_I1_J,axiom,
% 0.29/0.50 ! [A: $tType,A1: A,A22: list @ A] : ( member @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.set_intros(1)
% 0.29/0.50 thf(fact_93_list_Oset__intros_I2_J,axiom,
% 0.29/0.50 ! [A: $tType,X: A,A22: list @ A,A1: A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ A22 ) )
% 0.29/0.50 => ( member @ A @ X @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.set_intros(2)
% 0.29/0.50 thf(fact_94_map__tailrec__rev_Oinduct,axiom,
% 0.29/0.50 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.29/0.50 ( ! [F2: A > B,X12: list @ B] : ( P @ F2 @ ( nil @ A ) @ X12 )
% 0.29/0.50 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.29/0.50 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 0.29/0.50 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.29/0.50 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % map_tailrec_rev.induct
% 0.29/0.50 thf(fact_95_list__nonempty__induct,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.29/0.50 => ( ! [X3: A,Xs2: list @ A] :
% 0.29/0.50 ( ( Xs2
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ( P @ Xs2 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 0.29/0.50 => ( P @ Xs ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list_nonempty_induct
% 0.29/0.50 thf(fact_96_remdups__adj_Oinduct,axiom,
% 0.29/0.50 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.50 ( ( P @ ( nil @ A ) )
% 0.29/0.50 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.29/0.50 => ( ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.29/0.50 ( ( ( X3 = Y3 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.29/0.50 => ( ( ( X3 != Y3 )
% 0.29/0.50 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.29/0.50 => ( P @ A0 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % remdups_adj.induct
% 0.29/0.50 thf(fact_97_remdups__adj_Ocases,axiom,
% 0.29/0.50 ! [A: $tType,X: list @ A] :
% 0.29/0.50 ( ( X
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ! [X3: A] :
% 0.29/0.50 ( X
% 0.29/0.50 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.29/0.50 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 0.29/0.50 ( X
% 0.29/0.50 != ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % remdups_adj.cases
% 0.29/0.50 thf(fact_98_transpose_Ocases,axiom,
% 0.29/0.50 ! [A: $tType,X: list @ ( list @ A )] :
% 0.29/0.50 ( ( X
% 0.29/0.50 != ( nil @ ( list @ A ) ) )
% 0.29/0.50 => ( ! [Xss: list @ ( list @ A )] :
% 0.29/0.50 ( X
% 0.29/0.50 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.29/0.50 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.29/0.50 ( X
% 0.29/0.50 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % transpose.cases
% 0.29/0.50 thf(fact_99_not__Cons__self2,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( cons @ A @ X @ Xs )
% 0.29/0.50 != Xs ) ).
% 0.29/0.50
% 0.29/0.50 % not_Cons_self2
% 0.29/0.50 thf(fact_100_splice_Oinduct,axiom,
% 0.29/0.50 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.50 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.29/0.50 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 0.29/0.50 => ( ! [X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A] :
% 0.29/0.50 ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % splice.induct
% 0.29/0.50 thf(fact_101_list__induct2_H,axiom,
% 0.29/0.50 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.29/0.50 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.29/0.50 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 0.29/0.50 => ( ! [Y3: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys2 ) )
% 0.29/0.50 => ( ! [X3: A,Xs2: list @ A,Y3: B,Ys2: list @ B] :
% 0.29/0.50 ( ( P @ Xs2 @ Ys2 )
% 0.29/0.50 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) ) )
% 0.29/0.50 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list_induct2'
% 0.29/0.50 thf(fact_102_neq__Nil__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 = ( ? [Y2: A,Ys3: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( cons @ A @ Y2 @ Ys3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % neq_Nil_conv
% 0.29/0.50 thf(fact_103_list_Oinducts,axiom,
% 0.29/0.50 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.29/0.50 ( ( P @ ( nil @ A ) )
% 0.29/0.50 => ( ! [X12: A,X24: list @ A] :
% 0.29/0.50 ( ( P @ X24 )
% 0.29/0.50 => ( P @ ( cons @ A @ X12 @ X24 ) ) )
% 0.29/0.50 => ( P @ List ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.inducts
% 0.29/0.50 thf(fact_104_list_Oexhaust,axiom,
% 0.29/0.50 ! [A: $tType,Y: list @ A] :
% 0.29/0.50 ( ( Y
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ~ ! [X212: A,X222: list @ A] :
% 0.29/0.50 ( Y
% 0.29/0.50 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.exhaust
% 0.29/0.50 thf(fact_105_list_OdiscI,axiom,
% 0.29/0.50 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.29/0.50 ( ( List
% 0.29/0.50 = ( cons @ A @ X21 @ X22 ) )
% 0.29/0.50 => ( List
% 0.29/0.50 != ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.discI
% 0.29/0.50 thf(fact_106_list_Odistinct_I1_J,axiom,
% 0.29/0.50 ! [A: $tType,X21: A,X22: list @ A] :
% 0.29/0.50 ( ( nil @ A )
% 0.29/0.50 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.distinct(1)
% 0.29/0.50 thf(fact_107_ord_Olexordp_OCons__eq,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ~ ( Less2 @ X @ Y )
% 0.29/0.50 => ( ~ ( Less2 @ Y @ X )
% 0.29/0.50 => ( ( lexordp @ A @ Less2 @ Xs @ Ys )
% 0.29/0.50 => ( lexordp @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp.Cons_eq
% 0.29/0.50 thf(fact_108_ord_Olexordp_OCons,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( Less2 @ X @ Y )
% 0.29/0.50 => ( lexordp @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp.Cons
% 0.29/0.50 thf(fact_109_ord_Olexordp__eq_OCons__eq,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ~ ( Less2 @ X @ Y )
% 0.29/0.50 => ( ~ ( Less2 @ Y @ X )
% 0.29/0.50 => ( ( lexordp_eq @ A @ Less2 @ Xs @ Ys )
% 0.29/0.50 => ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq.Cons_eq
% 0.29/0.50 thf(fact_110_ord_Olexordp__eq_OCons,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( Less2 @ X @ Y )
% 0.29/0.50 => ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq.Cons
% 0.29/0.50 thf(fact_111_ord_Olexordp__eq_ONil,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less2 @ ( nil @ A ) @ Ys ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq.Nil
% 0.29/0.50 thf(fact_112_ord_Olexordp__irreflexive,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] :
% 0.29/0.50 ( ! [X3: A] :
% 0.29/0.50 ~ ( Less2 @ X3 @ X3 )
% 0.29/0.50 => ~ ( lexordp @ A @ Less2 @ Xs @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_irreflexive
% 0.29/0.50 thf(fact_113_ord_Olexordp__eq__refl,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less2 @ Xs @ Xs ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_eq_refl
% 0.29/0.50 thf(fact_114_local_Olexordp__append__rightI,axiom,
% 0.29/0.50 ! [Ys: list @ a,Xs: list @ a] :
% 0.29/0.50 ( ( Ys
% 0.29/0.50 != ( nil @ a ) )
% 0.29/0.50 => ( lexordp @ a @ less @ Xs @ ( append @ a @ Xs @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_append_rightI
% 0.29/0.50 thf(fact_115_local_Olexordp__append__left__rightI,axiom,
% 0.29/0.50 ! [X: a,Y: a,Us: list @ a,Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( less @ X @ Y )
% 0.29/0.50 => ( lexordp @ a @ less @ ( append @ a @ Us @ ( cons @ a @ X @ Xs ) ) @ ( append @ a @ Us @ ( cons @ a @ Y @ Ys ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_append_left_rightI
% 0.29/0.50 thf(fact_116_local_Olexordp__iff,axiom,
% 0.29/0.50 ! [Xs: list @ a,Ys: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.29/0.50 = ( ? [X2: a,Vs: list @ a] :
% 0.29/0.50 ( Ys
% 0.29/0.50 = ( append @ a @ Xs @ ( cons @ a @ X2 @ Vs ) ) )
% 0.29/0.50 | ? [Us2: list @ a,A5: a,B3: a,Vs: list @ a,Ws: list @ a] :
% 0.29/0.50 ( ( less @ A5 @ B3 )
% 0.29/0.50 & ( Xs
% 0.29/0.50 = ( append @ a @ Us2 @ ( cons @ a @ A5 @ Vs ) ) )
% 0.29/0.50 & ( Ys
% 0.29/0.50 = ( append @ a @ Us2 @ ( cons @ a @ B3 @ Ws ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_iff
% 0.29/0.50 thf(fact_117_the__elem__set,axiom,
% 0.29/0.50 ! [A: $tType,X: A] :
% 0.29/0.50 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.29/0.50 = X ) ).
% 0.29/0.50
% 0.29/0.50 % the_elem_set
% 0.29/0.50 thf(fact_118_local_Olexordp__append__leftD,axiom,
% 0.29/0.50 ! [Xs: list @ a,Us: list @ a,Vs2: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ ( append @ a @ Xs @ Us ) @ ( append @ a @ Xs @ Vs2 ) )
% 0.29/0.50 => ( ! [A4: a] :
% 0.29/0.50 ~ ( less @ A4 @ A4 )
% 0.29/0.50 => ( lexordp @ a @ less @ Us @ Vs2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_append_leftD
% 0.29/0.50 thf(fact_119_local_Olexordp__append__leftI,axiom,
% 0.29/0.50 ! [Us: list @ a,Vs2: list @ a,Xs: list @ a] :
% 0.29/0.50 ( ( lexordp @ a @ less @ Us @ Vs2 )
% 0.29/0.50 => ( lexordp @ a @ less @ ( append @ a @ Xs @ Us ) @ ( append @ a @ Xs @ Vs2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.lexordp_append_leftI
% 0.29/0.50 thf(fact_120_local_Ostrict__mono__imp__inj__on,axiom,
% 0.29/0.50 ! [B: $tType] :
% 0.29/0.50 ( ( order @ B @ ( type2 @ B ) )
% 0.29/0.50 => ! [F: a > B,A3: set @ a] :
% 0.29/0.50 ( ( strict_mono @ a @ B @ less @ F )
% 0.29/0.50 => ( inj_on @ a @ B @ F @ A3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.strict_mono_imp_inj_on
% 0.29/0.50 thf(fact_121_same__append__eq,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ Ys )
% 0.29/0.50 = ( append @ A @ Xs @ Zs ) )
% 0.29/0.50 = ( Ys = Zs ) ) ).
% 0.29/0.50
% 0.29/0.50 % same_append_eq
% 0.29/0.50 thf(fact_122_append__same__eq,axiom,
% 0.29/0.50 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Ys @ Xs )
% 0.29/0.50 = ( append @ A @ Zs @ Xs ) )
% 0.29/0.50 = ( Ys = Zs ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_same_eq
% 0.29/0.50 thf(fact_123_append__assoc,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.29/0.50 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 0.29/0.50 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_assoc
% 0.29/0.50 thf(fact_124_append__Nil2,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.29/0.50 = Xs ) ).
% 0.29/0.50
% 0.29/0.50 % append_Nil2
% 0.29/0.50 thf(fact_125_append__self__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ Ys )
% 0.29/0.50 = Xs )
% 0.29/0.50 = ( Ys
% 0.29/0.50 = ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_self_conv
% 0.29/0.50 thf(fact_126_self__append__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Xs @ Ys ) )
% 0.29/0.50 = ( Ys
% 0.29/0.50 = ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % self_append_conv
% 0.29/0.50 thf(fact_127_append__self__conv2,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ Ys )
% 0.29/0.50 = Ys )
% 0.29/0.50 = ( Xs
% 0.29/0.50 = ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_self_conv2
% 0.29/0.50 thf(fact_128_self__append__conv2,axiom,
% 0.29/0.50 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.29/0.50 ( ( Ys
% 0.29/0.50 = ( append @ A @ Xs @ Ys ) )
% 0.29/0.50 = ( Xs
% 0.29/0.50 = ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % self_append_conv2
% 0.29/0.50 thf(fact_129_Nil__is__append__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( ( nil @ A )
% 0.29/0.50 = ( append @ A @ Xs @ Ys ) )
% 0.29/0.50 = ( ( Xs
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 & ( Ys
% 0.29/0.50 = ( nil @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Nil_is_append_conv
% 0.29/0.50 thf(fact_130_append__is__Nil__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ Ys )
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 = ( ( Xs
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 & ( Ys
% 0.29/0.50 = ( nil @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_is_Nil_conv
% 0.29/0.50 thf(fact_131_append1__eq__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.50 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.29/0.50 = ( ( Xs = Ys )
% 0.29/0.50 & ( X = Y ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append1_eq_conv
% 0.29/0.50 thf(fact_132_append__eq__append__conv2,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ Ys )
% 0.29/0.50 = ( append @ A @ Zs @ Ts ) )
% 0.29/0.50 = ( ? [Us2: list @ A] :
% 0.29/0.50 ( ( ( Xs
% 0.29/0.50 = ( append @ A @ Zs @ Us2 ) )
% 0.29/0.50 & ( ( append @ A @ Us2 @ Ys )
% 0.29/0.50 = Ts ) )
% 0.29/0.50 | ( ( ( append @ A @ Xs @ Us2 )
% 0.29/0.50 = Zs )
% 0.29/0.50 & ( Ys
% 0.29/0.50 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_eq_append_conv2
% 0.29/0.50 thf(fact_133_append__eq__appendI,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Xs @ Xs1 )
% 0.29/0.50 = Zs )
% 0.29/0.50 => ( ( Ys
% 0.29/0.50 = ( append @ A @ Xs1 @ Us ) )
% 0.29/0.50 => ( ( append @ A @ Xs @ Ys )
% 0.29/0.50 = ( append @ A @ Zs @ Us ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_eq_appendI
% 0.29/0.50 thf(fact_134_Cons__eq__appendI,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.29/0.50 ( ( ( cons @ A @ X @ Xs1 )
% 0.29/0.50 = Ys )
% 0.29/0.50 => ( ( Xs
% 0.29/0.50 = ( append @ A @ Xs1 @ Zs ) )
% 0.29/0.50 => ( ( cons @ A @ X @ Xs )
% 0.29/0.50 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Cons_eq_appendI
% 0.29/0.50 thf(fact_135_append__Cons,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.29/0.50 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_Cons
% 0.29/0.50 thf(fact_136_eq__Nil__appendI,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( Xs = Ys )
% 0.29/0.50 => ( Xs
% 0.29/0.50 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_Nil_appendI
% 0.29/0.50 thf(fact_137_append__Nil,axiom,
% 0.29/0.50 ! [A: $tType,Ys: list @ A] :
% 0.29/0.50 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.29/0.50 = Ys ) ).
% 0.29/0.50
% 0.29/0.50 % append_Nil
% 0.29/0.50 thf(fact_138_ord_Olexordp__append__leftI,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Us: list @ A,Vs2: list @ A,Xs: list @ A] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ Us @ Vs2 )
% 0.29/0.50 => ( lexordp @ A @ Less2 @ ( append @ A @ Xs @ Us ) @ ( append @ A @ Xs @ Vs2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_append_leftI
% 0.29/0.50 thf(fact_139_ord_Olexordp__append__leftD,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,Xs: list @ A,Us: list @ A,Vs2: list @ A] :
% 0.29/0.50 ( ( lexordp @ A @ Less2 @ ( append @ A @ Xs @ Us ) @ ( append @ A @ Xs @ Vs2 ) )
% 0.29/0.50 => ( ! [A4: A] :
% 0.29/0.50 ~ ( Less2 @ A4 @ A4 )
% 0.29/0.50 => ( lexordp @ A @ Less2 @ Us @ Vs2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_append_leftD
% 0.29/0.50 thf(fact_140_rev__induct,axiom,
% 0.29/0.50 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.50 ( ( P @ ( nil @ A ) )
% 0.29/0.50 => ( ! [X3: A,Xs2: list @ A] :
% 0.29/0.50 ( ( P @ Xs2 )
% 0.29/0.50 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) )
% 0.29/0.50 => ( P @ Xs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % rev_induct
% 0.29/0.50 thf(fact_141_rev__exhaust,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ~ ! [Ys2: list @ A,Y3: A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 != ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % rev_exhaust
% 0.29/0.50 thf(fact_142_Cons__eq__append__conv,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.29/0.50 ( ( ( cons @ A @ X @ Xs )
% 0.29/0.50 = ( append @ A @ Ys @ Zs ) )
% 0.29/0.50 = ( ( ( Ys
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 & ( ( cons @ A @ X @ Xs )
% 0.29/0.50 = Zs ) )
% 0.29/0.50 | ? [Ys5: list @ A] :
% 0.29/0.50 ( ( ( cons @ A @ X @ Ys5 )
% 0.29/0.50 = Ys )
% 0.29/0.50 & ( Xs
% 0.29/0.50 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Cons_eq_append_conv
% 0.29/0.50 thf(fact_143_append__eq__Cons__conv,axiom,
% 0.29/0.50 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( ( append @ A @ Ys @ Zs )
% 0.29/0.50 = ( cons @ A @ X @ Xs ) )
% 0.29/0.50 = ( ( ( Ys
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 & ( Zs
% 0.29/0.50 = ( cons @ A @ X @ Xs ) ) )
% 0.29/0.50 | ? [Ys5: list @ A] :
% 0.29/0.50 ( ( Ys
% 0.29/0.50 = ( cons @ A @ X @ Ys5 ) )
% 0.29/0.50 & ( ( append @ A @ Ys5 @ Zs )
% 0.29/0.50 = Xs ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % append_eq_Cons_conv
% 0.29/0.50 thf(fact_144_rev__nonempty__induct,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.29/0.50 => ( ! [X3: A,Xs2: list @ A] :
% 0.29/0.50 ( ( Xs2
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ( P @ Xs2 )
% 0.29/0.50 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) )
% 0.29/0.50 => ( P @ Xs ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % rev_nonempty_induct
% 0.29/0.50 thf(fact_145_split__list__first__prop__iff,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ( ? [X2: A] :
% 0.29/0.50 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X2 ) ) )
% 0.29/0.50 = ( ? [Ys3: list @ A,X2: A] :
% 0.29/0.50 ( ? [Zs2: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 0.29/0.50 & ( P @ X2 )
% 0.29/0.50 & ! [Y2: A] :
% 0.29/0.50 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys3 ) )
% 0.29/0.50 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_first_prop_iff
% 0.29/0.50 thf(fact_146_split__list__last__prop__iff,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ( ? [X2: A] :
% 0.29/0.50 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X2 ) ) )
% 0.29/0.50 = ( ? [Ys3: list @ A,X2: A,Zs2: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 0.29/0.50 & ( P @ X2 )
% 0.29/0.50 & ! [Y2: A] :
% 0.29/0.50 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs2 ) )
% 0.29/0.50 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_last_prop_iff
% 0.29/0.50 thf(fact_147_in__set__conv__decomp__first,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.29/0.50 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % in_set_conv_decomp_first
% 0.29/0.50 thf(fact_148_in__set__conv__decomp__last,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 0.29/0.50 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % in_set_conv_decomp_last
% 0.29/0.50 thf(fact_149_split__list__first__propE,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ? [X4: A] :
% 0.29/0.50 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X4 ) )
% 0.29/0.50 => ~ ! [Ys2: list @ A,X3: A] :
% 0.29/0.50 ( ? [Zs3: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.29/0.50 => ( ( P @ X3 )
% 0.29/0.50 => ~ ! [Xa: A] :
% 0.29/0.50 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.29/0.50 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_first_propE
% 0.29/0.50 thf(fact_150_split__list__last__propE,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ? [X4: A] :
% 0.29/0.50 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X4 ) )
% 0.29/0.50 => ~ ! [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.29/0.50 => ( ( P @ X3 )
% 0.29/0.50 => ~ ! [Xa: A] :
% 0.29/0.50 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 0.29/0.50 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_last_propE
% 0.29/0.50 thf(fact_151_split__list__first__prop,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ? [X4: A] :
% 0.29/0.50 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X4 ) )
% 0.29/0.50 => ? [Ys2: list @ A,X3: A] :
% 0.29/0.50 ( ? [Zs3: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.29/0.50 & ( P @ X3 )
% 0.29/0.50 & ! [Xa: A] :
% 0.29/0.50 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.29/0.50 => ~ ( P @ Xa ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_first_prop
% 0.29/0.50 thf(fact_152_split__list__last__prop,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ? [X4: A] :
% 0.29/0.50 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X4 ) )
% 0.29/0.50 => ? [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.29/0.50 & ( P @ X3 )
% 0.29/0.50 & ! [Xa: A] :
% 0.29/0.50 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 0.29/0.50 => ~ ( P @ Xa ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_last_prop
% 0.29/0.50 thf(fact_153_in__set__conv__decomp,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % in_set_conv_decomp
% 0.29/0.50 thf(fact_154_split__list__propE,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ? [X4: A] :
% 0.29/0.50 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X4 ) )
% 0.29/0.50 => ~ ! [Ys2: list @ A,X3: A] :
% 0.29/0.50 ( ? [Zs3: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.29/0.50 => ~ ( P @ X3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_propE
% 0.29/0.50 thf(fact_155_split__list__first,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 => ? [Ys2: list @ A,Zs3: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.29/0.50 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_first
% 0.29/0.50 thf(fact_156_split__list__prop,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.29/0.50 ( ? [X4: A] :
% 0.29/0.50 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 & ( P @ X4 ) )
% 0.29/0.50 => ? [Ys2: list @ A,X3: A] :
% 0.29/0.50 ( ? [Zs3: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.29/0.50 & ( P @ X3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_prop
% 0.29/0.50 thf(fact_157_split__list__last,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 => ? [Ys2: list @ A,Zs3: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.29/0.50 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list_last
% 0.29/0.50 thf(fact_158_split__list,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 => ? [Ys2: list @ A,Zs3: list @ A] :
% 0.29/0.50 ( Xs
% 0.29/0.50 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % split_list
% 0.29/0.50 thf(fact_159_ord_Olexordp__append__left__rightI,axiom,
% 0.29/0.50 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Us: list @ A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.50 ( ( Less2 @ X @ Y )
% 0.29/0.50 => ( lexordp @ A @ Less2 @ ( append @ A @ Us @ ( cons @ A @ X @ Xs ) ) @ ( append @ A @ Us @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_append_left_rightI
% 0.29/0.50 thf(fact_160_ord_Olexordp__append__rightI,axiom,
% 0.29/0.50 ! [A: $tType,Ys: list @ A,Less2: A > A > $o,Xs: list @ A] :
% 0.29/0.50 ( ( Ys
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( lexordp @ A @ Less2 @ Xs @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord.lexordp_append_rightI
% 0.29/0.50 thf(fact_161_sublists_Osimps_I1_J,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( sublists @ A @ ( nil @ A ) )
% 0.29/0.50 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % sublists.simps(1)
% 0.29/0.50 thf(fact_162_product__lists_Osimps_I1_J,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.29/0.50 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % product_lists.simps(1)
% 0.29/0.50 thf(fact_163_bind__simps_I2_J,axiom,
% 0.29/0.50 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.29/0.50 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 0.29/0.50 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % bind_simps(2)
% 0.29/0.50 thf(fact_164_ord__class_Orbt__greater__prop,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType] :
% 0.29/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.50 => ( ( rBT_Im1332541288reater @ A @ B )
% 0.29/0.50 = ( ^ [K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.50 ! [X2: A] :
% 0.29/0.50 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 0.29/0.50 => ( ord_less @ A @ K2 @ X2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_class.rbt_greater_prop
% 0.29/0.50 thf(fact_165_bind__simps_I1_J,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.29/0.50 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.29/0.50 = ( nil @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % bind_simps(1)
% 0.29/0.50 thf(fact_166_order__class_Orbt__greater__trans,axiom,
% 0.29/0.50 ! [C2: $tType,A: $tType] :
% 0.29/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.29/0.50 => ! [X: A,Y: A,T: rBT_Im246033960le_rbt @ A @ C2] :
% 0.29/0.50 ( ( ord_less @ A @ X @ Y )
% 0.29/0.50 => ( ( rBT_Im1332541288reater @ A @ C2 @ Y @ T )
% 0.29/0.50 => ( rBT_Im1332541288reater @ A @ C2 @ X @ T ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_class.rbt_greater_trans
% 0.29/0.50 thf(fact_167_list__bind__cong,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 0.29/0.50 ( ( Xs = Ys )
% 0.29/0.50 => ( ! [X3: A] :
% 0.29/0.50 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.29/0.50 => ( ( F @ X3 )
% 0.29/0.50 = ( G @ X3 ) ) )
% 0.29/0.50 => ( ( bind @ A @ B @ Xs @ F )
% 0.29/0.50 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % list_bind_cong
% 0.29/0.50 thf(fact_168_ord__class_Orbt__less__prop,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType] :
% 0.29/0.50 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.50 => ( ( rBT_Im903026891t_less @ A @ B )
% 0.29/0.50 = ( ^ [K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.50 ! [X2: A] :
% 0.29/0.50 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 0.29/0.50 => ( ord_less @ A @ X2 @ K2 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ord_class.rbt_less_prop
% 0.29/0.50 thf(fact_169_maps__simps_I1_J,axiom,
% 0.29/0.50 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 0.29/0.50 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 0.29/0.50 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % maps_simps(1)
% 0.29/0.50 thf(fact_170_not__in__set__insert,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 => ( ( insert @ A @ X @ Xs )
% 0.29/0.50 = ( cons @ A @ X @ Xs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % not_in_set_insert
% 0.29/0.50 thf(fact_171_in__set__insert,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.50 => ( ( insert @ A @ X @ Xs )
% 0.29/0.50 = Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % in_set_insert
% 0.29/0.50 thf(fact_172_insert__Nil,axiom,
% 0.29/0.50 ! [A: $tType,X: A] :
% 0.29/0.50 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.29/0.50 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % insert_Nil
% 0.29/0.50 thf(fact_173_order__class_Orbt__less__trans,axiom,
% 0.29/0.50 ! [C2: $tType,A: $tType] :
% 0.29/0.50 ( ( order @ A @ ( type2 @ A ) )
% 0.29/0.50 => ! [X: A,T: rBT_Im246033960le_rbt @ A @ C2,Y: A] :
% 0.29/0.50 ( ( rBT_Im903026891t_less @ A @ C2 @ X @ T )
% 0.29/0.50 => ( ( ord_less @ A @ X @ Y )
% 0.29/0.50 => ( rBT_Im903026891t_less @ A @ C2 @ Y @ T ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % order_class.rbt_less_trans
% 0.29/0.50 thf(fact_174_maps__simps_I2_J,axiom,
% 0.29/0.50 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.29/0.50 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 0.29/0.50 = ( nil @ A ) ) ).
% 0.29/0.50
% 0.29/0.50 % maps_simps(2)
% 0.29/0.50 thf(fact_175_List_Oinsert__def,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( insert @ A )
% 0.29/0.50 = ( ^ [X2: A,Xs3: list @ A] : ( if @ ( list @ A ) @ ( member @ A @ X2 @ ( set2 @ A @ Xs3 ) ) @ Xs3 @ ( cons @ A @ X2 @ Xs3 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % List.insert_def
% 0.29/0.50 thf(fact_176_rotate1_Osimps_I2_J,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.50 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.50 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % rotate1.simps(2)
% 0.29/0.50 thf(fact_177_local_Orbt__less__simps_I1_J,axiom,
% 0.29/0.50 ! [B: $tType,K: a] : ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.29/0.50
% 0.29/0.50 % local.rbt_less_simps(1)
% 0.29/0.50 thf(fact_178_last__snoc,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A,X: A] :
% 0.29/0.50 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.29/0.50 = X ) ).
% 0.29/0.50
% 0.29/0.50 % last_snoc
% 0.29/0.50 thf(fact_179_rotate1__is__Nil__conv,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.51 ( ( ( rotate1 @ A @ Xs )
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 = ( Xs
% 0.29/0.51 = ( nil @ A ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % rotate1_is_Nil_conv
% 0.29/0.51 thf(fact_180_set__rotate1,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A] :
% 0.29/0.51 ( ( set2 @ A @ ( rotate1 @ A @ Xs ) )
% 0.29/0.51 = ( set2 @ A @ Xs ) ) ).
% 0.29/0.51
% 0.29/0.51 % set_rotate1
% 0.29/0.51 thf(fact_181_ord__class_Orbt__greater__simps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.51 => ! [K: A] : ( rBT_Im1332541288reater @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord_class.rbt_greater_simps(1)
% 0.29/0.51 thf(fact_182_ord__class_Orbt__less__simps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.51 => ! [K: A] : ( rBT_Im903026891t_less @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord_class.rbt_less_simps(1)
% 0.29/0.51 thf(fact_183_last__appendL,axiom,
% 0.29/0.51 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.29/0.51 ( ( Ys
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( last @ A @ Xs ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % last_appendL
% 0.29/0.51 thf(fact_184_last__appendR,axiom,
% 0.29/0.51 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.29/0.51 ( ( Ys
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( last @ A @ Ys ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % last_appendR
% 0.29/0.51 thf(fact_185_keys__simps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( rBT_Im380146495e_keys @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.29/0.51 = ( nil @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % keys_simps(1)
% 0.29/0.51 thf(fact_186_local_Orbt__greater__simps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,K: a] : ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_greater_simps(1)
% 0.29/0.51 thf(fact_187_rotate1_Osimps_I1_J,axiom,
% 0.29/0.51 ! [A: $tType] :
% 0.29/0.51 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.29/0.51 = ( nil @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % rotate1.simps(1)
% 0.29/0.51 thf(fact_188_ord_Orbt__less__simps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,Less2: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less2 @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_less_simps(1)
% 0.29/0.51 thf(fact_189_ord_Orbt__greater__simps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,Less2: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less2 @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_greater_simps(1)
% 0.29/0.51 thf(fact_190_last__ConsR,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,X: A] :
% 0.29/0.51 ( ( Xs
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = ( last @ A @ Xs ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % last_ConsR
% 0.29/0.51 thf(fact_191_last__ConsL,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,X: A] :
% 0.29/0.51 ( ( Xs
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = X ) ) ).
% 0.29/0.51
% 0.29/0.51 % last_ConsL
% 0.29/0.51 thf(fact_192_last_Osimps,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,X: A] :
% 0.29/0.51 ( ( ( Xs
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = X ) )
% 0.29/0.51 & ( ( Xs
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = ( last @ A @ Xs ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % last.simps
% 0.29/0.51 thf(fact_193_last__in__set,axiom,
% 0.29/0.51 ! [A: $tType,As2: list @ A] :
% 0.29/0.51 ( ( As2
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( member @ A @ ( last @ A @ As2 ) @ ( set2 @ A @ As2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % last_in_set
% 0.29/0.51 thf(fact_194_last__append,axiom,
% 0.29/0.51 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.29/0.51 ( ( ( Ys
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( last @ A @ Xs ) ) )
% 0.29/0.51 & ( ( Ys
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( last @ A @ Ys ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % last_append
% 0.29/0.51 thf(fact_195_longest__common__suffix,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.51 ? [Ss: list @ A,Xs4: list @ A,Ys4: list @ A] :
% 0.29/0.51 ( ( Xs
% 0.29/0.51 = ( append @ A @ Xs4 @ Ss ) )
% 0.29/0.51 & ( Ys
% 0.29/0.51 = ( append @ A @ Ys4 @ Ss ) )
% 0.29/0.51 & ( ( Xs4
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 | ( Ys4
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 | ( ( last @ A @ Xs4 )
% 0.29/0.51 != ( last @ A @ Ys4 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % longest_common_suffix
% 0.29/0.51 thf(fact_196_non__empty__rbt__keys,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( T
% 0.29/0.51 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.29/0.51 => ( ( rBT_Im380146495e_keys @ A @ B @ T )
% 0.29/0.51 != ( nil @ A ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % non_empty_rbt_keys
% 0.29/0.51 thf(fact_197_local_Orbt__sorted_Osimps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType] : ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_sorted.simps(1)
% 0.29/0.51 thf(fact_198_append__butlast__last__id,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A] :
% 0.29/0.51 ( ( Xs
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.29/0.51 = Xs ) ) ).
% 0.29/0.51
% 0.29/0.51 % append_butlast_last_id
% 0.29/0.51 thf(fact_199_snoc__eq__iff__butlast,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A] :
% 0.29/0.51 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.51 = Ys )
% 0.29/0.51 = ( ( Ys
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 & ( ( butlast @ A @ Ys )
% 0.29/0.51 = Xs )
% 0.29/0.51 & ( ( last @ A @ Ys )
% 0.29/0.51 = X ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % snoc_eq_iff_butlast
% 0.29/0.51 thf(fact_200_butlast__snoc,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,X: A] :
% 0.29/0.51 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.29/0.51 = Xs ) ).
% 0.29/0.51
% 0.29/0.51 % butlast_snoc
% 0.29/0.51 thf(fact_201_butlast_Osimps_I1_J,axiom,
% 0.29/0.51 ! [A: $tType] :
% 0.29/0.51 ( ( butlast @ A @ ( nil @ A ) )
% 0.29/0.51 = ( nil @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % butlast.simps(1)
% 0.29/0.51 thf(fact_202_in__set__butlastD,axiom,
% 0.29/0.51 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.51 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.29/0.51 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % in_set_butlastD
% 0.29/0.51 thf(fact_203_butlast_Osimps_I2_J,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,X: A] :
% 0.29/0.51 ( ( ( Xs
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = ( nil @ A ) ) )
% 0.29/0.51 & ( ( Xs
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % butlast.simps(2)
% 0.29/0.51 thf(fact_204_butlast__append,axiom,
% 0.29/0.51 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.29/0.51 ( ( ( Ys
% 0.29/0.51 = ( nil @ A ) )
% 0.29/0.51 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( butlast @ A @ Xs ) ) )
% 0.29/0.51 & ( ( Ys
% 0.29/0.51 != ( nil @ A ) )
% 0.29/0.51 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % butlast_append
% 0.29/0.51 thf(fact_205_in__set__butlast__appendI,axiom,
% 0.29/0.51 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.51 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.29/0.51 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 0.29/0.51 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % in_set_butlast_appendI
% 0.29/0.51 thf(fact_206_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,Less2: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less2 @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_sorted.simps(1)
% 0.29/0.51 thf(fact_207_local_Orbt__sorted_Osimps_I2_J,axiom,
% 0.29/0.51 ! [B: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,K: a,V2: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.51 ( ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ C @ L @ K @ V2 @ R ) )
% 0.29/0.51 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.29/0.51 & ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.29/0.51 & ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.29/0.51 & ( rBT_Im759614907sorted @ a @ B @ less @ R ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_sorted.simps(2)
% 0.29/0.51 thf(fact_208_local_Odistinct__keys,axiom,
% 0.29/0.51 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.51 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.29/0.51 => ( distinct @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.distinct_keys
% 0.29/0.51 thf(fact_209_rbt_Oinject,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X25: rBT_Im246033960le_rbt @ A @ B,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X232 @ X242 @ X25 )
% 0.29/0.51 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.29/0.51 = ( ( X21 = Y21 )
% 0.29/0.51 & ( X22 = Y22 )
% 0.29/0.51 & ( X232 = Y23 )
% 0.29/0.51 & ( X242 = Y24 )
% 0.29/0.51 & ( X25 = Y25 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % rbt.inject
% 0.29/0.51 thf(fact_210_distinct1__rotate,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A] :
% 0.29/0.51 ( ( distinct @ A @ ( rotate1 @ A @ Xs ) )
% 0.29/0.51 = ( distinct @ A @ Xs ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct1_rotate
% 0.29/0.51 thf(fact_211_distinct__insert,axiom,
% 0.29/0.51 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.51 ( ( distinct @ A @ ( insert @ A @ X @ Xs ) )
% 0.29/0.51 = ( distinct @ A @ Xs ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct_insert
% 0.29/0.51 thf(fact_212_ord__class_Orbt__greater__simps_I2_J,axiom,
% 0.29/0.51 ! [C2: $tType,A: $tType] :
% 0.29/0.51 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.51 => ! [K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.29/0.51 ( ( rBT_Im1332541288reater @ A @ C2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 0.29/0.51 = ( ( ord_less @ A @ K @ Kt )
% 0.29/0.51 & ( rBT_Im1332541288reater @ A @ C2 @ K @ Lt )
% 0.29/0.51 & ( rBT_Im1332541288reater @ A @ C2 @ K @ Rt ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord_class.rbt_greater_simps(2)
% 0.29/0.51 thf(fact_213_ord__class_Orbt__less__simps_I2_J,axiom,
% 0.29/0.51 ! [C2: $tType,A: $tType] :
% 0.29/0.51 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.51 => ! [K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.29/0.51 ( ( rBT_Im903026891t_less @ A @ C2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 0.29/0.51 = ( ( ord_less @ A @ Kt @ K )
% 0.29/0.51 & ( rBT_Im903026891t_less @ A @ C2 @ K @ Lt )
% 0.29/0.51 & ( rBT_Im903026891t_less @ A @ C2 @ K @ Rt ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord_class.rbt_less_simps(2)
% 0.29/0.51 thf(fact_214_local_Orbt__greater__simps_I2_J,axiom,
% 0.29/0.51 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V2: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 0.29/0.51 ( ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 0.29/0.51 = ( ( less @ K @ Kt )
% 0.29/0.51 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Lt )
% 0.29/0.51 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_greater_simps(2)
% 0.29/0.51 thf(fact_215_local_Orbt__less__simps_I2_J,axiom,
% 0.29/0.51 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V2: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 0.29/0.51 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 0.29/0.51 = ( ( less @ Kt @ K )
% 0.29/0.51 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Lt )
% 0.29/0.51 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_less_simps(2)
% 0.29/0.51 thf(fact_216_keys__simps_I2_J,axiom,
% 0.29/0.51 ! [D: $tType,C2: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ C2 @ D,K: C2,V2: D,R: rBT_Im246033960le_rbt @ C2 @ D] :
% 0.29/0.51 ( ( rBT_Im380146495e_keys @ C2 @ D @ ( rBT_Im480247531Branch @ C2 @ D @ C @ L @ K @ V2 @ R ) )
% 0.29/0.51 = ( append @ C2 @ ( rBT_Im380146495e_keys @ C2 @ D @ L ) @ ( cons @ C2 @ K @ ( rBT_Im380146495e_keys @ C2 @ D @ R ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % keys_simps(2)
% 0.29/0.51 thf(fact_217_rbt_Oexhaust,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( Y
% 0.29/0.51 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.29/0.51 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X233: A,X243: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( Y
% 0.29/0.51 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X233 @ X243 @ X252 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % rbt.exhaust
% 0.29/0.51 thf(fact_218_rbt_Oinduct,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.29/0.51 => ( ! [X12: rBT_Im1923302023_color,X24: rBT_Im246033960le_rbt @ A @ B,X32: A,X42: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( P @ X24 )
% 0.29/0.51 => ( ( P @ X5 )
% 0.29/0.51 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X12 @ X24 @ X32 @ X42 @ X5 ) ) ) )
% 0.29/0.51 => ( P @ Rbt ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % rbt.induct
% 0.29/0.51 thf(fact_219_rbt_Odistinct_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( rBT_Im418718756_Empty @ A @ B )
% 0.29/0.51 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X232 @ X242 @ X25 ) ) ).
% 0.29/0.51
% 0.29/0.51 % rbt.distinct(1)
% 0.29/0.51 thf(fact_220_distinct__butlast,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A] :
% 0.29/0.51 ( ( distinct @ A @ Xs )
% 0.29/0.51 => ( distinct @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct_butlast
% 0.29/0.51 thf(fact_221_distinct__singleton,axiom,
% 0.29/0.51 ! [A: $tType,X: A] : ( distinct @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct_singleton
% 0.29/0.51 thf(fact_222_distinct_Osimps_I2_J,axiom,
% 0.29/0.51 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.51 ( ( distinct @ A @ ( cons @ A @ X @ Xs ) )
% 0.29/0.51 = ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.29/0.51 & ( distinct @ A @ Xs ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct.simps(2)
% 0.29/0.51 thf(fact_223_distinct__length__2__or__more,axiom,
% 0.29/0.51 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 0.29/0.51 ( ( distinct @ A @ ( cons @ A @ A2 @ ( cons @ A @ B2 @ Xs ) ) )
% 0.29/0.51 = ( ( A2 != B2 )
% 0.29/0.51 & ( distinct @ A @ ( cons @ A @ A2 @ Xs ) )
% 0.29/0.51 & ( distinct @ A @ ( cons @ A @ B2 @ Xs ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct_length_2_or_more
% 0.29/0.51 thf(fact_224_distinct_Osimps_I1_J,axiom,
% 0.29/0.51 ! [A: $tType] : ( distinct @ A @ ( nil @ A ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct.simps(1)
% 0.29/0.51 thf(fact_225_ord_Orbt__less__simps_I2_J,axiom,
% 0.29/0.51 ! [C2: $tType,A: $tType,Less2: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.29/0.51 ( ( rBT_Im2075124343t_less @ A @ C2 @ Less2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 0.29/0.51 = ( ( Less2 @ Kt @ K )
% 0.29/0.51 & ( rBT_Im2075124343t_less @ A @ C2 @ Less2 @ K @ Lt )
% 0.29/0.51 & ( rBT_Im2075124343t_less @ A @ C2 @ Less2 @ K @ Rt ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_less_simps(2)
% 0.29/0.51 thf(fact_226_ord_Orbt__greater__simps_I2_J,axiom,
% 0.29/0.51 ! [C2: $tType,A: $tType,Less2: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.29/0.51 ( ( rBT_Im1259024060reater @ A @ C2 @ Less2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 0.29/0.51 = ( ( Less2 @ K @ Kt )
% 0.29/0.51 & ( rBT_Im1259024060reater @ A @ C2 @ Less2 @ K @ Lt )
% 0.29/0.51 & ( rBT_Im1259024060reater @ A @ C2 @ Less2 @ K @ Rt ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_greater_simps(2)
% 0.29/0.51 thf(fact_227_distinct__product__lists,axiom,
% 0.29/0.51 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 0.29/0.51 ( ! [X3: list @ A] :
% 0.29/0.51 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 0.29/0.51 => ( distinct @ A @ X3 ) )
% 0.29/0.51 => ( distinct @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct_product_lists
% 0.29/0.51 thf(fact_228_not__distinct__decomp,axiom,
% 0.29/0.51 ! [A: $tType,Ws2: list @ A] :
% 0.29/0.51 ( ~ ( distinct @ A @ Ws2 )
% 0.29/0.51 => ? [Xs2: list @ A,Ys2: list @ A,Zs3: list @ A,Y3: A] :
% 0.29/0.51 ( Ws2
% 0.29/0.51 = ( append @ A @ Xs2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ ( append @ A @ Ys2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_distinct_decomp
% 0.29/0.51 thf(fact_229_not__distinct__conv__prefix,axiom,
% 0.29/0.51 ! [A: $tType,As2: list @ A] :
% 0.29/0.51 ( ( ~ ( distinct @ A @ As2 ) )
% 0.29/0.51 = ( ? [Xs3: list @ A,Y2: A,Ys3: list @ A] :
% 0.29/0.51 ( ( member @ A @ Y2 @ ( set2 @ A @ Xs3 ) )
% 0.29/0.51 & ( distinct @ A @ Xs3 )
% 0.29/0.51 & ( As2
% 0.29/0.51 = ( append @ A @ Xs3 @ ( cons @ A @ Y2 @ Ys3 ) ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % not_distinct_conv_prefix
% 0.29/0.51 thf(fact_230_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,Less2: A > A > $o,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V2: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( rBT_Im759614907sorted @ A @ B @ Less2 @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V2 @ R ) )
% 0.29/0.51 = ( ( rBT_Im2075124343t_less @ A @ B @ Less2 @ K @ L )
% 0.29/0.51 & ( rBT_Im1259024060reater @ A @ B @ Less2 @ K @ R )
% 0.29/0.51 & ( rBT_Im759614907sorted @ A @ B @ Less2 @ L )
% 0.29/0.51 & ( rBT_Im759614907sorted @ A @ B @ Less2 @ R ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_sorted.simps(2)
% 0.29/0.51 thf(fact_231_distinct__union,axiom,
% 0.29/0.51 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.51 ( ( distinct @ A @ ( union @ A @ Xs @ Ys ) )
% 0.29/0.51 = ( distinct @ A @ Ys ) ) ).
% 0.29/0.51
% 0.29/0.51 % distinct_union
% 0.29/0.51 thf(fact_232_RBT__SORTED,axiom,
% 0.29/0.51 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ c @ t1 @ k @ v @ t2 ) ).
% 0.29/0.51
% 0.29/0.51 % RBT_SORTED
% 0.29/0.51 thf(fact_233_Branch_Oprems,axiom,
% 0.29/0.51 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ c @ t1 @ k @ v @ t2 ) ).
% 0.29/0.51
% 0.29/0.51 % Branch.prems
% 0.29/0.51 thf(fact_234_ord__class_Orbt__sorted_Osimps_I2_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.51 => ! [C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V2: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V2 @ R ) )
% 0.29/0.51 = ( ( rBT_Im903026891t_less @ A @ B @ K @ L )
% 0.29/0.51 & ( rBT_Im1332541288reater @ A @ B @ K @ R )
% 0.29/0.51 & ( rBT_Im1183586831sorted @ A @ B @ L )
% 0.29/0.51 & ( rBT_Im1183586831sorted @ A @ B @ R ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord_class.rbt_sorted.simps(2)
% 0.29/0.51 thf(fact_235_ord__class_Orbt__sorted_Osimps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/0.51 => ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord_class.rbt_sorted.simps(1)
% 0.29/0.51 thf(fact_236_linorder__class_Odistinct__keys,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/0.51 => ! [T: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( rBT_Im1183586831sorted @ A @ B @ T )
% 0.29/0.51 => ( distinct @ A @ ( rBT_Im380146495e_keys @ A @ B @ T ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % linorder_class.distinct_keys
% 0.29/0.51 thf(fact_237_local_OgreaterThan__def,axiom,
% 0.29/0.51 ! [L: a] :
% 0.29/0.51 ( ( set_greaterThan @ a @ less @ L )
% 0.29/0.51 = ( collect @ a @ ( less @ L ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.greaterThan_def
% 0.29/0.51 thf(fact_238_local_OlessThan__def,axiom,
% 0.29/0.51 ! [U: a] :
% 0.29/0.51 ( ( set_lessThan @ a @ less @ U )
% 0.29/0.51 = ( collect @ a
% 0.29/0.51 @ ^ [X2: a] : ( less @ X2 @ U ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.lessThan_def
% 0.29/0.51 thf(fact_239_local_OlessThan__iff,axiom,
% 0.29/0.51 ! [I: a,K: a] :
% 0.29/0.51 ( ( member @ a @ I @ ( set_lessThan @ a @ less @ K ) )
% 0.29/0.51 = ( less @ I @ K ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.lessThan_iff
% 0.29/0.51 thf(fact_240_local_OgreaterThan__iff,axiom,
% 0.29/0.51 ! [I: a,K: a] :
% 0.29/0.51 ( ( member @ a @ I @ ( set_greaterThan @ a @ less @ K ) )
% 0.29/0.51 = ( less @ K @ I ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.greaterThan_iff
% 0.29/0.51 thf(fact_241_DOM__T1,axiom,
% 0.29/0.51 ! [K3: a] :
% 0.29/0.51 ( ( member @ a @ K3 @ ( dom @ a @ b @ ( rBT_Im35466040lookup @ a @ b @ less @ t1 ) ) )
% 0.29/0.51 => ( less @ K3 @ k ) ) ).
% 0.29/0.51
% 0.29/0.51 % DOM_T1
% 0.29/0.51 thf(fact_242_local_Orbt__lookup__keys,axiom,
% 0.29/0.51 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.51 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.29/0.51 => ( ( dom @ a @ B @ ( rBT_Im35466040lookup @ a @ B @ less @ T ) )
% 0.29/0.51 = ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_lookup_keys
% 0.29/0.51 thf(fact_243_Branch_Ohyps_I1_J,axiom,
% 0.29/0.51 ( ( rBT_Im759614907sorted @ a @ b @ less @ t1 )
% 0.29/0.51 => ( ( map_of @ a @ b @ ( rBT_Im954575269ntries @ a @ b @ t1 ) )
% 0.29/0.51 = ( rBT_Im35466040lookup @ a @ b @ less @ t1 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Branch.hyps(1)
% 0.29/0.51 thf(fact_244_Branch_Ohyps_I2_J,axiom,
% 0.29/0.51 ( ( rBT_Im759614907sorted @ a @ b @ less @ t2 )
% 0.29/0.51 => ( ( map_of @ a @ b @ ( rBT_Im954575269ntries @ a @ b @ t2 ) )
% 0.29/0.51 = ( rBT_Im35466040lookup @ a @ b @ less @ t2 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % Branch.hyps(2)
% 0.29/0.51 thf(fact_245_entries_Osimps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType] :
% 0.29/0.51 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.29/0.51 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % entries.simps(1)
% 0.29/0.51 thf(fact_246_local_Orbt__lookup__Empty,axiom,
% 0.29/0.51 ! [B: $tType] :
% 0.29/0.51 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) )
% 0.29/0.51 = ( ^ [X2: a] : ( none @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_lookup_Empty
% 0.29/0.51 thf(fact_247_local_Orbt__lookup_Osimps_I1_J,axiom,
% 0.29/0.51 ! [B: $tType,K: a] :
% 0.29/0.51 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) @ K )
% 0.29/0.51 = ( none @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_lookup.simps(1)
% 0.29/0.51 thf(fact_248_local_Orbt__lookup__rbt__greater,axiom,
% 0.29/0.51 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.51 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.29/0.51 = ( none @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_lookup_rbt_greater
% 0.29/0.51 thf(fact_249_local_Orbt__lookup__rbt__less,axiom,
% 0.29/0.51 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.51 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.29/0.51 = ( none @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_lookup_rbt_less
% 0.29/0.51 thf(fact_250_ord_Orbt__lookup__rbt__less,axiom,
% 0.29/0.51 ! [A: $tType,B: $tType,Less2: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( rBT_Im2075124343t_less @ A @ B @ Less2 @ K @ T )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ T @ K )
% 0.29/0.51 = ( none @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_lookup_rbt_less
% 0.29/0.51 thf(fact_251_ord_Orbt__lookup__rbt__greater,axiom,
% 0.29/0.51 ! [A: $tType,B: $tType,Less2: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.29/0.51 ( ( rBT_Im1259024060reater @ A @ B @ Less2 @ K @ T )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ T @ K )
% 0.29/0.51 = ( none @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_lookup_rbt_greater
% 0.29/0.51 thf(fact_252_ord_Orbt__lookup_Osimps_I1_J,axiom,
% 0.29/0.51 ! [A: $tType,B: $tType,Less2: A > A > $o,K: A] :
% 0.29/0.51 ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ ( rBT_Im418718756_Empty @ A @ B ) @ K )
% 0.29/0.51 = ( none @ B ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_lookup.simps(1)
% 0.29/0.51 thf(fact_253_ord_Orbt__lookup__Empty,axiom,
% 0.29/0.51 ! [B: $tType,A: $tType,Less2: A > A > $o] :
% 0.29/0.51 ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.29/0.51 = ( ^ [X2: A] : ( none @ B ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % ord.rbt_lookup_Empty
% 0.29/0.51 thf(fact_254_local_Orbt__lookup_Osimps_I2_J,axiom,
% 0.29/0.51 ! [B: $tType,K: a,X: a,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.29/0.51 ( ( ( less @ K @ X )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.29/0.51 = ( rBT_Im35466040lookup @ a @ B @ less @ L @ K ) ) )
% 0.29/0.51 & ( ~ ( less @ K @ X )
% 0.29/0.51 => ( ( ( less @ X @ K )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.29/0.51 = ( rBT_Im35466040lookup @ a @ B @ less @ R @ K ) ) )
% 0.29/0.51 & ( ~ ( less @ X @ K )
% 0.29/0.51 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 0.29/0.51 = ( some @ B @ Y ) ) ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 % local.rbt_lookup.simps(2)
% 0.29/0.51
% 0.29/0.51 %----Type constructors (7)
% 0.29/0.51 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.51 ! [A6: $tType,A7: $tType] :
% 0.29/0.51 ( ( order @ A7 @ ( type2 @ A7 ) )
% 0.29/0.51 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.51 ! [A6: $tType,A7: $tType] :
% 0.29/0.51 ( ( ord @ A7 @ ( type2 @ A7 ) )
% 0.29/0.51 => ( ord @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.29/0.51
% 0.29/0.51 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 0.29/0.51 ! [A6: $tType] : ( order @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.29/0.51 ! [A6: $tType] : ( ord @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.29/0.51
% 0.29/0.51 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.29/0.51 linorder @ $o @ ( type2 @ $o ) ).
% 0.29/0.51
% 0.29/0.51 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 0.29/0.51 order @ $o @ ( type2 @ $o ) ).
% 0.29/0.51
% 0.29/0.51 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.29/0.51 ord @ $o @ ( type2 @ $o ) ).
% 0.29/0.51
% 0.29/0.51 %----Helper facts (3)
% 0.29/0.51 thf(help_If_3_1_T,axiom,
% 0.29/0.51 ! [P: $o] :
% 0.29/0.51 ( ( P = $true )
% 0.29/0.51 | ( P = $false ) ) ).
% 0.29/0.51
% 0.29/0.51 thf(help_If_2_1_T,axiom,
% 0.29/0.51 ! [A: $tType,X: A,Y: A] :
% 0.29/0.51 ( ( if @ A @ $false @ X @ Y )
% 0.29/0.51 = Y ) ).
% 0.29/0.51
% 0.29/0.51 thf(help_If_1_1_T,axiom,
% 0.29/0.51 ! [A: $tType,X: A,Y: A] :
% 0.29/0.51 ( ( if @ A @ $true @ X @ Y )
% 0.29/0.51 = X ) ).
% 0.29/0.51
% 0.29/0.51 %----Conjectures (1)
% 0.29/0.51 thf(conj_0,conjecture,
% 0.29/0.51 ! [X3: a] :
% 0.29/0.51 ( ( member @ a @ X3 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ b @ t2 ) ) )
% 0.29/0.51 => ( less @ k @ X3 ) ) ).
% 0.29/0.51
% 0.29/0.51 %------------------------------------------------------------------------------
% 0.29/0.51 ------------------------
% 2.37/1.40 ---- Embedded in THF ---
% 2.66/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.66/1.40 %%% Generated on Tue Feb 24 06:12:26 EST 2026
% 2.66/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 2.66/1.40 %%% Logic specification used:
% 2.66/1.40 %%% thf(spec, logic, $$dhol).
% 2.66/1.40
% 2.66/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oBDkFFmvot/DTF2DTF16703.p
% 2.66/1.40 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor, type, rBT_Im1923302023_color: $tType).
% 2.66/1.40 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt, type, rBT_Im246033960le_rbt: ($tType > ($tType > $tType))).
% 2.66/1.40 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.66/1.40 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.66/1.40 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.66/1.40 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.66/1.40 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.66/1.40 thf(ty_tf_b, type, b: $tType).
% 2.66/1.40 thf(ty_tf_a, type, a: $tType).
% 2.66/1.40 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.66/1.40 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.66/1.40 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.66/1.40 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.66/1.40 thf(sy_c_Fun_Oinj__on, type, inj_on: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > $o))))).
% 2.66/1.40 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.66/1.40 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.66/1.40 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.66/1.40 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.66/1.40 thf(sy_c_List_Odistinct, type, distinct: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.66/1.40 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.66/1.40 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.66/1.40 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.66/1.40 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.66/1.40 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.66/1.40 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.66/1.40 thf(sy_c_List_Oord_Olexordp, type, lexordp: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.66/1.40 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.66/1.40 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.66/1.40 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.66/1.40 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.66/1.40 thf(sy_c_List_Ounion, type, union: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.66/1.40 thf(sy_c_Map_Odom, type, dom: (!> [A:$tType,B:$tType]: (((A > (option @ B)) > (set @ A))))).
% 2.66/1.40 thf(sy_c_Map_Omap__of, type, map_of: (!> [A:$tType,B:$tType]: (((list @ ((product_prod @ A) @ B)) > (A > (option @ B)))))).
% 2.66/1.40 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.66/1.40 thf(sy_c_Option_Ooption_OSome, type, some: (!> [A:$tType]: ((A > (option @ A))))).
% 2.66/1.40 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.66/1.40 thf(sy_c_Orderings_Oorder_Ostrict__mono, type, strict_mono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.66/1.40 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries, type, rBT_Im954575269ntries: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (list @ ((product_prod @ A) @ B)))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Okeys, type, rBT_Im380146495e_keys: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (list @ A))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater, type, rBT_Im1259024060reater: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less, type, rBT_Im2075124343t_less: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup, type, rBT_Im35466040lookup: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (option @ B))))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted, type, rBT_Im759614907sorted: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__greater, type, rBT_Im1332541288reater: (!> [A:$tType,B:$tType]: ((A > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__less, type, rBT_Im903026891t_less: (!> [A:$tType,B:$tType]: ((A > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__sorted, type, rBT_Im1183586831sorted: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > $o)))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch, type, rBT_Im480247531Branch: (!> [A:$tType,B:$tType]: ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 2.66/1.40 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty, type, rBT_Im418718756_Empty: (!> [A:$tType,B:$tType]: (((rBT_Im246033960le_rbt @ A) @ B)))).
% 2.66/1.40 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.66/1.40 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.66/1.40 thf(sy_c_Set__Interval_Oord_OgreaterThan, type, set_greaterThan: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.66/1.40 thf(sy_c_Set__Interval_Oord_OlessThan, type, set_lessThan: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.66/1.40 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.66/1.40 thf(sy_v_c____, type, c: rBT_Im1923302023_color).
% 2.66/1.40 thf(sy_v_k____, type, k: a).
% 2.66/1.40 thf(sy_v_less, type, less: (a > (a > $o))).
% 2.66/1.40 thf(sy_v_t1____, type, t1: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.66/1.40 thf(sy_v_t2____, type, t2: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.66/1.40 thf(sy_v_v____, type, v: b).
% 2.66/1.40 thf(fact_0_local_Oantisym__conv3, axiom, (! [Y:a,X:a]: (((~ (((less @ Y) @ X))) => ((~ (((less @ X) @ Y))) = (X = Y)))))).
% 2.66/1.40 thf(fact_1_local_Odual__order_Oasym, axiom, (! [B2:a,A2:a]: ((((less @ B2) @ A2) => (~ (((less @ A2) @ B2))))))).
% 2.66/1.40 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq, axiom, (! [B2:a,A2:a]: ((((less @ B2) @ A2) => (A2 != B2))))).
% 2.66/1.40 thf(fact_3_local_Odual__order_Ostrict__trans, axiom, (! [B2:a,A2:a,C:a]: ((((less @ B2) @ A2) => (((less @ C) @ B2) => ((less @ C) @ A2)))))).
% 2.66/1.40 thf(fact_4_local_Oless__asym, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.66/1.40 thf(fact_5_local_Oless__asym_H, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (~ (((less @ B2) @ A2))))))).
% 2.66/1.40 thf(fact_6_local_Oless__imp__neq, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (X != Y))))).
% 2.66/1.40 thf(fact_7_local_Oless__imp__not__eq, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (X != Y))))).
% 2.66/1.40 thf(fact_8_local_Oless__imp__not__eq2, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (Y != X))))).
% 2.66/1.40 thf(fact_9_local_Oless__imp__not__less, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.66/1.40 thf(fact_10_local_Oless__imp__triv, axiom, (! [X:a,Y:a,P:$o]: ((((less @ X) @ Y) => (((less @ Y) @ X) => P))))).
% 2.66/1.40 thf(fact_11_local_Oless__irrefl, axiom, (! [X:a]: ((~ (((less @ X) @ X)))))).
% 2.66/1.40 thf(fact_12_local_Oless__linear, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) | ((X = Y) | ((less @ Y) @ X)))))).
% 2.66/1.40 thf(fact_13_local_Oless__not__sym, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.66/1.40 thf(fact_14_local_Oless__trans, axiom, (! [X:a,Y:a,Z:a]: ((((less @ X) @ Y) => (((less @ Y) @ Z) => ((less @ X) @ Z)))))).
% 2.66/1.40 thf(fact_15_local_Olinorder__cases, axiom, (! [X:a,Y:a]: (((~ (((less @ X) @ Y))) => ((X != Y) => ((less @ Y) @ X)))))).
% 2.66/1.40 thf(fact_16_local_OneqE, axiom, (! [X:a,Y:a]: (((X != Y) => ((~ (((less @ X) @ Y))) => ((less @ Y) @ X)))))).
% 2.66/1.40 thf(fact_17_local_Oneq__iff, axiom, (! [X:a,Y:a]: (((X != Y) = (((less @ X) @ Y) | ((less @ Y) @ X)))))).
% 2.66/1.40 thf(fact_18_local_Onot__less__iff__gr__or__eq, axiom, (! [X:a,Y:a]: (((~ (((less @ X) @ Y))) = (((less @ Y) @ X) | (X = Y)))))).
% 2.66/1.40 thf(fact_19_local_Oord__eq__less__trans, axiom, (! [A2:a,B2:a,C:a]: (((A2 = B2) => (((less @ B2) @ C) => ((less @ A2) @ C)))))).
% 2.66/1.40 thf(fact_20_local_Oord__less__eq__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less @ A2) @ B2) => ((B2 = C) => ((less @ A2) @ C)))))).
% 2.66/1.40 thf(fact_21_local_Oorder_Oasym, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (~ (((less @ B2) @ A2))))))).
% 2.66/1.40 thf(fact_22_local_Oorder_Oirrefl, axiom, (! [A2:a]: ((~ (((less @ A2) @ A2)))))).
% 2.66/1.40 thf(fact_23_local_Oorder_Ostrict__implies__not__eq, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (A2 != B2))))).
% 2.66/1.40 thf(fact_24_local_Oorder_Ostrict__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less @ A2) @ B2) => (((less @ B2) @ C) => ((less @ A2) @ C)))))).
% 2.66/1.40 thf(fact_25_local_Orbt__greater__prop, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ T) = (! [X2:a]: (((((member @ a) @ X2) @ ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T))) => ((less @ K) @ X2)))))))).
% 2.66/1.40 thf(fact_26_local_Orbt__greater__trans, axiom, (! [C2:$tType,X:a,Y:a,T:((rBT_Im246033960le_rbt @ a) @ C2)]: ((((less @ X) @ Y) => ((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ Y) @ T) => (((((rBT_Im1259024060reater @ a) @ C2) @ less) @ X) @ T)))))).
% 2.66/1.40 thf(fact_27__092_060open_062k_A_092_060guillemotleft_062_124_At2_092_060close_062, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ k) @ t2)).
% 2.66/1.40 thf(fact_28_local_Ostrict__mono__eq, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => (((F @ X) = (F @ Y)) = (X = Y))))))))).
% 2.66/1.40 thf(fact_29_local_Orbt__less__prop, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ T) = (! [X2:a]: (((((member @ a) @ X2) @ ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T))) => ((less @ X2) @ K)))))))).
% 2.66/1.40 thf(fact_30_ord_Orbt__greater__prop, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im1259024060reater @ A) @ B) = (^ [Less:(A > (A > $o)),K2:A,T2:((rBT_Im246033960le_rbt @ A) @ B)]: ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T2))) => ((Less @ K2) @ X2)))))))))).
% 2.66/1.40 thf(fact_31_local_Orbt__less__trans, axiom, (! [C2:$tType,X:a,T:((rBT_Im246033960le_rbt @ a) @ C2),Y:a]: (((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ X) @ T) => (((less @ X) @ Y) => (((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ Y) @ T)))))).
% 2.66/1.40 thf(fact_32_local_Olexordp__eq__antisym, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) => (((((lexordp_eq @ a) @ less) @ Ys) @ Xs) => (Xs = Ys)))))).
% 2.66/1.40 thf(fact_33_local_Olexordp__eq__linear, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) | ((((lexordp_eq @ a) @ less) @ Ys) @ Xs))))).
% 2.66/1.40 thf(fact_34_local_Olexordp__eq__refl, axiom, (! [Xs:(list @ a)]: (((((lexordp_eq @ a) @ less) @ Xs) @ Xs)))).
% 2.66/1.40 thf(fact_35_local_Olexordp__eq__trans, axiom, (! [Xs:(list @ a),Ys:(list @ a),Zs:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) => (((((lexordp_eq @ a) @ less) @ Ys) @ Zs) => ((((lexordp_eq @ a) @ less) @ Xs) @ Zs)))))).
% 2.66/1.40 thf(fact_36_ord_Orbt__less__prop, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im2075124343t_less @ A) @ B) = (^ [Less:(A > (A > $o)),K2:A,T2:((rBT_Im246033960le_rbt @ A) @ B)]: ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T2))) => ((Less @ X2) @ K2)))))))))).
% 2.66/1.40 thf(fact_37_local_Olexordp__antisym, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (~ (((((lexordp @ a) @ less) @ Ys) @ Xs))))))).
% 2.66/1.40 thf(fact_38_local_Olexordp__irreflexive, axiom, (! [Xs:(list @ a)]: (((! [X3:a]: ((~ (((less @ X3) @ X3))))) => (~ (((((lexordp @ a) @ less) @ Xs) @ Xs))))))).
% 2.66/1.40 thf(fact_39_local_Olexordp__irreflexive_H, axiom, (! [Xs:(list @ a)]: ((~ (((((lexordp @ a) @ less) @ Xs) @ Xs)))))).
% 2.66/1.40 thf(fact_40_local_Olexordp__linear, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) | ((Xs = Ys) | ((((lexordp @ a) @ less) @ Ys) @ Xs)))))).
% 2.66/1.40 thf(fact_41_local_Olexordp__trans, axiom, (! [Xs:(list @ a),Ys:(list @ a),Zs:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (((((lexordp @ a) @ less) @ Ys) @ Zs) => ((((lexordp @ a) @ less) @ Xs) @ Zs)))))).
% 2.66/1.40 thf(fact_42_local_Olexordp__into__lexordp__eq, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => ((((lexordp_eq @ a) @ less) @ Xs) @ Ys))))).
% 2.66/1.40 thf(fact_43_local_Olexordp__eq__conv__lexord, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) = ((Xs = Ys) | ((((lexordp @ a) @ less) @ Xs) @ Ys)))))).
% 2.66/1.40 thf(fact_44_local_Olexordp__conv__lexordp__eq, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) = (((((lexordp_eq @ a) @ less) @ Xs) @ Ys) & (~ (((((lexordp_eq @ a) @ less) @ Ys) @ Xs)))))))).
% 2.66/1.40 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.66/1.40 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 2.66/1.40 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.66/1.40 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.66/1.40 thf(fact_49_local_Ostrict__mono__less, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => ((((ord_less @ B) @ (F @ X)) @ (F @ Y)) = ((less @ X) @ Y))))))))).
% 2.66/1.40 thf(fact_50_local_Ostrict__mono__def, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B)]: ((((((strict_mono @ a) @ B) @ less) @ F) = (! [X2:a,Y2:a]: ((((less @ X2) @ Y2) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y2)))))))))))).
% 2.66/1.40 thf(fact_51_local_Ostrict__monoI, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B)]: (((! [X3:a,Y3:a]: ((((less @ X3) @ Y3) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y3))))) => ((((strict_mono @ a) @ B) @ less) @ F)))))))).
% 2.66/1.40 thf(fact_52_local_Ostrict__monoD, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => (((less @ X) @ Y) => (((ord_less @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.66/1.40 thf(fact_53_local_Olexordp__eq_ONil, axiom, (! [Ys:(list @ a)]: (((((lexordp_eq @ a) @ less) @ (nil @ a)) @ Ys)))).
% 2.66/1.40 thf(fact_54_ord_Olexordp__into__lexordp__eq, axiom, (! [A:$tType,Less2:(A > (A > $o)),Xs:(list @ A),Ys:(list @ A)]: ((((((lexordp @ A) @ Less2) @ Xs) @ Ys) => ((((lexordp_eq @ A) @ Less2) @ Xs) @ Ys))))).
% 2.66/1.40 thf(fact_55_local_Olexordp__eq_OCons__eq, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: (((~ (((less @ X) @ Y))) => ((~ (((less @ Y) @ X))) => (((((lexordp_eq @ a) @ less) @ Xs) @ Ys) => ((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))))).
% 2.66/1.40 thf(fact_56_local_Olexordp__eq_OCons, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: ((((less @ X) @ Y) => ((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))).
% 2.66/1.40 thf(fact_57_local_Olexordp_OCons, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: ((((less @ X) @ Y) => ((((lexordp @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))).
% 2.66/1.40 thf(fact_58_local_Olexordp_OCons__eq, axiom, (! [X:a,Y:a,Xs:(list @ a),Ys:(list @ a)]: (((~ (((less @ X) @ Y))) => ((~ (((less @ Y) @ X))) => (((((lexordp @ a) @ less) @ Xs) @ Ys) => ((((lexordp @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)))))))).
% 2.66/1.40 thf(fact_59_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.66/1.40 thf(fact_60_local_Olexordp_ONil, axiom, (! [Y:a,Ys:(list @ a)]: (((((lexordp @ a) @ less) @ (nil @ a)) @ (((cons @ a) @ Y) @ Ys))))).
% 2.66/1.40 thf(fact_61_local_Olexordp_Ocases, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp @ a) @ less) @ A1) @ A22) => (((A1 = (nil @ a)) => (! [Y3:a,Ys2:(list @ a)]: ((A22 != (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a]: (((? [Xs2:(list @ a)]: ((A1 = (((cons @ a) @ X3) @ Xs2)))) => (! [Y3:a]: (((? [Ys2:(list @ a)]: ((A22 = (((cons @ a) @ Y3) @ Ys2)))) => (~ (((less @ X3) @ Y3))))))))) => (~ ((! [X3:a,Y3:a,Xs2:(list @ a)]: (((A1 = (((cons @ a) @ X3) @ Xs2)) => (! [Ys2:(list @ a)]: (((A22 = (((cons @ a) @ Y3) @ Ys2)) => ((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (~ (((((lexordp @ a) @ less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.66/1.40 thf(fact_62_local_Olexordp_Oinducts, axiom, (! [X1:(list @ a),X23:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp @ a) @ less) @ X1) @ X23) => ((! [Y3:a,Ys2:(list @ a)]: (((P @ (nil @ a)) @ (((cons @ a) @ Y3) @ Ys2)))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((less @ X3) @ Y3) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: (((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (((((lexordp @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2)))))))) => ((P @ X1) @ X23)))))))).
% 2.66/1.40 thf(fact_63_local_Olexordp_Osimps, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp @ a) @ less) @ A1) @ A22) = ((? [Y2:a,Ys3:(list @ a)]: (((A1 = (nil @ a)) & (A22 = (((cons @ a) @ Y2) @ Ys3))))) | ((? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((less @ X2) @ Y2))))) | (? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((~ (((less @ X2) @ Y2))) & ((~ (((less @ Y2) @ X2))) & ((((lexordp @ a) @ less) @ Xs3) @ Ys3))))))))))))).
% 2.66/1.40 thf(fact_64_local_Olexordp__cases, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (((Xs = (nil @ a)) => (! [Y3:a,Ys4:(list @ a)]: ((Ys != (((cons @ a) @ Y3) @ Ys4))))) => ((! [X3:a]: (((? [Xs4:(list @ a)]: ((Xs = (((cons @ a) @ X3) @ Xs4)))) => (! [Y3:a]: (((? [Ys4:(list @ a)]: ((Ys = (((cons @ a) @ Y3) @ Ys4)))) => (~ (((less @ X3) @ Y3))))))))) => (~ ((! [X3:a,Xs4:(list @ a)]: (((Xs = (((cons @ a) @ X3) @ Xs4)) => (! [Ys4:(list @ a)]: (((Ys = (((cons @ a) @ X3) @ Ys4)) => (~ (((((lexordp @ a) @ less) @ Xs4) @ Ys4))))))))))))))))).
% 2.66/1.40 thf(fact_65_local_Olexordp__induct, axiom, (! [Xs:(list @ a),Ys:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => ((! [Y3:a,Ys2:(list @ a)]: (((P @ (nil @ a)) @ (((cons @ a) @ Y3) @ Ys2)))) => ((! [X3:a,Xs2:(list @ a),Y3:a,Ys2:(list @ a)]: ((((less @ X3) @ Y3) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ X3) @ Ys2)))))) => ((P @ Xs) @ Ys)))))))).
% 2.66/1.40 thf(fact_66_local_Olexordp__eq_Ocases, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ A1) @ A22) => (((A1 = (nil @ a)) => (! [Ys2:(list @ a)]: ((A22 != Ys2)))) => ((! [X3:a]: (((? [Xs2:(list @ a)]: ((A1 = (((cons @ a) @ X3) @ Xs2)))) => (! [Y3:a]: (((? [Ys2:(list @ a)]: ((A22 = (((cons @ a) @ Y3) @ Ys2)))) => (~ (((less @ X3) @ Y3))))))))) => (~ ((! [X3:a,Y3:a,Xs2:(list @ a)]: (((A1 = (((cons @ a) @ X3) @ Xs2)) => (! [Ys2:(list @ a)]: (((A22 = (((cons @ a) @ Y3) @ Ys2)) => ((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (~ (((((lexordp_eq @ a) @ less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.66/1.40 thf(fact_67_local_Olexordp__eq_Oinducts, axiom, (! [X1:(list @ a),X23:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp_eq @ a) @ less) @ X1) @ X23) => ((! [X12:(list @ a)]: (((P @ (nil @ a)) @ X12))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((less @ X3) @ Y3) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2))))) => ((! [X3:a,Y3:a,Xs2:(list @ a),Ys2:(list @ a)]: (((~ (((less @ X3) @ Y3))) => ((~ (((less @ Y3) @ X3))) => (((((lexordp_eq @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y3) @ Ys2)))))))) => ((P @ X1) @ X23)))))))).
% 2.66/1.40 thf(fact_68_local_Olexordp__eq_Osimps, axiom, (! [A1:(list @ a),A22:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ A1) @ A22) = ((? [Ys3:(list @ a)]: (((A1 = (nil @ a)) & (A22 = Ys3)))) | ((? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((less @ X2) @ Y2))))) | (? [X2:a,Y2:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y2) @ Ys3)) & ((~ (((less @ X2) @ Y2))) & ((~ (((less @ Y2) @ X2))) & ((((lexordp_eq @ a) @ less) @ Xs3) @ Ys3))))))))))))).
% 2.66/1.40 thf(fact_69_ord_Olexordp__simps_I3_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: ((((((lexordp @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((Less2 @ X) @ Y) | ((~ (((Less2 @ Y) @ X))) & ((((lexordp @ A) @ Less2) @ Xs) @ Ys))))))).
% 2.66/1.40 thf(fact_70_ord_Olexordp__simps_I1_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),Ys:(list @ A)]: ((((((lexordp @ A) @ Less2) @ (nil @ A)) @ Ys) = (Ys != (nil @ A)))))).
% 2.66/1.40 thf(fact_71_ord_Olexordp__simps_I2_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),Xs:(list @ A)]: ((~ (((((lexordp @ A) @ Less2) @ Xs) @ (nil @ A))))))).
% 2.66/1.40 thf(fact_72_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: ((((((lexordp_eq @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((Less2 @ X) @ Y) | ((~ (((Less2 @ Y) @ X))) & ((((lexordp_eq @ A) @ Less2) @ Xs) @ Ys))))))).
% 2.66/1.40 thf(fact_73_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less2) @ (nil @ A)) @ Ys)))).
% 2.66/1.40 thf(fact_74_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less2) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.66/1.40 thf(fact_75_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A))))))).
% 2.66/1.40 thf(fact_76_local_Olexordp__simps_I3_J, axiom, (! [X:a,Xs:(list @ a),Y:a,Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)) = (((less @ X) @ Y) | ((~ (((less @ Y) @ X))) & ((((lexordp @ a) @ less) @ Xs) @ Ys))))))).
% 2.66/1.40 thf(fact_77_local_Olexordp__eq__simps_I4_J, axiom, (! [X:a,Xs:(list @ a),Y:a,Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)) = (((less @ X) @ Y) | ((~ (((less @ Y) @ X))) & ((((lexordp_eq @ a) @ less) @ Xs) @ Ys))))))).
% 2.66/1.40 thf(fact_78_local_Olexordp__simps_I2_J, axiom, (! [Xs:(list @ a)]: ((~ (((((lexordp @ a) @ less) @ Xs) @ (nil @ a))))))).
% 2.66/1.40 thf(fact_79_local_Olexordp__simps_I1_J, axiom, (! [Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ (nil @ a)) @ Ys) = (Ys != (nil @ a)))))).
% 2.66/1.40 thf(fact_80_local_Olexordp__eq__simps_I2_J, axiom, (! [Xs:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ (nil @ a)) = (Xs = (nil @ a)))))).
% 2.66/1.40 thf(fact_81_local_Olexordp__eq__simps_I1_J, axiom, (! [Ys:(list @ a)]: (((((lexordp_eq @ a) @ less) @ (nil @ a)) @ Ys)))).
% 2.66/1.40 thf(fact_82_local_Olexordp__eq__simps_I3_J, axiom, (! [X:a,Xs:(list @ a)]: ((~ (((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (nil @ a))))))).
% 2.66/1.40 thf(fact_83_ord_Olexordp_ONil, axiom, (! [A:$tType,Less2:(A > (A > $o)),Y:A,Ys:(list @ A)]: (((((lexordp @ A) @ Less2) @ (nil @ A)) @ (((cons @ A) @ Y) @ Ys))))).
% 2.66/1.40 thf(fact_84_ord_Olexordp_Ocases, axiom, (! [A:$tType,Less2:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp @ A) @ Less2) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Y3:A,Ys2:(list @ A)]: ((A22 != (((cons @ A) @ Y3) @ Ys2))))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y3:A]: (((? [Ys2:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys2)))) => (~ (((Less2 @ X3) @ Y3))))))))) => (~ ((! [X3:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys2)) => ((~ (((Less2 @ X3) @ Y3))) => ((~ (((Less2 @ Y3) @ X3))) => (~ (((((lexordp @ A) @ Less2) @ Xs2) @ Ys2))))))))))))))))))).
% 2.66/1.40 thf(fact_85_ord_Olexordp_Osimps, axiom, (! [A:$tType]: (((lexordp @ A) = (^ [Less:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Y2:A,Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A23 = (((cons @ A) @ Y2) @ Ys3))))) | ((? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((Less @ X2) @ Y2))))) | (? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((~ (((Less @ X2) @ Y2))) & ((~ (((Less @ Y2) @ X2))) & ((((lexordp @ A) @ Less) @ Xs3) @ Ys3))))))))))))))).
% 2.66/1.40 thf(fact_86_ord_Olexordp_Oinducts, axiom, (! [A:$tType,Less2:(A > (A > $o)),X1:(list @ A),X23:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp @ A) @ Less2) @ X1) @ X23) => ((! [Y3:A,Ys2:(list @ A)]: (((P @ (nil @ A)) @ (((cons @ A) @ Y3) @ Ys2)))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((Less2 @ X3) @ Y3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ (((Less2 @ X3) @ Y3))) => ((~ (((Less2 @ Y3) @ X3))) => (((((lexordp @ A) @ Less2) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2)))))))) => ((P @ X1) @ X23)))))))).
% 2.66/1.40 thf(fact_87_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less2:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp_eq @ A) @ Less2) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Ys2:(list @ A)]: ((A22 != Ys2)))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y3:A]: (((? [Ys2:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys2)))) => (~ (((Less2 @ X3) @ Y3))))))))) => (~ ((! [X3:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys2)) => ((~ (((Less2 @ X3) @ Y3))) => ((~ (((Less2 @ Y3) @ X3))) => (~ (((((lexordp_eq @ A) @ Less2) @ Xs2) @ Ys2))))))))))))))))))).
% 2.66/1.40 thf(fact_88_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys3)))) | ((? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((Less @ X2) @ Y2))))) | (? [X2:A,Y2:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys3)) & ((~ (((Less @ X2) @ Y2))) & ((~ (((Less @ Y2) @ X2))) & ((((lexordp_eq @ A) @ Less) @ Xs3) @ Ys3))))))))))))))).
% 2.66/1.40 thf(fact_89_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less2:(A > (A > $o)),X1:(list @ A),X23:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less2) @ X1) @ X23) => ((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((Less2 @ X3) @ Y3) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))))) => ((! [X3:A,Y3:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ (((Less2 @ X3) @ Y3))) => ((~ (((Less2 @ Y3) @ X3))) => (((((lexordp_eq @ A) @ Less2) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2)))))))) => ((P @ X1) @ X23)))))))).
% 2.66/1.40 thf(fact_90_list_Oset__cases, axiom, (! [A:$tType,E:A,A2:(list @ A)]: (((((member @ A) @ E) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((set2 @ A) @ Z2)))))))))))))).
% 2.66/1.40 thf(fact_91_set__ConsD, axiom, (! [A:$tType,Y:A,X:A,Xs:(list @ A)]: (((((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs))) => ((Y = X) | (((member @ A) @ Y) @ ((set2 @ A) @ Xs))))))).
% 2.66/1.40 thf(fact_92_list_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(list @ A)]: ((((member @ A) @ A1) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A22)))))).
% 2.66/1.40 thf(fact_93_list_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(list @ A),A1:A]: (((((member @ A) @ X) @ ((set2 @ A) @ A22)) => (((member @ A) @ X) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A22))))))).
% 2.66/1.40 thf(fact_94_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X12:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X12))) => ((! [F2:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A4)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.66/1.40 thf(fact_95_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X3) @ Xs2)))))) => (P @ Xs))))))).
% 2.66/1.40 thf(fact_96_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y3:A,Xs2:(list @ A)]: ((((X3 = Y3) => (P @ (((cons @ A) @ X3) @ Xs2))) => (((X3 != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 2.66/1.40 thf(fact_97_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X3:A]: ((X != (((cons @ A) @ X3) @ (nil @ A))))) => (~ ((! [X3:A,Y3:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X3) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 2.66/1.40 thf(fact_98_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X3:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X3) @ Xs2)) @ Xss))))))))))).
% 2.66/1.40 thf(fact_99_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.66/1.40 thf(fact_100_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [V:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V) @ Va)) @ (nil @ A)))) => ((! [X3:A,Xs2:(list @ A),Y3:A,Ys2:(list @ A)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys2))))) => ((P @ A0) @ A1))))))).
% 2.66/1.40 thf(fact_101_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X3) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys2)))) => ((! [X3:A,Xs2:(list @ A),Y3:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.66/1.40 thf(fact_102_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y2:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y2) @ Ys3)))))))).
% 2.66/1.40 thf(fact_103_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X12:A,X24:(list @ A)]: (((P @ X24) => (P @ (((cons @ A) @ X12) @ X24))))) => (P @ List)))))).
% 2.66/1.40 thf(fact_104_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.66/1.40 thf(fact_105_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.66/1.40 thf(fact_106_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.66/1.40 thf(fact_107_ord_Olexordp_OCons__eq, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ (((Less2 @ X) @ Y))) => ((~ (((Less2 @ Y) @ X))) => (((((lexordp @ A) @ Less2) @ Xs) @ Ys) => ((((lexordp @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))))).
% 2.66/1.40 thf(fact_108_ord_Olexordp_OCons, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: ((((Less2 @ X) @ Y) => ((((lexordp @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.66/1.40 thf(fact_109_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ (((Less2 @ X) @ Y))) => ((~ (((Less2 @ Y) @ X))) => (((((lexordp_eq @ A) @ Less2) @ Xs) @ Ys) => ((((lexordp_eq @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))))).
% 2.66/1.40 thf(fact_110_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: ((((Less2 @ X) @ Y) => ((((lexordp_eq @ A) @ Less2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.66/1.40 thf(fact_111_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less2:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less2) @ (nil @ A)) @ Ys)))).
% 2.66/1.40 thf(fact_112_ord_Olexordp__irreflexive, axiom, (! [A:$tType,Less2:(A > (A > $o)),Xs:(list @ A)]: (((! [X3:A]: ((~ (((Less2 @ X3) @ X3))))) => (~ (((((lexordp @ A) @ Less2) @ Xs) @ Xs))))))).
% 2.66/1.40 thf(fact_113_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less2:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less2) @ Xs) @ Xs)))).
% 2.66/1.40 thf(fact_114_local_Olexordp__append__rightI, axiom, (! [Ys:(list @ a),Xs:(list @ a)]: (((Ys != (nil @ a)) => ((((lexordp @ a) @ less) @ Xs) @ (((append @ a) @ Xs) @ Ys)))))).
% 2.66/1.40 thf(fact_115_local_Olexordp__append__left__rightI, axiom, (! [X:a,Y:a,Us:(list @ a),Xs:(list @ a),Ys:(list @ a)]: ((((less @ X) @ Y) => ((((lexordp @ a) @ less) @ (((append @ a) @ Us) @ (((cons @ a) @ X) @ Xs))) @ (((append @ a) @ Us) @ (((cons @ a) @ Y) @ Ys))))))).
% 2.66/1.40 thf(fact_116_local_Olexordp__iff, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) = ((? [X2:a,Vs:(list @ a)]: ((Ys = (((append @ a) @ Xs) @ (((cons @ a) @ X2) @ Vs))))) | (? [Us2:(list @ a),A5:a,B3:a,Vs:(list @ a),Ws:(list @ a)]: ((((less @ A5) @ B3) & ((Xs = (((append @ a) @ Us2) @ (((cons @ a) @ A5) @ Vs))) & (Ys = (((append @ a) @ Us2) @ (((cons @ a) @ B3) @ Ws)))))))))))).
% 2.66/1.40 thf(fact_117_the__elem__set, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ ((set2 @ A) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.66/1.40 thf(fact_118_local_Olexordp__append__leftD, axiom, (! [Xs:(list @ a),Us:(list @ a),Vs2:(list @ a)]: ((((((lexordp @ a) @ less) @ (((append @ a) @ Xs) @ Us)) @ (((append @ a) @ Xs) @ Vs2)) => ((! [A4:a]: ((~ (((less @ A4) @ A4))))) => ((((lexordp @ a) @ less) @ Us) @ Vs2)))))).
% 2.66/1.40 thf(fact_119_local_Olexordp__append__leftI, axiom, (! [Us:(list @ a),Vs2:(list @ a),Xs:(list @ a)]: ((((((lexordp @ a) @ less) @ Us) @ Vs2) => ((((lexordp @ a) @ less) @ (((append @ a) @ Xs) @ Us)) @ (((append @ a) @ Xs) @ Vs2)))))).
% 2.66/1.40 thf(fact_120_local_Ostrict__mono__imp__inj__on, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),A3:(set @ a)]: ((((((strict_mono @ a) @ B) @ less) @ F) => ((((inj_on @ a) @ B) @ F) @ A3)))))))).
% 2.66/1.40 thf(fact_121_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs)) = (Ys = Zs))))).
% 2.66/1.40 thf(fact_122_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys = Zs))))).
% 2.66/1.40 thf(fact_123_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)))))).
% 2.66/1.40 thf(fact_124_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.66/1.40 thf(fact_125_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.66/1.40 thf(fact_126_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.66/1.40 thf(fact_127_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.66/1.40 thf(fact_128_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.66/1.40 thf(fact_129_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.66/1.40 thf(fact_130_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.66/1.40 thf(fact_131_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.66/1.40 thf(fact_132_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Ts)) = (? [Us2:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us2)) & ((((append @ A) @ Us2) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us2) = Zs) & (Ys = (((append @ A) @ Us2) @ Ts)))))))))).
% 2.66/1.40 thf(fact_133_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys:(list @ A),Us:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs) => ((Ys = (((append @ A) @ Xs1) @ Us)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs) @ Us))))))).
% 2.66/1.40 thf(fact_134_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs))))))).
% 2.66/1.40 thf(fact_135_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.66/1.40 thf(fact_136_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.66/1.40 thf(fact_137_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.66/1.40 thf(fact_138_ord_Olexordp__append__leftI, axiom, (! [A:$tType,Less2:(A > (A > $o)),Us:(list @ A),Vs2:(list @ A),Xs:(list @ A)]: ((((((lexordp @ A) @ Less2) @ Us) @ Vs2) => ((((lexordp @ A) @ Less2) @ (((append @ A) @ Xs) @ Us)) @ (((append @ A) @ Xs) @ Vs2)))))).
% 2.66/1.40 thf(fact_139_ord_Olexordp__append__leftD, axiom, (! [A:$tType,Less2:(A > (A > $o)),Xs:(list @ A),Us:(list @ A),Vs2:(list @ A)]: ((((((lexordp @ A) @ Less2) @ (((append @ A) @ Xs) @ Us)) @ (((append @ A) @ Xs) @ Vs2)) => ((! [A4:A]: ((~ (((Less2 @ A4) @ A4))))) => ((((lexordp @ A) @ Less2) @ Us) @ Vs2)))))).
% 2.66/1.40 thf(fact_140_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.66/1.40 thf(fact_141_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys2:(list @ A),Y3:A]: ((Xs != (((append @ A) @ Ys2) @ (((cons @ A) @ Y3) @ (nil @ A)))))))))))).
% 2.66/1.40 thf(fact_142_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys5:(list @ A)]: ((((((cons @ A) @ X) @ Ys5) = Ys) & (Xs = (((append @ A) @ Ys5) @ Zs)))))))))).
% 2.66/1.40 thf(fact_143_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs = (((cons @ A) @ X) @ Xs))) | (? [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) & ((((append @ A) @ Ys5) @ Zs) = Xs))))))))).
% 2.66/1.40 thf(fact_144_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X3) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.66/1.40 thf(fact_145_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) = (? [Ys3:(list @ A),X2:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs2))))) & ((P @ X2) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Y2)))))))))))))).
% 2.66/1.40 thf(fact_146_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) & (P @ X2)))) = (? [Ys3:(list @ A),X2:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X2) @ Zs2))) & ((P @ X2) & (! [Y2:A]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Zs2)) => (~ ((P @ Y2)))))))))))))).
% 2.66/1.40 thf(fact_147_in__set__conv__decomp__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys3))))))))))).
% 2.66/1.40 thf(fact_148_in__set__conv__decomp__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs2))))))))))).
% 2.66/1.40 thf(fact_149_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) => ((P @ X3) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))))))).
% 2.66/1.40 thf(fact_150_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys2:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))) => ((P @ X3) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Xa)))))))))))))))))).
% 2.66/1.40 thf(fact_151_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) & ((P @ X3) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))).
% 2.66/1.40 thf(fact_152_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys2:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))) & ((P @ X3) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Xa)))))))))))))).
% 2.66/1.40 thf(fact_153_in__set__conv__decomp, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs2))))))))).
% 2.66/1.40 thf(fact_154_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (~ ((! [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) => (~ ((P @ X3)))))))))))).
% 2.66/1.40 thf(fact_155_split__list__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys2))))))))))).
% 2.66/1.40 thf(fact_156_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P @ X4)))) => (? [Ys2:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs3))))) & (P @ X3)))))))).
% 2.66/1.40 thf(fact_157_split__list__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs3))))))))))).
% 2.66/1.40 thf(fact_158_split__list, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs3))))))))).
% 2.66/1.40 thf(fact_159_ord_Olexordp__append__left__rightI, axiom, (! [A:$tType,Less2:(A > (A > $o)),X:A,Y:A,Us:(list @ A),Xs:(list @ A),Ys:(list @ A)]: ((((Less2 @ X) @ Y) => ((((lexordp @ A) @ Less2) @ (((append @ A) @ Us) @ (((cons @ A) @ X) @ Xs))) @ (((append @ A) @ Us) @ (((cons @ A) @ Y) @ Ys))))))).
% 2.66/1.40 thf(fact_160_ord_Olexordp__append__rightI, axiom, (! [A:$tType,Ys:(list @ A),Less2:(A > (A > $o)),Xs:(list @ A)]: (((Ys != (nil @ A)) => ((((lexordp @ A) @ Less2) @ Xs) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.66/1.40 thf(fact_161_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.66/1.40 thf(fact_162_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.66/1.40 thf(fact_163_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F) = (((append @ A) @ (F @ X)) @ ((((bind @ B) @ A) @ Xs) @ F)))))).
% 2.66/1.40 thf(fact_164_ord__class_Orbt__greater__prop, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (((rBT_Im1332541288reater @ A) @ B) = (^ [K2:A,T2:((rBT_Im246033960le_rbt @ A) @ B)]: ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T2))) => (((ord_less @ A) @ K2) @ X2))))))))))).
% 2.66/1.40 thf(fact_165_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F) = (nil @ A))))).
% 2.66/1.40 thf(fact_166_order__class_Orbt__greater__trans, axiom, (! [C2:$tType,A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A,T:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((ord_less @ A) @ X) @ Y) => (((((rBT_Im1332541288reater @ A) @ C2) @ Y) @ T) => ((((rBT_Im1332541288reater @ A) @ C2) @ X) @ T))))))))).
% 2.66/1.40 thf(fact_167_list__bind__cong, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Ys:(list @ A),F:(A > (list @ B)),G:(A > (list @ B))]: (((Xs = Ys) => ((! [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) => ((F @ X3) = (G @ X3))))) => (((((bind @ A) @ B) @ Xs) @ F) = ((((bind @ A) @ B) @ Ys) @ G))))))).
% 2.66/1.40 thf(fact_168_ord__class_Orbt__less__prop, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (((rBT_Im903026891t_less @ A) @ B) = (^ [K2:A,T2:((rBT_Im246033960le_rbt @ A) @ B)]: ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T2))) => (((ord_less @ A) @ X2) @ K2))))))))))).
% 2.66/1.40 thf(fact_169_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F:(B > (list @ A)),X:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F) @ (((cons @ B) @ X) @ Xs)) = (((append @ A) @ (F @ X)) @ ((((maps @ B) @ A) @ F) @ Xs)))))).
% 2.66/1.40 thf(fact_170_not__in__set__insert, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((~ ((((member @ A) @ X) @ ((set2 @ A) @ Xs)))) => ((((insert @ A) @ X) @ Xs) = (((cons @ A) @ X) @ Xs)))))).
% 2.66/1.40 thf(fact_171_in__set__insert, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((insert @ A) @ X) @ Xs) = Xs))))).
% 2.66/1.40 thf(fact_172_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.66/1.40 thf(fact_173_order__class_Orbt__less__trans, axiom, (! [C2:$tType,A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,T:((rBT_Im246033960le_rbt @ A) @ C2),Y:A]: ((((((rBT_Im903026891t_less @ A) @ C2) @ X) @ T) => ((((ord_less @ A) @ X) @ Y) => ((((rBT_Im903026891t_less @ A) @ C2) @ Y) @ T))))))))).
% 2.66/1.40 thf(fact_174_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((maps @ B) @ A) @ F) @ (nil @ B)) = (nil @ A))))).
% 2.66/1.40 thf(fact_175_List_Oinsert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [X2:A,Xs3:(list @ A)]: (((((if @ (list @ A)) @ (((member @ A) @ X2) @ ((set2 @ A) @ Xs3))) @ Xs3) @ (((cons @ A) @ X2) @ Xs3)))))))).
% 2.66/1.40 thf(fact_176_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.66/1.40 thf(fact_177_local_Orbt__less__simps_I1_J, axiom, (! [B:$tType,K:a]: ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.66/1.40 thf(fact_178_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.66/1.40 thf(fact_179_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.66/1.40 thf(fact_180_set__rotate1, axiom, (! [A:$tType,Xs:(list @ A)]: ((((set2 @ A) @ ((rotate1 @ A) @ Xs)) = ((set2 @ A) @ Xs))))).
% 2.66/1.40 thf(fact_181_ord__class_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A]: (((((rBT_Im1332541288reater @ A) @ B) @ K) @ ((rBT_Im418718756_Empty @ A) @ B)))))))).
% 2.66/1.40 thf(fact_182_ord__class_Orbt__less__simps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A]: (((((rBT_Im903026891t_less @ A) @ B) @ K) @ ((rBT_Im418718756_Empty @ A) @ B)))))))).
% 2.66/1.40 thf(fact_183_last__appendL, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs)))))).
% 2.66/1.40 thf(fact_184_last__appendR, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys)))))).
% 2.66/1.40 thf(fact_185_keys__simps_I1_J, axiom, (! [B:$tType,A:$tType]: (((((rBT_Im380146495e_keys @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (nil @ A))))).
% 2.66/1.40 thf(fact_186_local_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,K:a]: ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.66/1.40 thf(fact_187_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 2.66/1.40 thf(fact_188_ord_Orbt__less__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less2:(A > (A > $o)),K:A]: ((((((rBT_Im2075124343t_less @ A) @ B) @ Less2) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.66/1.40 thf(fact_189_ord_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less2:(A > (A > $o)),K:A]: ((((((rBT_Im1259024060reater @ A) @ B) @ Less2) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.66/1.40 thf(fact_190_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.66/1.40 thf(fact_191_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X))))).
% 2.66/1.40 thf(fact_192_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs))))))).
% 2.66/1.40 thf(fact_193_last__in__set, axiom, (! [A:$tType,As2:(list @ A)]: (((As2 != (nil @ A)) => (((member @ A) @ ((last @ A) @ As2)) @ ((set2 @ A) @ As2)))))).
% 2.66/1.40 thf(fact_194_last__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs))) & ((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys))))))).
% 2.66/1.40 thf(fact_195_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ss:(list @ A),Xs4:(list @ A),Ys4:(list @ A)]: (((Xs = (((append @ A) @ Xs4) @ Ss)) & ((Ys = (((append @ A) @ Ys4) @ Ss)) & ((Xs4 = (nil @ A)) | ((Ys4 = (nil @ A)) | (((last @ A) @ Xs4) != ((last @ A) @ Ys4))))))))))).
% 2.66/1.40 thf(fact_196_non__empty__rbt__keys, axiom, (! [B:$tType,A:$tType,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((T != ((rBT_Im418718756_Empty @ A) @ B)) => ((((rBT_Im380146495e_keys @ A) @ B) @ T) != (nil @ A)))))).
% 2.66/1.40 thf(fact_197_local_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType]: (((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.66/1.40 thf(fact_198_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 2.66/1.40 thf(fact_199_snoc__eq__iff__butlast, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A)]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = Ys) = ((Ys != (nil @ A)) & ((((butlast @ A) @ Ys) = Xs) & (((last @ A) @ Ys) = X))))))).
% 2.66/1.40 thf(fact_200_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = Xs)))).
% 2.66/1.40 thf(fact_201_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.66/1.40 thf(fact_202_in__set__butlastD, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) => (((member @ A) @ X) @ ((set2 @ A) @ Xs)))))).
% 2.66/1.40 thf(fact_203_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((butlast @ A) @ Xs)))))))).
% 2.66/1.40 thf(fact_204_butlast__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = ((butlast @ A) @ Xs))) & ((Ys != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys)))))))).
% 2.66/1.40 thf(fact_205_in__set__butlast__appendI, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: ((((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) | (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Ys)))) => (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ (((append @ A) @ Xs) @ Ys)))))))).
% 2.66/1.40 thf(fact_206_ord_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Less2:(A > (A > $o))]: (((((rBT_Im759614907sorted @ A) @ B) @ Less2) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.66/1.40 thf(fact_207_local_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ a) @ B),K:a,V2:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ C) @ L) @ K) @ V2) @ R)) = ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) & ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) & (((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) & ((((rBT_Im759614907sorted @ a) @ B) @ less) @ R)))))))).
% 2.66/1.40 thf(fact_208_local_Odistinct__keys, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((distinct @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T)))))).
% 2.66/1.40 thf(fact_209_rbt_Oinject, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X232:A,X242:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X232) @ X242) @ X25) = (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & ((X22 = Y22) & ((X232 = Y23) & ((X242 = Y24) & (X25 = Y25))))))))).
% 2.66/1.40 thf(fact_210_distinct1__rotate, axiom, (! [A:$tType,Xs:(list @ A)]: ((((distinct @ A) @ ((rotate1 @ A) @ Xs)) = ((distinct @ A) @ Xs))))).
% 2.66/1.40 thf(fact_211_distinct__insert, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((distinct @ A) @ (((insert @ A) @ X) @ Xs)) = ((distinct @ A) @ Xs))))).
% 2.66/1.40 thf(fact_212_ord__class_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V2:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: ((((((rBT_Im1332541288reater @ A) @ C2) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V2) @ Rt)) = ((((ord_less @ A) @ K) @ Kt) & (((((rBT_Im1332541288reater @ A) @ C2) @ K) @ Lt) & ((((rBT_Im1332541288reater @ A) @ C2) @ K) @ Rt)))))))))).
% 2.66/1.40 thf(fact_213_ord__class_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V2:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: ((((((rBT_Im903026891t_less @ A) @ C2) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V2) @ Rt)) = ((((ord_less @ A) @ Kt) @ K) & (((((rBT_Im903026891t_less @ A) @ C2) @ K) @ Lt) & ((((rBT_Im903026891t_less @ A) @ C2) @ K) @ Rt)))))))))).
% 2.66/1.40 thf(fact_214_local_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,K:a,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ a) @ C2),Kt:a,V2:C2,Rt:((rBT_Im246033960le_rbt @ a) @ C2)]: (((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ (((((((rBT_Im480247531Branch @ a) @ C2) @ C) @ Lt) @ Kt) @ V2) @ Rt)) = (((less @ K) @ Kt) & ((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ Lt) & (((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ Rt))))))).
% 2.66/1.40 thf(fact_215_local_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,K:a,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ a) @ C2),Kt:a,V2:C2,Rt:((rBT_Im246033960le_rbt @ a) @ C2)]: (((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ (((((((rBT_Im480247531Branch @ a) @ C2) @ C) @ Lt) @ Kt) @ V2) @ Rt)) = (((less @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ Rt))))))).
% 2.66/1.40 thf(fact_216_keys__simps_I2_J, axiom, (! [D:$tType,C2:$tType,C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ C2) @ D),K:C2,V2:D,R:((rBT_Im246033960le_rbt @ C2) @ D)]: (((((rBT_Im380146495e_keys @ C2) @ D) @ (((((((rBT_Im480247531Branch @ C2) @ D) @ C) @ L) @ K) @ V2) @ R)) = (((append @ C2) @ (((rBT_Im380146495e_keys @ C2) @ D) @ L)) @ (((cons @ C2) @ K) @ (((rBT_Im380146495e_keys @ C2) @ D) @ R))))))).
% 2.66/1.40 thf(fact_217_rbt_Oexhaust, axiom, (! [B:$tType,A:$tType,Y:((rBT_Im246033960le_rbt @ A) @ B)]: (((Y != ((rBT_Im418718756_Empty @ A) @ B)) => (~ ((! [X212:rBT_Im1923302023_color,X222:((rBT_Im246033960le_rbt @ A) @ B),X233:A,X243:B,X252:((rBT_Im246033960le_rbt @ A) @ B)]: ((Y != (((((((rBT_Im480247531Branch @ A) @ B) @ X212) @ X222) @ X233) @ X243) @ X252)))))))))).
% 2.66/1.40 thf(fact_218_rbt_Oinduct, axiom, (! [B:$tType,A:$tType,P:(((rBT_Im246033960le_rbt @ A) @ B) > $o),Rbt:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ ((rBT_Im418718756_Empty @ A) @ B)) => ((! [X12:rBT_Im1923302023_color,X24:((rBT_Im246033960le_rbt @ A) @ B),X32:A,X42:B,X5:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ X24) => ((P @ X5) => (P @ (((((((rBT_Im480247531Branch @ A) @ B) @ X12) @ X24) @ X32) @ X42) @ X5)))))) => (P @ Rbt)))))).
% 2.66/1.40 thf(fact_219_rbt_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X232:A,X242:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((rBT_Im418718756_Empty @ A) @ B) != (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X232) @ X242) @ X25))))).
% 2.66/1.40 thf(fact_220_distinct__butlast, axiom, (! [A:$tType,Xs:(list @ A)]: ((((distinct @ A) @ Xs) => ((distinct @ A) @ ((butlast @ A) @ Xs)))))).
% 2.66/1.40 thf(fact_221_distinct__singleton, axiom, (! [A:$tType,X:A]: (((distinct @ A) @ (((cons @ A) @ X) @ (nil @ A)))))).
% 2.66/1.40 thf(fact_222_distinct_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((distinct @ A) @ (((cons @ A) @ X) @ Xs)) = ((~ ((((member @ A) @ X) @ ((set2 @ A) @ Xs)))) & ((distinct @ A) @ Xs)))))).
% 2.66/1.40 thf(fact_223_distinct__length__2__or__more, axiom, (! [A:$tType,A2:A,B2:A,Xs:(list @ A)]: ((((distinct @ A) @ (((cons @ A) @ A2) @ (((cons @ A) @ B2) @ Xs))) = ((A2 != B2) & (((distinct @ A) @ (((cons @ A) @ A2) @ Xs)) & ((distinct @ A) @ (((cons @ A) @ B2) @ Xs)))))))).
% 2.66/1.40 thf(fact_224_distinct_Osimps_I1_J, axiom, (! [A:$tType]: (((distinct @ A) @ (nil @ A))))).
% 2.66/1.40 thf(fact_225_ord_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,A:$tType,Less2:(A > (A > $o)),K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V2:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((((rBT_Im2075124343t_less @ A) @ C2) @ Less2) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V2) @ Rt)) = (((Less2 @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ A) @ C2) @ Less2) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ A) @ C2) @ Less2) @ K) @ Rt))))))).
% 2.66/1.40 thf(fact_226_ord_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,A:$tType,Less2:(A > (A > $o)),K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V2:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((((rBT_Im1259024060reater @ A) @ C2) @ Less2) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V2) @ Rt)) = (((Less2 @ K) @ Kt) & ((((((rBT_Im1259024060reater @ A) @ C2) @ Less2) @ K) @ Lt) & (((((rBT_Im1259024060reater @ A) @ C2) @ Less2) @ K) @ Rt))))))).
% 2.66/1.40 thf(fact_227_distinct__product__lists, axiom, (! [A:$tType,Xss2:(list @ (list @ A))]: (((! [X3:(list @ A)]: (((((member @ (list @ A)) @ X3) @ ((set2 @ (list @ A)) @ Xss2)) => ((distinct @ A) @ X3)))) => ((distinct @ (list @ A)) @ ((product_lists @ A) @ Xss2)))))).
% 2.66/1.40 thf(fact_228_not__distinct__decomp, axiom, (! [A:$tType,Ws2:(list @ A)]: (((~ (((distinct @ A) @ Ws2))) => (? [Xs2:(list @ A),Ys2:(list @ A),Zs3:(list @ A),Y3:A]: ((Ws2 = (((append @ A) @ Xs2) @ (((append @ A) @ (((cons @ A) @ Y3) @ (nil @ A))) @ (((append @ A) @ Ys2) @ (((append @ A) @ (((cons @ A) @ Y3) @ (nil @ A))) @ Zs3))))))))))).
% 2.66/1.40 thf(fact_229_not__distinct__conv__prefix, axiom, (! [A:$tType,As2:(list @ A)]: (((~ (((distinct @ A) @ As2))) = (? [Xs3:(list @ A),Y2:A,Ys3:(list @ A)]: (((((member @ A) @ Y2) @ ((set2 @ A) @ Xs3)) & (((distinct @ A) @ Xs3) & (As2 = (((append @ A) @ Xs3) @ (((cons @ A) @ Y2) @ Ys3))))))))))).
% 2.66/1.40 thf(fact_230_ord_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,Less2:(A > (A > $o)),C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V2:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im759614907sorted @ A) @ B) @ Less2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C) @ L) @ K) @ V2) @ R)) = ((((((rBT_Im2075124343t_less @ A) @ B) @ Less2) @ K) @ L) & ((((((rBT_Im1259024060reater @ A) @ B) @ Less2) @ K) @ R) & (((((rBT_Im759614907sorted @ A) @ B) @ Less2) @ L) & ((((rBT_Im759614907sorted @ A) @ B) @ Less2) @ R)))))))).
% 2.66/1.40 thf(fact_231_distinct__union, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((distinct @ A) @ (((union @ A) @ Xs) @ Ys)) = ((distinct @ A) @ Ys))))).
% 2.66/1.40 thf(fact_232_RBT__SORTED, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ (((((((rBT_Im480247531Branch @ a) @ b) @ c) @ t1) @ k) @ v) @ t2))).
% 2.66/1.40 thf(fact_233_Branch_Oprems, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ (((((((rBT_Im480247531Branch @ a) @ b) @ c) @ t1) @ k) @ v) @ t2))).
% 2.66/1.40 thf(fact_234_ord__class_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V2:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1183586831sorted @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C) @ L) @ K) @ V2) @ R)) = (((((rBT_Im903026891t_less @ A) @ B) @ K) @ L) & (((((rBT_Im1332541288reater @ A) @ B) @ K) @ R) & ((((rBT_Im1183586831sorted @ A) @ B) @ L) & (((rBT_Im1183586831sorted @ A) @ B) @ R))))))))))).
% 2.66/1.40 thf(fact_235_ord__class_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (((rBT_Im1183586831sorted @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.66/1.40 thf(fact_236_linorder__class_Odistinct__keys, axiom, (! [B:$tType,A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im1183586831sorted @ A) @ B) @ T) => ((distinct @ A) @ (((rBT_Im380146495e_keys @ A) @ B) @ T))))))))).
% 2.66/1.40 thf(fact_237_local_OgreaterThan__def, axiom, (! [L:a]: (((((set_greaterThan @ a) @ less) @ L) = ((collect @ a) @ (less @ L)))))).
% 2.66/1.40 thf(fact_238_local_OlessThan__def, axiom, (! [U:a]: (((((set_lessThan @ a) @ less) @ U) = ((collect @ a) @ (^ [X2:a]: (((less @ X2) @ U)))))))).
% 2.66/1.40 thf(fact_239_local_OlessThan__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_lessThan @ a) @ less) @ K)) = ((less @ I) @ K))))).
% 2.66/1.40 thf(fact_240_local_OgreaterThan__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_greaterThan @ a) @ less) @ K)) = ((less @ K) @ I))))).
% 2.66/1.40 thf(fact_241_DOM__T1, axiom, (! [K3:a]: (((((member @ a) @ K3) @ (((dom @ a) @ b) @ ((((rBT_Im35466040lookup @ a) @ b) @ less) @ t1))) => ((less @ K3) @ k))))).
% 2.66/1.40 thf(fact_242_local_Orbt__lookup__keys, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((dom @ a) @ B) @ ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T)) = ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ B) @ T))))))).
% 2.66/1.40 thf(fact_243_Branch_Ohyps_I1_J, axiom, (((((rBT_Im759614907sorted @ a) @ b) @ less) @ t1) => ((((map_of @ a) @ b) @ (((rBT_Im954575269ntries @ a) @ b) @ t1)) = ((((rBT_Im35466040lookup @ a) @ b) @ less) @ t1)))).
% 2.66/1.40 thf(fact_244_Branch_Ohyps_I2_J, axiom, (((((rBT_Im759614907sorted @ a) @ b) @ less) @ t2) => ((((map_of @ a) @ b) @ (((rBT_Im954575269ntries @ a) @ b) @ t2)) = ((((rBT_Im35466040lookup @ a) @ b) @ less) @ t2)))).
% 2.66/1.40 thf(fact_245_entries_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: (((((rBT_Im954575269ntries @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (nil @ ((product_prod @ A) @ B)))))).
% 2.66/1.40 thf(fact_246_local_Orbt__lookup__Empty, axiom, (! [B:$tType]: ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B)) = (^ [X2:a]: ((none @ B))))))).
% 2.66/1.40 thf(fact_247_local_Orbt__lookup_Osimps_I1_J, axiom, (! [B:$tType,K:a]: (((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B)) @ K) = (none @ B))))).
% 2.66/1.40 thf(fact_248_local_Orbt__lookup__rbt__greater, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ T) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T) @ K) = (none @ B)))))).
% 2.66/1.40 thf(fact_249_local_Orbt__lookup__rbt__less, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ T) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T) @ K) = (none @ B)))))).
% 2.66/1.40 thf(fact_250_ord_Orbt__lookup__rbt__less, axiom, (! [A:$tType,B:$tType,Less2:(A > (A > $o)),K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im2075124343t_less @ A) @ B) @ Less2) @ K) @ T) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less2) @ T) @ K) = (none @ B)))))).
% 2.66/1.40 thf(fact_251_ord_Orbt__lookup__rbt__greater, axiom, (! [A:$tType,B:$tType,Less2:(A > (A > $o)),K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1259024060reater @ A) @ B) @ Less2) @ K) @ T) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less2) @ T) @ K) = (none @ B)))))).
% 2.66/1.40 thf(fact_252_ord_Orbt__lookup_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,Less2:(A > (A > $o)),K:A]: (((((((rBT_Im35466040lookup @ A) @ B) @ Less2) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) = (none @ B))))).
% 2.66/1.40 thf(fact_253_ord_Orbt__lookup__Empty, axiom, (! [B:$tType,A:$tType,Less2:(A > (A > $o))]: ((((((rBT_Im35466040lookup @ A) @ B) @ Less2) @ ((rBT_Im418718756_Empty @ A) @ B)) = (^ [X2:A]: ((none @ B))))))).
% 2.66/1.40 thf(fact_254_local_Orbt__lookup_Osimps_I2_J, axiom, (! [B:$tType,K:a,X:a,Uu:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ a) @ B),Y:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: (((((less @ K) @ X) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ L) @ K))) & ((~ (((less @ K) @ X))) => ((((less @ X) @ K) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ R) @ K))) & ((~ (((less @ X) @ K))) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ Uu) @ L) @ X) @ Y) @ R)) @ K) = ((some @ B) @ Y))))))))).
% 2.66/1.40 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: ((((order @ A7) @ (type2 @ A7)) => ((order @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.66/1.40 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: ((((ord @ A7) @ (type2 @ A7)) => ((ord @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.66/1.40 thf(tcon_Set_Oset___Orderings_Oorder_1, axiom, (! [A6:$tType]: (((order @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.66/1.40 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A6:$tType]: (((ord @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.66/1.40 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.66/1.40 thf(tcon_HOL_Obool___Orderings_Oorder_3, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.66/1.40 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.66/1.40 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.66/1.40 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.66/1.40 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.66/1.40 thf(conj_0, conjecture, (! [X3:a]: (((((member @ a) @ X3) @ ((set2 @ a) @ (((rBT_Im380146495e_keys @ a) @ b) @ t2))) => ((less @ k) @ X3))))).
% 2.66/1.40 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.oBDkFFmvot/DTF2DTF16703.p
% 2.66/1.40 ------------------------
% 2.66/1.43 ---- Cleaned THF ---
% 2.66/1.43 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 2.66/1.43 rBT_Im1923302023_color: $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 2.66/1.43 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_t_Product__Type_Oprod,type,
% 2.66/1.43 product_prod: $tType > $tType > $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_t_Option_Ooption,type,
% 2.66/1.43 option: $tType > $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_t_List_Olist,type,
% 2.66/1.43 list: $tType > $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_t_Set_Oset,type,
% 2.66/1.43 set: $tType > $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_t_itself,type,
% 2.66/1.43 itself: $tType > $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_tf_b,type,
% 2.66/1.43 b: $tType ).
% 2.66/1.43
% 2.66/1.43 thf(ty_tf_a,type,
% 2.66/1.43 a: $tType ).
% 2.66/1.43
% 2.66/1.43 thf(sy_cl_HOL_Otype,type,
% 2.66/1.43 type:
% 2.66/1.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_cl_Orderings_Oord,type,
% 2.66/1.43 ord:
% 2.66/1.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_cl_Orderings_Oorder,type,
% 2.66/1.43 order:
% 2.66/1.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_cl_Orderings_Olinorder,type,
% 2.66/1.43 linorder:
% 2.66/1.43 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Fun_Oinj__on,type,
% 2.66/1.43 inj_on:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_If,type,
% 2.66/1.43 if:
% 2.66/1.43 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Oappend,type,
% 2.66/1.43 append:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Obind,type,
% 2.66/1.43 bind:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Obutlast,type,
% 2.66/1.43 butlast:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Odistinct,type,
% 2.66/1.43 distinct:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Oinsert,type,
% 2.66/1.43 insert:
% 2.66/1.43 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Olast,type,
% 2.66/1.43 last:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Olist_OCons,type,
% 2.66/1.43 cons:
% 2.66/1.43 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Olist_ONil,type,
% 2.66/1.43 nil:
% 2.66/1.43 !>[A: $tType] : ( list @ A ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Olist_Oset,type,
% 2.66/1.43 set2:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Omaps,type,
% 2.66/1.43 maps:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Oord_Olexordp,type,
% 2.66/1.43 lexordp:
% 2.66/1.43 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Oord_Olexordp__eq,type,
% 2.66/1.43 lexordp_eq:
% 2.66/1.43 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Oproduct__lists,type,
% 2.66/1.43 product_lists:
% 2.66/1.43 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Orotate1,type,
% 2.66/1.43 rotate1:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Osublists,type,
% 2.66/1.43 sublists:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_List_Ounion,type,
% 2.66/1.43 union:
% 2.66/1.43 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Map_Odom,type,
% 2.66/1.43 dom:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > ( option @ B ) ) > ( set @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Map_Omap__of,type,
% 2.66/1.43 map_of:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( list @ ( product_prod @ A @ B ) ) > A > ( option @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Option_Ooption_ONone,type,
% 2.66/1.43 none:
% 2.66/1.43 !>[A: $tType] : ( option @ A ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Option_Ooption_OSome,type,
% 2.66/1.43 some:
% 2.66/1.43 !>[A: $tType] : ( A > ( option @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.66/1.43 ord_less:
% 2.66/1.43 !>[A: $tType] : ( A > A > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Orderings_Oorder_Ostrict__mono,type,
% 2.66/1.43 strict_mono:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Pure_Otype,type,
% 2.66/1.43 type2:
% 2.66/1.43 !>[A: $tType] : ( itself @ A ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries,type,
% 2.66/1.43 rBT_Im954575269ntries:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Okeys,type,
% 2.66/1.43 rBT_Im380146495e_keys:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 2.66/1.43 rBT_Im1259024060reater:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 2.66/1.43 rBT_Im2075124343t_less:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup,type,
% 2.66/1.43 rBT_Im35466040lookup:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > A > ( option @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 2.66/1.43 rBT_Im759614907sorted:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__greater,type,
% 2.66/1.43 rBT_Im1332541288reater:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__less,type,
% 2.66/1.43 rBT_Im903026891t_less:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord__class_Orbt__sorted,type,
% 2.66/1.43 rBT_Im1183586831sorted:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 2.66/1.43 rBT_Im480247531Branch:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 2.66/1.43 rBT_Im418718756_Empty:
% 2.66/1.43 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Set_OCollect,type,
% 2.66/1.43 collect:
% 2.66/1.43 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Set_Othe__elem,type,
% 2.66/1.43 the_elem:
% 2.66/1.43 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Set__Interval_Oord_OgreaterThan,type,
% 2.66/1.43 set_greaterThan:
% 2.66/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_Set__Interval_Oord_OlessThan,type,
% 2.66/1.43 set_lessThan:
% 2.66/1.43 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_c_member,type,
% 2.66/1.43 member:
% 2.66/1.43 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(sy_v_c____,type,
% 2.66/1.43 c: rBT_Im1923302023_color ).
% 2.66/1.43
% 2.66/1.43 thf(sy_v_k____,type,
% 2.66/1.43 k: a ).
% 2.66/1.43
% 2.66/1.43 thf(sy_v_less,type,
% 2.66/1.43 less: a > a > $o ).
% 2.66/1.43
% 2.66/1.43 thf(sy_v_t1____,type,
% 2.66/1.43 t1: rBT_Im246033960le_rbt @ a @ b ).
% 2.66/1.43
% 2.66/1.43 thf(sy_v_t2____,type,
% 2.66/1.43 t2: rBT_Im246033960le_rbt @ a @ b ).
% 2.66/1.43
% 2.66/1.43 thf(sy_v_v____,type,
% 2.66/1.43 v: b ).
% 2.66/1.43
% 2.66/1.43 thf(fact_0_local_Oantisym__conv3,axiom,
% 2.66/1.43 ! [Y: a,X: a] :
% 2.66/1.43 ( ~ ( less @ Y @ X )
% 2.66/1.43 => ( ( ~ ( less @ X @ Y ) )
% 2.66/1.43 = ( X = Y ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_1_local_Odual__order_Oasym,axiom,
% 2.66/1.43 ! [B2: a,A2: a] :
% 2.66/1.43 ( ( less @ B2 @ A2 )
% 2.66/1.43 => ~ ( less @ A2 @ B2 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 2.66/1.43 ! [B2: a,A2: a] :
% 2.66/1.43 ( ( less @ B2 @ A2 )
% 2.66/1.43 => ( A2 != B2 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_3_local_Odual__order_Ostrict__trans,axiom,
% 2.66/1.43 ! [B2: a,A2: a,C: a] :
% 2.66/1.43 ( ( less @ B2 @ A2 )
% 2.66/1.43 => ( ( less @ C @ B2 )
% 2.66/1.43 => ( less @ C @ A2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_4_local_Oless__asym,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ~ ( less @ Y @ X ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_5_local_Oless__asym_H,axiom,
% 2.66/1.43 ! [A2: a,B2: a] :
% 2.66/1.43 ( ( less @ A2 @ B2 )
% 2.66/1.43 => ~ ( less @ B2 @ A2 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_6_local_Oless__imp__neq,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( X != Y ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_7_local_Oless__imp__not__eq,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( X != Y ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_8_local_Oless__imp__not__eq2,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( Y != X ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_9_local_Oless__imp__not__less,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ~ ( less @ Y @ X ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_10_local_Oless__imp__triv,axiom,
% 2.66/1.43 ! [X: a,Y: a,P: $o] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( ( less @ Y @ X )
% 2.66/1.43 => P ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_11_local_Oless__irrefl,axiom,
% 2.66/1.43 ! [X: a] :
% 2.66/1.43 ~ ( less @ X @ X ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_12_local_Oless__linear,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 | ( X = Y )
% 2.66/1.43 | ( less @ Y @ X ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_13_local_Oless__not__sym,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ~ ( less @ Y @ X ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_14_local_Oless__trans,axiom,
% 2.66/1.43 ! [X: a,Y: a,Z: a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( ( less @ Y @ Z )
% 2.66/1.43 => ( less @ X @ Z ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_15_local_Olinorder__cases,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ~ ( less @ X @ Y )
% 2.66/1.43 => ( ( X != Y )
% 2.66/1.43 => ( less @ Y @ X ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_16_local_OneqE,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( X != Y )
% 2.66/1.43 => ( ~ ( less @ X @ Y )
% 2.66/1.43 => ( less @ Y @ X ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_17_local_Oneq__iff,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( X != Y )
% 2.66/1.43 = ( ( less @ X @ Y )
% 2.66/1.43 | ( less @ Y @ X ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_18_local_Onot__less__iff__gr__or__eq,axiom,
% 2.66/1.43 ! [X: a,Y: a] :
% 2.66/1.43 ( ( ~ ( less @ X @ Y ) )
% 2.66/1.43 = ( ( less @ Y @ X )
% 2.66/1.43 | ( X = Y ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_19_local_Oord__eq__less__trans,axiom,
% 2.66/1.43 ! [A2: a,B2: a,C: a] :
% 2.66/1.43 ( ( A2 = B2 )
% 2.66/1.43 => ( ( less @ B2 @ C )
% 2.66/1.43 => ( less @ A2 @ C ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_20_local_Oord__less__eq__trans,axiom,
% 2.66/1.43 ! [A2: a,B2: a,C: a] :
% 2.66/1.43 ( ( less @ A2 @ B2 )
% 2.66/1.43 => ( ( B2 = C )
% 2.66/1.43 => ( less @ A2 @ C ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_21_local_Oorder_Oasym,axiom,
% 2.66/1.43 ! [A2: a,B2: a] :
% 2.66/1.43 ( ( less @ A2 @ B2 )
% 2.66/1.43 => ~ ( less @ B2 @ A2 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_22_local_Oorder_Oirrefl,axiom,
% 2.66/1.43 ! [A2: a] :
% 2.66/1.43 ~ ( less @ A2 @ A2 ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_23_local_Oorder_Ostrict__implies__not__eq,axiom,
% 2.66/1.43 ! [A2: a,B2: a] :
% 2.66/1.43 ( ( less @ A2 @ B2 )
% 2.66/1.43 => ( A2 != B2 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_24_local_Oorder_Ostrict__trans,axiom,
% 2.66/1.43 ! [A2: a,B2: a,C: a] :
% 2.66/1.43 ( ( less @ A2 @ B2 )
% 2.66/1.43 => ( ( less @ B2 @ C )
% 2.66/1.43 => ( less @ A2 @ C ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_25_local_Orbt__greater__prop,axiom,
% 2.66/1.43 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 2.66/1.43 = ( ! [X2: a] :
% 2.66/1.43 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 2.66/1.43 => ( less @ K @ X2 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_26_local_Orbt__greater__trans,axiom,
% 2.66/1.43 ! [C2: $tType,X: a,Y: a,T: rBT_Im246033960le_rbt @ a @ C2] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( ( rBT_Im1259024060reater @ a @ C2 @ less @ Y @ T )
% 2.66/1.43 => ( rBT_Im1259024060reater @ a @ C2 @ less @ X @ T ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_27__092_060open_062k_A_092_060guillemotleft_062_124_At2_092_060close_062,axiom,
% 2.66/1.43 rBT_Im1259024060reater @ a @ b @ less @ k @ t2 ).
% 2.66/1.43
% 2.66/1.43 thf(fact_28_local_Ostrict__mono__eq,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( order @ B @ ( type2 @ B ) )
% 2.66/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.66/1.43 ( ( strict_mono @ a @ B @ less @ F )
% 2.66/1.43 => ( ( ( F @ X )
% 2.66/1.43 = ( F @ Y ) )
% 2.66/1.43 = ( X = Y ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_29_local_Orbt__less__prop,axiom,
% 2.66/1.43 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 2.66/1.43 = ( ! [X2: a] :
% 2.66/1.43 ( ( member @ a @ X2 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) )
% 2.66/1.43 => ( less @ X2 @ K ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_30_ord_Orbt__greater__prop,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( rBT_Im1259024060reater @ A @ B )
% 2.66/1.43 = ( ^ [Less: A > A > $o,K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ! [X2: A] :
% 2.66/1.43 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 2.66/1.43 => ( Less @ K2 @ X2 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_31_local_Orbt__less__trans,axiom,
% 2.66/1.43 ! [C2: $tType,X: a,T: rBT_Im246033960le_rbt @ a @ C2,Y: a] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ X @ T )
% 2.66/1.43 => ( ( less @ X @ Y )
% 2.66/1.43 => ( rBT_Im2075124343t_less @ a @ C2 @ less @ Y @ T ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_32_local_Olexordp__eq__antisym,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( ( lexordp_eq @ a @ less @ Ys @ Xs )
% 2.66/1.43 => ( Xs = Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_33_local_Olexordp__eq__linear,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.66/1.43 | ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_34_local_Olexordp__eq__refl,axiom,
% 2.66/1.43 ! [Xs: list @ a] : ( lexordp_eq @ a @ less @ Xs @ Xs ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_35_local_Olexordp__eq__trans,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( ( lexordp_eq @ a @ less @ Ys @ Zs )
% 2.66/1.43 => ( lexordp_eq @ a @ less @ Xs @ Zs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_36_ord_Orbt__less__prop,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ A @ B )
% 2.66/1.43 = ( ^ [Less: A > A > $o,K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ! [X2: A] :
% 2.66/1.43 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 2.66/1.43 => ( Less @ X2 @ K2 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_37_local_Olexordp__antisym,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ~ ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_38_local_Olexordp__irreflexive,axiom,
% 2.66/1.43 ! [Xs: list @ a] :
% 2.66/1.43 ( ! [X3: a] :
% 2.66/1.43 ~ ( less @ X3 @ X3 )
% 2.66/1.43 => ~ ( lexordp @ a @ less @ Xs @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_39_local_Olexordp__irreflexive_H,axiom,
% 2.66/1.43 ! [Xs: list @ a] :
% 2.66/1.43 ~ ( lexordp @ a @ less @ Xs @ Xs ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_40_local_Olexordp__linear,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 | ( Xs = Ys )
% 2.66/1.43 | ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_41_local_Olexordp__trans,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( ( lexordp @ a @ less @ Ys @ Zs )
% 2.66/1.43 => ( lexordp @ a @ less @ Xs @ Zs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_42_local_Olexordp__into__lexordp__eq,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_43_local_Olexordp__eq__conv__lexord,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.66/1.43 = ( ( Xs = Ys )
% 2.66/1.43 | ( lexordp @ a @ less @ Xs @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_44_local_Olexordp__conv__lexordp__eq,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 = ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.66/1.43 & ~ ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_45_mem__Collect__eq,axiom,
% 2.66/1.43 ! [A: $tType,A2: A,P: A > $o] :
% 2.66/1.43 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.66/1.43 = ( P @ A2 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_46_Collect__mem__eq,axiom,
% 2.66/1.43 ! [A: $tType,A3: set @ A] :
% 2.66/1.43 ( ( collect @ A
% 2.66/1.43 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.66/1.43 = A3 ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_47_Collect__cong,axiom,
% 2.66/1.43 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.66/1.43 ( ! [X3: A] :
% 2.66/1.43 ( ( P @ X3 )
% 2.66/1.43 = ( Q @ X3 ) )
% 2.66/1.43 => ( ( collect @ A @ P )
% 2.66/1.43 = ( collect @ A @ Q ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_48_ext,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.66/1.43 ( ! [X3: A] :
% 2.66/1.43 ( ( F @ X3 )
% 2.66/1.43 = ( G @ X3 ) )
% 2.66/1.43 => ( F = G ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_49_local_Ostrict__mono__less,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( order @ B @ ( type2 @ B ) )
% 2.66/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.66/1.43 ( ( strict_mono @ a @ B @ less @ F )
% 2.66/1.43 => ( ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) )
% 2.66/1.43 = ( less @ X @ Y ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_50_local_Ostrict__mono__def,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( order @ B @ ( type2 @ B ) )
% 2.66/1.43 => ! [F: a > B] :
% 2.66/1.43 ( ( strict_mono @ a @ B @ less @ F )
% 2.66/1.43 = ( ! [X2: a,Y2: a] :
% 2.66/1.43 ( ( less @ X2 @ Y2 )
% 2.66/1.43 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y2 ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_51_local_Ostrict__monoI,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( order @ B @ ( type2 @ B ) )
% 2.66/1.43 => ! [F: a > B] :
% 2.66/1.43 ( ! [X3: a,Y3: a] :
% 2.66/1.43 ( ( less @ X3 @ Y3 )
% 2.66/1.43 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.66/1.43 => ( strict_mono @ a @ B @ less @ F ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_52_local_Ostrict__monoD,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( order @ B @ ( type2 @ B ) )
% 2.66/1.43 => ! [F: a > B,X: a,Y: a] :
% 2.66/1.43 ( ( strict_mono @ a @ B @ less @ F )
% 2.66/1.43 => ( ( less @ X @ Y )
% 2.66/1.43 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_53_local_Olexordp__eq_ONil,axiom,
% 2.66/1.43 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_54_ord_Olexordp__into__lexordp__eq,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ Xs @ Ys )
% 2.66/1.43 => ( lexordp_eq @ A @ Less2 @ Xs @ Ys ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_55_local_Olexordp__eq_OCons__eq,axiom,
% 2.66/1.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ~ ( less @ X @ Y )
% 2.66/1.43 => ( ~ ( less @ Y @ X )
% 2.66/1.43 => ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_56_local_Olexordp__eq_OCons,axiom,
% 2.66/1.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_57_local_Olexordp_OCons,axiom,
% 2.66/1.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_58_local_Olexordp_OCons__eq,axiom,
% 2.66/1.43 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ~ ( less @ X @ Y )
% 2.66/1.43 => ( ~ ( less @ Y @ X )
% 2.66/1.43 => ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_59_list_Oinject,axiom,
% 2.66/1.43 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.66/1.43 ( ( ( cons @ A @ X21 @ X22 )
% 2.66/1.43 = ( cons @ A @ Y21 @ Y22 ) )
% 2.66/1.43 = ( ( X21 = Y21 )
% 2.66/1.43 & ( X22 = Y22 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_60_local_Olexordp_ONil,axiom,
% 2.66/1.43 ! [Y: a,Ys: list @ a] : ( lexordp @ a @ less @ ( nil @ a ) @ ( cons @ a @ Y @ Ys ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_61_local_Olexordp_Ocases,axiom,
% 2.66/1.43 ! [A1: list @ a,A22: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ A1 @ A22 )
% 2.66/1.43 => ( ( ( A1
% 2.66/1.43 = ( nil @ a ) )
% 2.66/1.43 => ! [Y3: a,Ys2: list @ a] :
% 2.66/1.43 ( A22
% 2.66/1.43 != ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: a] :
% 2.66/1.43 ( ? [Xs2: list @ a] :
% 2.66/1.43 ( A1
% 2.66/1.43 = ( cons @ a @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Y3: a] :
% 2.66/1.43 ( ? [Ys2: list @ a] :
% 2.66/1.43 ( A22
% 2.66/1.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.66/1.43 => ~ ( less @ X3 @ Y3 ) ) )
% 2.66/1.43 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ a @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Ys2: list @ a] :
% 2.66/1.43 ( ( A22
% 2.66/1.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ~ ( less @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( less @ Y3 @ X3 )
% 2.66/1.43 => ~ ( lexordp @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_62_local_Olexordp_Oinducts,axiom,
% 2.66/1.43 ! [X1: list @ a,X23: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.66/1.43 ( ( lexordp @ a @ less @ X1 @ X23 )
% 2.66/1.43 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.66/1.43 ( ( less @ X3 @ Y3 )
% 2.66/1.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.66/1.43 ( ~ ( less @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( less @ Y3 @ X3 )
% 2.66/1.43 => ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 2.66/1.43 => ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 2.66/1.43 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_63_local_Olexordp_Osimps,axiom,
% 2.66/1.43 ! [A1: list @ a,A22: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ A1 @ A22 )
% 2.66/1.43 = ( ? [Y2: a,Ys3: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( nil @ a ) )
% 2.66/1.43 & ( A22
% 2.66/1.43 = ( cons @ a @ Y2 @ Ys3 ) ) )
% 2.66/1.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ a @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A22
% 2.66/1.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.66/1.43 & ( less @ X2 @ Y2 ) )
% 2.66/1.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ a @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A22
% 2.66/1.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.66/1.43 & ~ ( less @ X2 @ Y2 )
% 2.66/1.43 & ~ ( less @ Y2 @ X2 )
% 2.66/1.43 & ( lexordp @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_64_local_Olexordp__cases,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( ( ( Xs
% 2.66/1.43 = ( nil @ a ) )
% 2.66/1.43 => ! [Y3: a,Ys4: list @ a] :
% 2.66/1.43 ( Ys
% 2.66/1.43 != ( cons @ a @ Y3 @ Ys4 ) ) )
% 2.66/1.43 => ( ! [X3: a] :
% 2.66/1.43 ( ? [Xs4: list @ a] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( cons @ a @ X3 @ Xs4 ) )
% 2.66/1.43 => ! [Y3: a] :
% 2.66/1.43 ( ? [Ys4: list @ a] :
% 2.66/1.43 ( Ys
% 2.66/1.43 = ( cons @ a @ Y3 @ Ys4 ) )
% 2.66/1.43 => ~ ( less @ X3 @ Y3 ) ) )
% 2.66/1.43 => ~ ! [X3: a,Xs4: list @ a] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( cons @ a @ X3 @ Xs4 ) )
% 2.66/1.43 => ! [Ys4: list @ a] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 = ( cons @ a @ X3 @ Ys4 ) )
% 2.66/1.43 => ~ ( lexordp @ a @ less @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_65_local_Olexordp__induct,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 => ( ! [Y3: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ! [X3: a,Xs2: list @ a,Y3: a,Ys2: list @ a] :
% 2.66/1.43 ( ( less @ X3 @ Y3 )
% 2.66/1.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 2.66/1.43 => ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ X3 @ Ys2 ) ) ) )
% 2.66/1.43 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_66_local_Olexordp__eq_Ocases,axiom,
% 2.66/1.43 ! [A1: list @ a,A22: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 2.66/1.43 => ( ( ( A1
% 2.66/1.43 = ( nil @ a ) )
% 2.66/1.43 => ! [Ys2: list @ a] : ( A22 != Ys2 ) )
% 2.66/1.43 => ( ! [X3: a] :
% 2.66/1.43 ( ? [Xs2: list @ a] :
% 2.66/1.43 ( A1
% 2.66/1.43 = ( cons @ a @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Y3: a] :
% 2.66/1.43 ( ? [Ys2: list @ a] :
% 2.66/1.43 ( A22
% 2.66/1.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.66/1.43 => ~ ( less @ X3 @ Y3 ) ) )
% 2.66/1.43 => ~ ! [X3: a,Y3: a,Xs2: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ a @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Ys2: list @ a] :
% 2.66/1.43 ( ( A22
% 2.66/1.43 = ( cons @ a @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ~ ( less @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( less @ Y3 @ X3 )
% 2.66/1.43 => ~ ( lexordp_eq @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_67_local_Olexordp__eq_Oinducts,axiom,
% 2.66/1.43 ! [X1: list @ a,X23: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ X1 @ X23 )
% 2.66/1.43 => ( ! [X12: list @ a] : ( P @ ( nil @ a ) @ X12 )
% 2.66/1.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.66/1.43 ( ( less @ X3 @ Y3 )
% 2.66/1.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: a,Y3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.66/1.43 ( ~ ( less @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( less @ Y3 @ X3 )
% 2.66/1.43 => ( ( lexordp_eq @ a @ less @ Xs2 @ Ys2 )
% 2.66/1.43 => ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y3 @ Ys2 ) ) ) ) ) )
% 2.66/1.43 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_68_local_Olexordp__eq_Osimps,axiom,
% 2.66/1.43 ! [A1: list @ a,A22: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 2.66/1.43 = ( ? [Ys3: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( nil @ a ) )
% 2.66/1.43 & ( A22 = Ys3 ) )
% 2.66/1.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ a @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A22
% 2.66/1.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.66/1.43 & ( less @ X2 @ Y2 ) )
% 2.66/1.43 | ? [X2: a,Y2: a,Xs3: list @ a,Ys3: list @ a] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ a @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A22
% 2.66/1.43 = ( cons @ a @ Y2 @ Ys3 ) )
% 2.66/1.43 & ~ ( less @ X2 @ Y2 )
% 2.66/1.43 & ~ ( less @ Y2 @ X2 )
% 2.66/1.43 & ( lexordp_eq @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_69_ord_Olexordp__simps_I3_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.66/1.43 = ( ( Less2 @ X @ Y )
% 2.66/1.43 | ( ~ ( Less2 @ Y @ X )
% 2.66/1.43 & ( lexordp @ A @ Less2 @ Xs @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_70_ord_Olexordp__simps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Ys: list @ A] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ ( nil @ A ) @ Ys )
% 2.66/1.43 = ( Ys
% 2.66/1.43 != ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_71_ord_Olexordp__simps_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] :
% 2.66/1.43 ~ ( lexordp @ A @ Less2 @ Xs @ ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_72_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.66/1.43 ( ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.66/1.43 = ( ( Less2 @ X @ Y )
% 2.66/1.43 | ( ~ ( Less2 @ Y @ X )
% 2.66/1.43 & ( lexordp_eq @ A @ Less2 @ Xs @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_73_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less2 @ ( nil @ A ) @ Ys ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_74_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] :
% 2.66/1.43 ( ( lexordp_eq @ A @ Less2 @ Xs @ ( nil @ A ) )
% 2.66/1.43 = ( Xs
% 2.66/1.43 = ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_75_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Xs: list @ A] :
% 2.66/1.43 ~ ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_76_local_Olexordp__simps_I3_J,axiom,
% 2.66/1.43 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 2.66/1.43 = ( ( less @ X @ Y )
% 2.66/1.43 | ( ~ ( less @ Y @ X )
% 2.66/1.43 & ( lexordp @ a @ less @ Xs @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_77_local_Olexordp__eq__simps_I4_J,axiom,
% 2.66/1.43 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 2.66/1.43 = ( ( less @ X @ Y )
% 2.66/1.43 | ( ~ ( less @ Y @ X )
% 2.66/1.43 & ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_78_local_Olexordp__simps_I2_J,axiom,
% 2.66/1.43 ! [Xs: list @ a] :
% 2.66/1.43 ~ ( lexordp @ a @ less @ Xs @ ( nil @ a ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_79_local_Olexordp__simps_I1_J,axiom,
% 2.66/1.43 ! [Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ ( nil @ a ) @ Ys )
% 2.66/1.43 = ( Ys
% 2.66/1.43 != ( nil @ a ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_80_local_Olexordp__eq__simps_I2_J,axiom,
% 2.66/1.43 ! [Xs: list @ a] :
% 2.66/1.43 ( ( lexordp_eq @ a @ less @ Xs @ ( nil @ a ) )
% 2.66/1.43 = ( Xs
% 2.66/1.43 = ( nil @ a ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_81_local_Olexordp__eq__simps_I1_J,axiom,
% 2.66/1.43 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_82_local_Olexordp__eq__simps_I3_J,axiom,
% 2.66/1.43 ! [X: a,Xs: list @ a] :
% 2.66/1.43 ~ ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( nil @ a ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_83_ord_Olexordp_ONil,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Y: A,Ys: list @ A] : ( lexordp @ A @ Less2 @ ( nil @ A ) @ ( cons @ A @ Y @ Ys ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_84_ord_Olexordp_Ocases,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ A1 @ A22 )
% 2.66/1.43 => ( ( ( A1
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ! [Y3: A,Ys2: list @ A] :
% 2.66/1.43 ( A22
% 2.66/1.43 != ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: A] :
% 2.66/1.43 ( ? [Xs2: list @ A] :
% 2.66/1.43 ( A1
% 2.66/1.43 = ( cons @ A @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Y3: A] :
% 2.66/1.43 ( ? [Ys2: list @ A] :
% 2.66/1.43 ( A22
% 2.66/1.43 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.66/1.43 => ~ ( Less2 @ X3 @ Y3 ) ) )
% 2.66/1.43 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ A @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Ys2: list @ A] :
% 2.66/1.43 ( ( A22
% 2.66/1.43 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ~ ( Less2 @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( Less2 @ Y3 @ X3 )
% 2.66/1.43 => ~ ( lexordp @ A @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_85_ord_Olexordp_Osimps,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( lexordp @ A )
% 2.66/1.43 = ( ^ [Less: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.66/1.43 ( ? [Y2: A,Ys3: list @ A] :
% 2.66/1.43 ( ( A12
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 & ( A23
% 2.66/1.43 = ( cons @ A @ Y2 @ Ys3 ) ) )
% 2.66/1.43 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.66/1.43 ( ( A12
% 2.66/1.43 = ( cons @ A @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A23
% 2.66/1.43 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.66/1.43 & ( Less @ X2 @ Y2 ) )
% 2.66/1.43 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.66/1.43 ( ( A12
% 2.66/1.43 = ( cons @ A @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A23
% 2.66/1.43 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.66/1.43 & ~ ( Less @ X2 @ Y2 )
% 2.66/1.43 & ~ ( Less @ Y2 @ X2 )
% 2.66/1.43 & ( lexordp @ A @ Less @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_86_ord_Olexordp_Oinducts,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ X1 @ X23 )
% 2.66/1.43 => ( ! [Y3: A,Ys2: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.66/1.43 ( ( Less2 @ X3 @ Y3 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.66/1.43 ( ~ ( Less2 @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( Less2 @ Y3 @ X3 )
% 2.66/1.43 => ( ( lexordp @ A @ Less2 @ Xs2 @ Ys2 )
% 2.66/1.43 => ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 2.66/1.43 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_87_ord_Olexordp__eq_Ocases,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.66/1.43 ( ( lexordp_eq @ A @ Less2 @ A1 @ A22 )
% 2.66/1.43 => ( ( ( A1
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ! [Ys2: list @ A] : ( A22 != Ys2 ) )
% 2.66/1.43 => ( ! [X3: A] :
% 2.66/1.43 ( ? [Xs2: list @ A] :
% 2.66/1.43 ( A1
% 2.66/1.43 = ( cons @ A @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Y3: A] :
% 2.66/1.43 ( ? [Ys2: list @ A] :
% 2.66/1.43 ( A22
% 2.66/1.43 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.66/1.43 => ~ ( Less2 @ X3 @ Y3 ) ) )
% 2.66/1.43 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.66/1.43 ( ( A1
% 2.66/1.43 = ( cons @ A @ X3 @ Xs2 ) )
% 2.66/1.43 => ! [Ys2: list @ A] :
% 2.66/1.43 ( ( A22
% 2.66/1.43 = ( cons @ A @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ~ ( Less2 @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( Less2 @ Y3 @ X3 )
% 2.66/1.43 => ~ ( lexordp_eq @ A @ Less2 @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_88_ord_Olexordp__eq_Osimps,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( lexordp_eq @ A )
% 2.66/1.43 = ( ^ [Less: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.66/1.43 ( ? [Ys3: list @ A] :
% 2.66/1.43 ( ( A12
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 & ( A23 = Ys3 ) )
% 2.66/1.43 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.66/1.43 ( ( A12
% 2.66/1.43 = ( cons @ A @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A23
% 2.66/1.43 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.66/1.43 & ( Less @ X2 @ Y2 ) )
% 2.66/1.43 | ? [X2: A,Y2: A,Xs3: list @ A,Ys3: list @ A] :
% 2.66/1.43 ( ( A12
% 2.66/1.43 = ( cons @ A @ X2 @ Xs3 ) )
% 2.66/1.43 & ( A23
% 2.66/1.43 = ( cons @ A @ Y2 @ Ys3 ) )
% 2.66/1.43 & ~ ( Less @ X2 @ Y2 )
% 2.66/1.43 & ~ ( Less @ Y2 @ X2 )
% 2.66/1.43 & ( lexordp_eq @ A @ Less @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_89_ord_Olexordp__eq_Oinducts,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.66/1.43 ( ( lexordp_eq @ A @ Less2 @ X1 @ X23 )
% 2.66/1.43 => ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.66/1.43 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.66/1.43 ( ( Less2 @ X3 @ Y3 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( ! [X3: A,Y3: A,Xs2: list @ A,Ys2: list @ A] :
% 2.66/1.43 ( ~ ( Less2 @ X3 @ Y3 )
% 2.66/1.43 => ( ~ ( Less2 @ Y3 @ X3 )
% 2.66/1.43 => ( ( lexordp_eq @ A @ Less2 @ Xs2 @ Ys2 )
% 2.66/1.43 => ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) ) ) ) )
% 2.66/1.43 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_90_list_Oset__cases,axiom,
% 2.66/1.43 ! [A: $tType,E: A,A2: list @ A] :
% 2.66/1.43 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 2.66/1.43 => ( ! [Z2: list @ A] :
% 2.66/1.43 ( A2
% 2.66/1.43 != ( cons @ A @ E @ Z2 ) )
% 2.66/1.43 => ~ ! [Z1: A,Z2: list @ A] :
% 2.66/1.43 ( ( A2
% 2.66/1.43 = ( cons @ A @ Z1 @ Z2 ) )
% 2.66/1.43 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_91_set__ConsD,axiom,
% 2.66/1.43 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 2.66/1.43 => ( ( Y = X )
% 2.66/1.43 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_92_list_Oset__intros_I1_J,axiom,
% 2.66/1.43 ! [A: $tType,A1: A,A22: list @ A] : ( member @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_93_list_Oset__intros_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,X: A,A22: list @ A,A1: A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ A22 ) )
% 2.66/1.43 => ( member @ A @ X @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_94_map__tailrec__rev_Oinduct,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.66/1.43 ( ! [F2: A > B,X12: list @ B] : ( P @ F2 @ ( nil @ A ) @ X12 )
% 2.66/1.43 => ( ! [F2: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.66/1.43 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A4 ) @ Bs ) )
% 2.66/1.43 => ( P @ F2 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.66/1.43 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_95_list__nonempty__induct,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.66/1.43 => ( ! [X3: A,Xs2: list @ A] :
% 2.66/1.43 ( ( Xs2
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( P @ Xs2 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 2.66/1.43 => ( P @ Xs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_96_remdups__adj_Oinduct,axiom,
% 2.66/1.43 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.66/1.43 ( ( P @ ( nil @ A ) )
% 2.66/1.43 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.66/1.43 => ( ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.66/1.43 ( ( ( X3 = Y3 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 2.66/1.43 => ( ( ( X3 != Y3 )
% 2.66/1.43 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 2.66/1.43 => ( P @ A0 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_97_remdups__adj_Ocases,axiom,
% 2.66/1.43 ! [A: $tType,X: list @ A] :
% 2.66/1.43 ( ( X
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ! [X3: A] :
% 2.66/1.43 ( X
% 2.66/1.43 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.66/1.43 => ~ ! [X3: A,Y3: A,Xs2: list @ A] :
% 2.66/1.43 ( X
% 2.66/1.43 != ( cons @ A @ X3 @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_98_transpose_Ocases,axiom,
% 2.66/1.43 ! [A: $tType,X: list @ ( list @ A )] :
% 2.66/1.43 ( ( X
% 2.66/1.43 != ( nil @ ( list @ A ) ) )
% 2.66/1.43 => ( ! [Xss: list @ ( list @ A )] :
% 2.66/1.43 ( X
% 2.66/1.43 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.66/1.43 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.66/1.43 ( X
% 2.66/1.43 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_99_not__Cons__self2,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( cons @ A @ X @ Xs )
% 2.66/1.43 != Xs ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_100_splice_Oinduct,axiom,
% 2.66/1.43 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.66/1.43 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.66/1.43 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 2.66/1.43 => ( ! [X3: A,Xs2: list @ A,Y3: A,Ys2: list @ A] :
% 2.66/1.43 ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_101_list__induct2_H,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.66/1.43 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.66/1.43 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 2.66/1.43 => ( ! [Y3: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys2 ) )
% 2.66/1.43 => ( ! [X3: A,Xs2: list @ A,Y3: B,Ys2: list @ B] :
% 2.66/1.43 ( ( P @ Xs2 @ Ys2 )
% 2.66/1.43 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y3 @ Ys2 ) ) )
% 2.66/1.43 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_102_neq__Nil__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 = ( ? [Y2: A,Ys3: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( cons @ A @ Y2 @ Ys3 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_103_list_Oinducts,axiom,
% 2.66/1.43 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.66/1.43 ( ( P @ ( nil @ A ) )
% 2.66/1.43 => ( ! [X12: A,X24: list @ A] :
% 2.66/1.43 ( ( P @ X24 )
% 2.66/1.43 => ( P @ ( cons @ A @ X12 @ X24 ) ) )
% 2.66/1.43 => ( P @ List ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_104_list_Oexhaust,axiom,
% 2.66/1.43 ! [A: $tType,Y: list @ A] :
% 2.66/1.43 ( ( Y
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ~ ! [X212: A,X222: list @ A] :
% 2.66/1.43 ( Y
% 2.66/1.43 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_105_list_OdiscI,axiom,
% 2.66/1.43 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.66/1.43 ( ( List
% 2.66/1.43 = ( cons @ A @ X21 @ X22 ) )
% 2.66/1.43 => ( List
% 2.66/1.43 != ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_106_list_Odistinct_I1_J,axiom,
% 2.66/1.43 ! [A: $tType,X21: A,X22: list @ A] :
% 2.66/1.43 ( ( nil @ A )
% 2.66/1.43 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_107_ord_Olexordp_OCons__eq,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ~ ( Less2 @ X @ Y )
% 2.66/1.43 => ( ~ ( Less2 @ Y @ X )
% 2.66/1.43 => ( ( lexordp @ A @ Less2 @ Xs @ Ys )
% 2.66/1.43 => ( lexordp @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_108_ord_Olexordp_OCons,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( Less2 @ X @ Y )
% 2.66/1.43 => ( lexordp @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_109_ord_Olexordp__eq_OCons__eq,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ~ ( Less2 @ X @ Y )
% 2.66/1.43 => ( ~ ( Less2 @ Y @ X )
% 2.66/1.43 => ( ( lexordp_eq @ A @ Less2 @ Xs @ Ys )
% 2.66/1.43 => ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_110_ord_Olexordp__eq_OCons,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( Less2 @ X @ Y )
% 2.66/1.43 => ( lexordp_eq @ A @ Less2 @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_111_ord_Olexordp__eq_ONil,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less2 @ ( nil @ A ) @ Ys ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_112_ord_Olexordp__irreflexive,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] :
% 2.66/1.43 ( ! [X3: A] :
% 2.66/1.43 ~ ( Less2 @ X3 @ X3 )
% 2.66/1.43 => ~ ( lexordp @ A @ Less2 @ Xs @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_113_ord_Olexordp__eq__refl,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less2 @ Xs @ Xs ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_114_local_Olexordp__append__rightI,axiom,
% 2.66/1.43 ! [Ys: list @ a,Xs: list @ a] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 != ( nil @ a ) )
% 2.66/1.43 => ( lexordp @ a @ less @ Xs @ ( append @ a @ Xs @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_115_local_Olexordp__append__left__rightI,axiom,
% 2.66/1.43 ! [X: a,Y: a,Us: list @ a,Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( less @ X @ Y )
% 2.66/1.43 => ( lexordp @ a @ less @ ( append @ a @ Us @ ( cons @ a @ X @ Xs ) ) @ ( append @ a @ Us @ ( cons @ a @ Y @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_116_local_Olexordp__iff,axiom,
% 2.66/1.43 ! [Xs: list @ a,Ys: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.66/1.43 = ( ? [X2: a,Vs: list @ a] :
% 2.66/1.43 ( Ys
% 2.66/1.43 = ( append @ a @ Xs @ ( cons @ a @ X2 @ Vs ) ) )
% 2.66/1.43 | ? [Us2: list @ a,A5: a,B3: a,Vs: list @ a,Ws: list @ a] :
% 2.66/1.43 ( ( less @ A5 @ B3 )
% 2.66/1.43 & ( Xs
% 2.66/1.43 = ( append @ a @ Us2 @ ( cons @ a @ A5 @ Vs ) ) )
% 2.66/1.43 & ( Ys
% 2.66/1.43 = ( append @ a @ Us2 @ ( cons @ a @ B3 @ Ws ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_117_the__elem__set,axiom,
% 2.66/1.43 ! [A: $tType,X: A] :
% 2.66/1.43 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.66/1.43 = X ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_118_local_Olexordp__append__leftD,axiom,
% 2.66/1.43 ! [Xs: list @ a,Us: list @ a,Vs2: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ ( append @ a @ Xs @ Us ) @ ( append @ a @ Xs @ Vs2 ) )
% 2.66/1.43 => ( ! [A4: a] :
% 2.66/1.43 ~ ( less @ A4 @ A4 )
% 2.66/1.43 => ( lexordp @ a @ less @ Us @ Vs2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_119_local_Olexordp__append__leftI,axiom,
% 2.66/1.43 ! [Us: list @ a,Vs2: list @ a,Xs: list @ a] :
% 2.66/1.43 ( ( lexordp @ a @ less @ Us @ Vs2 )
% 2.66/1.43 => ( lexordp @ a @ less @ ( append @ a @ Xs @ Us ) @ ( append @ a @ Xs @ Vs2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_120_local_Ostrict__mono__imp__inj__on,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( order @ B @ ( type2 @ B ) )
% 2.66/1.43 => ! [F: a > B,A3: set @ a] :
% 2.66/1.43 ( ( strict_mono @ a @ B @ less @ F )
% 2.66/1.43 => ( inj_on @ a @ B @ F @ A3 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_121_same__append__eq,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ Ys )
% 2.66/1.43 = ( append @ A @ Xs @ Zs ) )
% 2.66/1.43 = ( Ys = Zs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_122_append__same__eq,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Ys @ Xs )
% 2.66/1.43 = ( append @ A @ Zs @ Xs ) )
% 2.66/1.43 = ( Ys = Zs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_123_append__assoc,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.66/1.43 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 2.66/1.43 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_124_append__Nil2,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.66/1.43 = Xs ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_125_append__self__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ Ys )
% 2.66/1.43 = Xs )
% 2.66/1.43 = ( Ys
% 2.66/1.43 = ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_126_self__append__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( Ys
% 2.66/1.43 = ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_127_append__self__conv2,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ Ys )
% 2.66/1.43 = Ys )
% 2.66/1.43 = ( Xs
% 2.66/1.43 = ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_128_self__append__conv2,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 = ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( Xs
% 2.66/1.43 = ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_129_Nil__is__append__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( ( nil @ A )
% 2.66/1.43 = ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( ( Xs
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 & ( Ys
% 2.66/1.43 = ( nil @ A ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_130_append__is__Nil__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ Ys )
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 = ( ( Xs
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 & ( Ys
% 2.66/1.43 = ( nil @ A ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_131_append1__eq__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.66/1.43 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.66/1.43 = ( ( Xs = Ys )
% 2.66/1.43 & ( X = Y ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_132_append__eq__append__conv2,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ Ys )
% 2.66/1.43 = ( append @ A @ Zs @ Ts ) )
% 2.66/1.43 = ( ? [Us2: list @ A] :
% 2.66/1.43 ( ( ( Xs
% 2.66/1.43 = ( append @ A @ Zs @ Us2 ) )
% 2.66/1.43 & ( ( append @ A @ Us2 @ Ys )
% 2.66/1.43 = Ts ) )
% 2.66/1.43 | ( ( ( append @ A @ Xs @ Us2 )
% 2.66/1.43 = Zs )
% 2.66/1.43 & ( Ys
% 2.66/1.43 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_133_append__eq__appendI,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys: list @ A,Us: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ Xs1 )
% 2.66/1.43 = Zs )
% 2.66/1.43 => ( ( Ys
% 2.66/1.43 = ( append @ A @ Xs1 @ Us ) )
% 2.66/1.43 => ( ( append @ A @ Xs @ Ys )
% 2.66/1.43 = ( append @ A @ Zs @ Us ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_134_Cons__eq__appendI,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.66/1.43 ( ( ( cons @ A @ X @ Xs1 )
% 2.66/1.43 = Ys )
% 2.66/1.43 => ( ( Xs
% 2.66/1.43 = ( append @ A @ Xs1 @ Zs ) )
% 2.66/1.43 => ( ( cons @ A @ X @ Xs )
% 2.66/1.43 = ( append @ A @ Ys @ Zs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_135_append__Cons,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.66/1.43 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_136_eq__Nil__appendI,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( Xs = Ys )
% 2.66/1.43 => ( Xs
% 2.66/1.43 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_137_append__Nil,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A] :
% 2.66/1.43 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.66/1.43 = Ys ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_138_ord_Olexordp__append__leftI,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Us: list @ A,Vs2: list @ A,Xs: list @ A] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ Us @ Vs2 )
% 2.66/1.43 => ( lexordp @ A @ Less2 @ ( append @ A @ Xs @ Us ) @ ( append @ A @ Xs @ Vs2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_139_ord_Olexordp__append__leftD,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,Xs: list @ A,Us: list @ A,Vs2: list @ A] :
% 2.66/1.43 ( ( lexordp @ A @ Less2 @ ( append @ A @ Xs @ Us ) @ ( append @ A @ Xs @ Vs2 ) )
% 2.66/1.43 => ( ! [A4: A] :
% 2.66/1.43 ~ ( Less2 @ A4 @ A4 )
% 2.66/1.43 => ( lexordp @ A @ Less2 @ Us @ Vs2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_140_rev__induct,axiom,
% 2.66/1.43 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.66/1.43 ( ( P @ ( nil @ A ) )
% 2.66/1.43 => ( ! [X3: A,Xs2: list @ A] :
% 2.66/1.43 ( ( P @ Xs2 )
% 2.66/1.43 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) )
% 2.66/1.43 => ( P @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_141_rev__exhaust,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ~ ! [Ys2: list @ A,Y3: A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 != ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_142_Cons__eq__append__conv,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.66/1.43 ( ( ( cons @ A @ X @ Xs )
% 2.66/1.43 = ( append @ A @ Ys @ Zs ) )
% 2.66/1.43 = ( ( ( Ys
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 & ( ( cons @ A @ X @ Xs )
% 2.66/1.43 = Zs ) )
% 2.66/1.43 | ? [Ys5: list @ A] :
% 2.66/1.43 ( ( ( cons @ A @ X @ Ys5 )
% 2.66/1.43 = Ys )
% 2.66/1.43 & ( Xs
% 2.66/1.43 = ( append @ A @ Ys5 @ Zs ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_143_append__eq__Cons__conv,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Ys @ Zs )
% 2.66/1.43 = ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( ( ( Ys
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 & ( Zs
% 2.66/1.43 = ( cons @ A @ X @ Xs ) ) )
% 2.66/1.43 | ? [Ys5: list @ A] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 = ( cons @ A @ X @ Ys5 ) )
% 2.66/1.43 & ( ( append @ A @ Ys5 @ Zs )
% 2.66/1.43 = Xs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_144_rev__nonempty__induct,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.66/1.43 => ( ! [X3: A,Xs2: list @ A] :
% 2.66/1.43 ( ( Xs2
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( P @ Xs2 )
% 2.66/1.43 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) )
% 2.66/1.43 => ( P @ Xs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_145_split__list__first__prop__iff,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ( ? [X2: A] :
% 2.66/1.43 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X2 ) ) )
% 2.66/1.43 = ( ? [Ys3: list @ A,X2: A] :
% 2.66/1.43 ( ? [Zs2: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 2.66/1.43 & ( P @ X2 )
% 2.66/1.43 & ! [Y2: A] :
% 2.66/1.43 ( ( member @ A @ Y2 @ ( set2 @ A @ Ys3 ) )
% 2.66/1.43 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_146_split__list__last__prop__iff,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ( ? [X2: A] :
% 2.66/1.43 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X2 ) ) )
% 2.66/1.43 = ( ? [Ys3: list @ A,X2: A,Zs2: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys3 @ ( cons @ A @ X2 @ Zs2 ) ) )
% 2.66/1.43 & ( P @ X2 )
% 2.66/1.43 & ! [Y2: A] :
% 2.66/1.43 ( ( member @ A @ Y2 @ ( set2 @ A @ Zs2 ) )
% 2.66/1.43 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_147_in__set__conv__decomp__first,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.66/1.43 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_148_in__set__conv__decomp__last,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) )
% 2.66/1.43 & ~ ( member @ A @ X @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_149_split__list__first__propE,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ? [X4: A] :
% 2.66/1.43 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X4 ) )
% 2.66/1.43 => ~ ! [Ys2: list @ A,X3: A] :
% 2.66/1.43 ( ? [Zs3: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.66/1.43 => ( ( P @ X3 )
% 2.66/1.43 => ~ ! [Xa: A] :
% 2.66/1.43 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.66/1.43 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_150_split__list__last__propE,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ? [X4: A] :
% 2.66/1.43 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X4 ) )
% 2.66/1.43 => ~ ! [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.66/1.43 => ( ( P @ X3 )
% 2.66/1.43 => ~ ! [Xa: A] :
% 2.66/1.43 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 2.66/1.43 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_151_split__list__first__prop,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ? [X4: A] :
% 2.66/1.43 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X4 ) )
% 2.66/1.43 => ? [Ys2: list @ A,X3: A] :
% 2.66/1.43 ( ? [Zs3: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.66/1.43 & ( P @ X3 )
% 2.66/1.43 & ! [Xa: A] :
% 2.66/1.43 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.66/1.43 => ~ ( P @ Xa ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_152_split__list__last__prop,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ? [X4: A] :
% 2.66/1.43 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X4 ) )
% 2.66/1.43 => ? [Ys2: list @ A,X3: A,Zs3: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.66/1.43 & ( P @ X3 )
% 2.66/1.43 & ! [Xa: A] :
% 2.66/1.43 ( ( member @ A @ Xa @ ( set2 @ A @ Zs3 ) )
% 2.66/1.43 => ~ ( P @ Xa ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_153_in__set__conv__decomp,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_154_split__list__propE,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ? [X4: A] :
% 2.66/1.43 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X4 ) )
% 2.66/1.43 => ~ ! [Ys2: list @ A,X3: A] :
% 2.66/1.43 ( ? [Zs3: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.66/1.43 => ~ ( P @ X3 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_155_split__list__first,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 => ? [Ys2: list @ A,Zs3: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.66/1.43 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_156_split__list__prop,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.66/1.43 ( ? [X4: A] :
% 2.66/1.43 ( ( member @ A @ X4 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( P @ X4 ) )
% 2.66/1.43 => ? [Ys2: list @ A,X3: A] :
% 2.66/1.43 ( ? [Zs3: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.66/1.43 & ( P @ X3 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_157_split__list__last,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 => ? [Ys2: list @ A,Zs3: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.66/1.43 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_158_split__list,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 => ? [Ys2: list @ A,Zs3: list @ A] :
% 2.66/1.43 ( Xs
% 2.66/1.43 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs3 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_159_ord_Olexordp__append__left__rightI,axiom,
% 2.66/1.43 ! [A: $tType,Less2: A > A > $o,X: A,Y: A,Us: list @ A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( Less2 @ X @ Y )
% 2.66/1.43 => ( lexordp @ A @ Less2 @ ( append @ A @ Us @ ( cons @ A @ X @ Xs ) ) @ ( append @ A @ Us @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_160_ord_Olexordp__append__rightI,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Less2: A > A > $o,Xs: list @ A] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( lexordp @ A @ Less2 @ Xs @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_161_sublists_Osimps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( sublists @ A @ ( nil @ A ) )
% 2.66/1.43 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_162_product__lists_Osimps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.66/1.43 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_163_bind__simps_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 2.66/1.43 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 2.66/1.43 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_164_ord__class_Orbt__greater__prop,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ( ( rBT_Im1332541288reater @ A @ B )
% 2.66/1.43 = ( ^ [K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ! [X2: A] :
% 2.66/1.43 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 2.66/1.43 => ( ord_less @ A @ K2 @ X2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_165_bind__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.66/1.43 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 2.66/1.43 = ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_166_order__class_Orbt__greater__trans,axiom,
% 2.66/1.43 ! [C2: $tType,A: $tType] :
% 2.66/1.43 ( ( order @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [X: A,Y: A,T: rBT_Im246033960le_rbt @ A @ C2] :
% 2.66/1.43 ( ( ord_less @ A @ X @ Y )
% 2.66/1.43 => ( ( rBT_Im1332541288reater @ A @ C2 @ Y @ T )
% 2.66/1.43 => ( rBT_Im1332541288reater @ A @ C2 @ X @ T ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_167_list__bind__cong,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 2.66/1.43 ( ( Xs = Ys )
% 2.66/1.43 => ( ! [X3: A] :
% 2.66/1.43 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.66/1.43 => ( ( F @ X3 )
% 2.66/1.43 = ( G @ X3 ) ) )
% 2.66/1.43 => ( ( bind @ A @ B @ Xs @ F )
% 2.66/1.43 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_168_ord__class_Orbt__less__prop,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ( ( rBT_Im903026891t_less @ A @ B )
% 2.66/1.43 = ( ^ [K2: A,T2: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ! [X2: A] :
% 2.66/1.43 ( ( member @ A @ X2 @ ( set2 @ A @ ( rBT_Im380146495e_keys @ A @ B @ T2 ) ) )
% 2.66/1.43 => ( ord_less @ A @ X2 @ K2 ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_169_maps__simps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 2.66/1.43 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 2.66/1.43 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_170_not__in__set__insert,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 => ( ( insert @ A @ X @ Xs )
% 2.66/1.43 = ( cons @ A @ X @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_171_in__set__insert,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 => ( ( insert @ A @ X @ Xs )
% 2.66/1.43 = Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_172_insert__Nil,axiom,
% 2.66/1.43 ! [A: $tType,X: A] :
% 2.66/1.43 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.66/1.43 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_173_order__class_Orbt__less__trans,axiom,
% 2.66/1.43 ! [C2: $tType,A: $tType] :
% 2.66/1.43 ( ( order @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [X: A,T: rBT_Im246033960le_rbt @ A @ C2,Y: A] :
% 2.66/1.43 ( ( rBT_Im903026891t_less @ A @ C2 @ X @ T )
% 2.66/1.43 => ( ( ord_less @ A @ X @ Y )
% 2.66/1.43 => ( rBT_Im903026891t_less @ A @ C2 @ Y @ T ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_174_maps__simps_I2_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.66/1.43 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 2.66/1.43 = ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_175_List_Oinsert__def,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( insert @ A )
% 2.66/1.43 = ( ^ [X2: A,Xs3: list @ A] : ( if @ ( list @ A ) @ ( member @ A @ X2 @ ( set2 @ A @ Xs3 ) ) @ Xs3 @ ( cons @ A @ X2 @ Xs3 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_176_rotate1_Osimps_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_177_local_Orbt__less__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,K: a] : ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_178_last__snoc,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A] :
% 2.66/1.43 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.66/1.43 = X ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_179_rotate1__is__Nil__conv,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( ( rotate1 @ A @ Xs )
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 = ( Xs
% 2.66/1.43 = ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_180_set__rotate1,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( set2 @ A @ ( rotate1 @ A @ Xs ) )
% 2.66/1.43 = ( set2 @ A @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_181_ord__class_Orbt__greater__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [K: A] : ( rBT_Im1332541288reater @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_182_ord__class_Orbt__less__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [K: A] : ( rBT_Im903026891t_less @ A @ B @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_183_last__appendL,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( last @ A @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_184_last__appendR,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.66/1.43 ( ( Ys
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( last @ A @ Ys ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_185_keys__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( rBT_Im380146495e_keys @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.66/1.43 = ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_186_local_Orbt__greater__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,K: a] : ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_187_rotate1_Osimps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( rotate1 @ A @ ( nil @ A ) )
% 2.66/1.43 = ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_188_ord_Orbt__less__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Less2: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less2 @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_189_ord_Orbt__greater__simps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Less2: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less2 @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_190_last__ConsR,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( last @ A @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_191_last__ConsL,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = X ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_192_last_Osimps,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A] :
% 2.66/1.43 ( ( ( Xs
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = X ) )
% 2.66/1.43 & ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( last @ A @ Xs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_193_last__in__set,axiom,
% 2.66/1.43 ! [A: $tType,As2: list @ A] :
% 2.66/1.43 ( ( As2
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( member @ A @ ( last @ A @ As2 ) @ ( set2 @ A @ As2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_194_last__append,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.66/1.43 ( ( ( Ys
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( last @ A @ Xs ) ) )
% 2.66/1.43 & ( ( Ys
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( last @ A @ Ys ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_195_longest__common__suffix,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ? [Ss: list @ A,Xs4: list @ A,Ys4: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 = ( append @ A @ Xs4 @ Ss ) )
% 2.66/1.43 & ( Ys
% 2.66/1.43 = ( append @ A @ Ys4 @ Ss ) )
% 2.66/1.43 & ( ( Xs4
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 | ( Ys4
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 | ( ( last @ A @ Xs4 )
% 2.66/1.43 != ( last @ A @ Ys4 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_196_non__empty__rbt__keys,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( T
% 2.66/1.43 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.66/1.43 => ( ( rBT_Im380146495e_keys @ A @ B @ T )
% 2.66/1.43 != ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_197_local_Orbt__sorted_Osimps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType] : ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_198_append__butlast__last__id,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 2.66/1.43 = Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_199_snoc__eq__iff__butlast,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A] :
% 2.66/1.43 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.66/1.43 = Ys )
% 2.66/1.43 = ( ( Ys
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 & ( ( butlast @ A @ Ys )
% 2.66/1.43 = Xs )
% 2.66/1.43 & ( ( last @ A @ Ys )
% 2.66/1.43 = X ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_200_butlast__snoc,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A] :
% 2.66/1.43 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.66/1.43 = Xs ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_201_butlast_Osimps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType] :
% 2.66/1.43 ( ( butlast @ A @ ( nil @ A ) )
% 2.66/1.43 = ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_202_in__set__butlastD,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.66/1.43 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_203_butlast_Osimps_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,X: A] :
% 2.66/1.43 ( ( ( Xs
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( nil @ A ) ) )
% 2.66/1.43 & ( ( Xs
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_204_butlast__append,axiom,
% 2.66/1.43 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.66/1.43 ( ( ( Ys
% 2.66/1.43 = ( nil @ A ) )
% 2.66/1.43 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( butlast @ A @ Xs ) ) )
% 2.66/1.43 & ( ( Ys
% 2.66/1.43 != ( nil @ A ) )
% 2.66/1.43 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_205_in__set__butlast__appendI,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.66/1.43 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 2.66/1.43 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_206_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Less2: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less2 @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_207_local_Orbt__sorted_Osimps_I2_J,axiom,
% 2.66/1.43 ! [B: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,K: a,V2: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ C @ L @ K @ V2 @ R ) )
% 2.66/1.43 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.66/1.43 & ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.66/1.43 & ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.66/1.43 & ( rBT_Im759614907sorted @ a @ B @ less @ R ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_208_local_Odistinct__keys,axiom,
% 2.66/1.43 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.66/1.43 => ( distinct @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_209_rbt_Oinject,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X25: rBT_Im246033960le_rbt @ A @ B,Y21: rBT_Im1923302023_color,Y22: rBT_Im246033960le_rbt @ A @ B,Y23: A,Y24: B,Y25: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X232 @ X242 @ X25 )
% 2.66/1.43 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 2.66/1.43 = ( ( X21 = Y21 )
% 2.66/1.43 & ( X22 = Y22 )
% 2.66/1.43 & ( X232 = Y23 )
% 2.66/1.43 & ( X242 = Y24 )
% 2.66/1.43 & ( X25 = Y25 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_210_distinct1__rotate,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( distinct @ A @ ( rotate1 @ A @ Xs ) )
% 2.66/1.43 = ( distinct @ A @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_211_distinct__insert,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( distinct @ A @ ( insert @ A @ X @ Xs ) )
% 2.66/1.43 = ( distinct @ A @ Xs ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_212_ord__class_Orbt__greater__simps_I2_J,axiom,
% 2.66/1.43 ! [C2: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.66/1.43 ( ( rBT_Im1332541288reater @ A @ C2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 2.66/1.43 = ( ( ord_less @ A @ K @ Kt )
% 2.66/1.43 & ( rBT_Im1332541288reater @ A @ C2 @ K @ Lt )
% 2.66/1.43 & ( rBT_Im1332541288reater @ A @ C2 @ K @ Rt ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_213_ord__class_Orbt__less__simps_I2_J,axiom,
% 2.66/1.43 ! [C2: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.66/1.43 ( ( rBT_Im903026891t_less @ A @ C2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 2.66/1.43 = ( ( ord_less @ A @ Kt @ K )
% 2.66/1.43 & ( rBT_Im903026891t_less @ A @ C2 @ K @ Lt )
% 2.66/1.43 & ( rBT_Im903026891t_less @ A @ C2 @ K @ Rt ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_214_local_Orbt__greater__simps_I2_J,axiom,
% 2.66/1.43 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V2: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 2.66/1.43 ( ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 2.66/1.43 = ( ( less @ K @ Kt )
% 2.66/1.43 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Lt )
% 2.66/1.43 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_215_local_Orbt__less__simps_I2_J,axiom,
% 2.66/1.43 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V2: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 2.66/1.43 = ( ( less @ Kt @ K )
% 2.66/1.43 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Lt )
% 2.66/1.43 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_216_keys__simps_I2_J,axiom,
% 2.66/1.43 ! [D: $tType,C2: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ C2 @ D,K: C2,V2: D,R: rBT_Im246033960le_rbt @ C2 @ D] :
% 2.66/1.43 ( ( rBT_Im380146495e_keys @ C2 @ D @ ( rBT_Im480247531Branch @ C2 @ D @ C @ L @ K @ V2 @ R ) )
% 2.66/1.43 = ( append @ C2 @ ( rBT_Im380146495e_keys @ C2 @ D @ L ) @ ( cons @ C2 @ K @ ( rBT_Im380146495e_keys @ C2 @ D @ R ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_217_rbt_Oexhaust,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( Y
% 2.66/1.43 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.66/1.43 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X233: A,X243: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( Y
% 2.66/1.43 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X233 @ X243 @ X252 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_218_rbt_Oinduct,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.66/1.43 => ( ! [X12: rBT_Im1923302023_color,X24: rBT_Im246033960le_rbt @ A @ B,X32: A,X42: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( P @ X24 )
% 2.66/1.43 => ( ( P @ X5 )
% 2.66/1.43 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X12 @ X24 @ X32 @ X42 @ X5 ) ) ) )
% 2.66/1.43 => ( P @ Rbt ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_219_rbt_Odistinct_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( rBT_Im418718756_Empty @ A @ B )
% 2.66/1.43 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X232 @ X242 @ X25 ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_220_distinct__butlast,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A] :
% 2.66/1.43 ( ( distinct @ A @ Xs )
% 2.66/1.43 => ( distinct @ A @ ( butlast @ A @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_221_distinct__singleton,axiom,
% 2.66/1.43 ! [A: $tType,X: A] : ( distinct @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_222_distinct_Osimps_I2_J,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Xs: list @ A] :
% 2.66/1.43 ( ( distinct @ A @ ( cons @ A @ X @ Xs ) )
% 2.66/1.43 = ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.66/1.43 & ( distinct @ A @ Xs ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_223_distinct__length__2__or__more,axiom,
% 2.66/1.43 ! [A: $tType,A2: A,B2: A,Xs: list @ A] :
% 2.66/1.43 ( ( distinct @ A @ ( cons @ A @ A2 @ ( cons @ A @ B2 @ Xs ) ) )
% 2.66/1.43 = ( ( A2 != B2 )
% 2.66/1.43 & ( distinct @ A @ ( cons @ A @ A2 @ Xs ) )
% 2.66/1.43 & ( distinct @ A @ ( cons @ A @ B2 @ Xs ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_224_distinct_Osimps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType] : ( distinct @ A @ ( nil @ A ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_225_ord_Orbt__less__simps_I2_J,axiom,
% 2.66/1.43 ! [C2: $tType,A: $tType,Less2: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ A @ C2 @ Less2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 2.66/1.43 = ( ( Less2 @ Kt @ K )
% 2.66/1.43 & ( rBT_Im2075124343t_less @ A @ C2 @ Less2 @ K @ Lt )
% 2.66/1.43 & ( rBT_Im2075124343t_less @ A @ C2 @ Less2 @ K @ Rt ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_226_ord_Orbt__greater__simps_I2_J,axiom,
% 2.66/1.43 ! [C2: $tType,A: $tType,Less2: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V2: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.66/1.43 ( ( rBT_Im1259024060reater @ A @ C2 @ Less2 @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V2 @ Rt ) )
% 2.66/1.43 = ( ( Less2 @ K @ Kt )
% 2.66/1.43 & ( rBT_Im1259024060reater @ A @ C2 @ Less2 @ K @ Lt )
% 2.66/1.43 & ( rBT_Im1259024060reater @ A @ C2 @ Less2 @ K @ Rt ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_227_distinct__product__lists,axiom,
% 2.66/1.43 ! [A: $tType,Xss2: list @ ( list @ A )] :
% 2.66/1.43 ( ! [X3: list @ A] :
% 2.66/1.43 ( ( member @ ( list @ A ) @ X3 @ ( set2 @ ( list @ A ) @ Xss2 ) )
% 2.66/1.43 => ( distinct @ A @ X3 ) )
% 2.66/1.43 => ( distinct @ ( list @ A ) @ ( product_lists @ A @ Xss2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_228_not__distinct__decomp,axiom,
% 2.66/1.43 ! [A: $tType,Ws2: list @ A] :
% 2.66/1.43 ( ~ ( distinct @ A @ Ws2 )
% 2.66/1.43 => ? [Xs2: list @ A,Ys2: list @ A,Zs3: list @ A,Y3: A] :
% 2.66/1.43 ( Ws2
% 2.66/1.43 = ( append @ A @ Xs2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ ( append @ A @ Ys2 @ ( append @ A @ ( cons @ A @ Y3 @ ( nil @ A ) ) @ Zs3 ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_229_not__distinct__conv__prefix,axiom,
% 2.66/1.43 ! [A: $tType,As2: list @ A] :
% 2.66/1.43 ( ( ~ ( distinct @ A @ As2 ) )
% 2.66/1.43 = ( ? [Xs3: list @ A,Y2: A,Ys3: list @ A] :
% 2.66/1.43 ( ( member @ A @ Y2 @ ( set2 @ A @ Xs3 ) )
% 2.66/1.43 & ( distinct @ A @ Xs3 )
% 2.66/1.43 & ( As2
% 2.66/1.43 = ( append @ A @ Xs3 @ ( cons @ A @ Y2 @ Ys3 ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_230_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Less2: A > A > $o,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V2: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( rBT_Im759614907sorted @ A @ B @ Less2 @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V2 @ R ) )
% 2.66/1.43 = ( ( rBT_Im2075124343t_less @ A @ B @ Less2 @ K @ L )
% 2.66/1.43 & ( rBT_Im1259024060reater @ A @ B @ Less2 @ K @ R )
% 2.66/1.43 & ( rBT_Im759614907sorted @ A @ B @ Less2 @ L )
% 2.66/1.43 & ( rBT_Im759614907sorted @ A @ B @ Less2 @ R ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_231_distinct__union,axiom,
% 2.66/1.43 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.66/1.43 ( ( distinct @ A @ ( union @ A @ Xs @ Ys ) )
% 2.66/1.43 = ( distinct @ A @ Ys ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_232_RBT__SORTED,axiom,
% 2.66/1.43 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ c @ t1 @ k @ v @ t2 ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_233_Branch_Oprems,axiom,
% 2.66/1.43 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ c @ t1 @ k @ v @ t2 ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_234_ord__class_Orbt__sorted_Osimps_I2_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V2: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V2 @ R ) )
% 2.66/1.43 = ( ( rBT_Im903026891t_less @ A @ B @ K @ L )
% 2.66/1.43 & ( rBT_Im1332541288reater @ A @ B @ K @ R )
% 2.66/1.43 & ( rBT_Im1183586831sorted @ A @ B @ L )
% 2.66/1.43 & ( rBT_Im1183586831sorted @ A @ B @ R ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_235_ord__class_Orbt__sorted_Osimps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( ord @ A @ ( type2 @ A ) )
% 2.66/1.43 => ( rBT_Im1183586831sorted @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_236_linorder__class_Odistinct__keys,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( linorder @ A @ ( type2 @ A ) )
% 2.66/1.43 => ! [T: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( rBT_Im1183586831sorted @ A @ B @ T )
% 2.66/1.43 => ( distinct @ A @ ( rBT_Im380146495e_keys @ A @ B @ T ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_237_local_OgreaterThan__def,axiom,
% 2.66/1.43 ! [L: a] :
% 2.66/1.43 ( ( set_greaterThan @ a @ less @ L )
% 2.66/1.43 = ( collect @ a @ ( less @ L ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_238_local_OlessThan__def,axiom,
% 2.66/1.43 ! [U: a] :
% 2.66/1.43 ( ( set_lessThan @ a @ less @ U )
% 2.66/1.43 = ( collect @ a
% 2.66/1.43 @ ^ [X2: a] : ( less @ X2 @ U ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_239_local_OlessThan__iff,axiom,
% 2.66/1.43 ! [I: a,K: a] :
% 2.66/1.43 ( ( member @ a @ I @ ( set_lessThan @ a @ less @ K ) )
% 2.66/1.43 = ( less @ I @ K ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_240_local_OgreaterThan__iff,axiom,
% 2.66/1.43 ! [I: a,K: a] :
% 2.66/1.43 ( ( member @ a @ I @ ( set_greaterThan @ a @ less @ K ) )
% 2.66/1.43 = ( less @ K @ I ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_241_DOM__T1,axiom,
% 2.66/1.43 ! [K3: a] :
% 2.66/1.43 ( ( member @ a @ K3 @ ( dom @ a @ b @ ( rBT_Im35466040lookup @ a @ b @ less @ t1 ) ) )
% 2.66/1.43 => ( less @ K3 @ k ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_242_local_Orbt__lookup__keys,axiom,
% 2.66/1.43 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.66/1.43 => ( ( dom @ a @ B @ ( rBT_Im35466040lookup @ a @ B @ less @ T ) )
% 2.66/1.43 = ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ B @ T ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_243_Branch_Ohyps_I1_J,axiom,
% 2.66/1.43 ( ( rBT_Im759614907sorted @ a @ b @ less @ t1 )
% 2.66/1.43 => ( ( map_of @ a @ b @ ( rBT_Im954575269ntries @ a @ b @ t1 ) )
% 2.66/1.43 = ( rBT_Im35466040lookup @ a @ b @ less @ t1 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_244_Branch_Ohyps_I2_J,axiom,
% 2.66/1.43 ( ( rBT_Im759614907sorted @ a @ b @ less @ t2 )
% 2.66/1.43 => ( ( map_of @ a @ b @ ( rBT_Im954575269ntries @ a @ b @ t2 ) )
% 2.66/1.43 = ( rBT_Im35466040lookup @ a @ b @ less @ t2 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_245_entries_Osimps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType] :
% 2.66/1.43 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.66/1.43 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_246_local_Orbt__lookup__Empty,axiom,
% 2.66/1.43 ! [B: $tType] :
% 2.66/1.43 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) )
% 2.66/1.43 = ( ^ [X2: a] : ( none @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_247_local_Orbt__lookup_Osimps_I1_J,axiom,
% 2.66/1.43 ! [B: $tType,K: a] :
% 2.66/1.43 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) @ K )
% 2.66/1.43 = ( none @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_248_local_Orbt__lookup__rbt__greater,axiom,
% 2.66/1.43 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.66/1.43 = ( none @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_249_local_Orbt__lookup__rbt__less,axiom,
% 2.66/1.43 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.66/1.43 = ( none @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_250_ord_Orbt__lookup__rbt__less,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,Less2: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( rBT_Im2075124343t_less @ A @ B @ Less2 @ K @ T )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ T @ K )
% 2.66/1.43 = ( none @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_251_ord_Orbt__lookup__rbt__greater,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,Less2: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.66/1.43 ( ( rBT_Im1259024060reater @ A @ B @ Less2 @ K @ T )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ T @ K )
% 2.66/1.43 = ( none @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_252_ord_Orbt__lookup_Osimps_I1_J,axiom,
% 2.66/1.43 ! [A: $tType,B: $tType,Less2: A > A > $o,K: A] :
% 2.66/1.43 ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ ( rBT_Im418718756_Empty @ A @ B ) @ K )
% 2.66/1.43 = ( none @ B ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_253_ord_Orbt__lookup__Empty,axiom,
% 2.66/1.43 ! [B: $tType,A: $tType,Less2: A > A > $o] :
% 2.66/1.43 ( ( rBT_Im35466040lookup @ A @ B @ Less2 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.66/1.43 = ( ^ [X2: A] : ( none @ B ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(fact_254_local_Orbt__lookup_Osimps_I2_J,axiom,
% 2.66/1.43 ! [B: $tType,K: a,X: a,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.66/1.43 ( ( ( less @ K @ X )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.66/1.43 = ( rBT_Im35466040lookup @ a @ B @ less @ L @ K ) ) )
% 2.66/1.43 & ( ~ ( less @ K @ X )
% 2.66/1.43 => ( ( ( less @ X @ K )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.66/1.43 = ( rBT_Im35466040lookup @ a @ B @ less @ R @ K ) ) )
% 2.66/1.43 & ( ~ ( less @ X @ K )
% 2.66/1.43 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ Uu @ L @ X @ Y @ R ) @ K )
% 2.66/1.43 = ( some @ B @ Y ) ) ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.66/1.43 ! [A6: $tType,A7: $tType] :
% 2.66/1.43 ( ( order @ A7 @ ( type2 @ A7 ) )
% 2.66/1.43 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_fun___Orderings_Oord,axiom,
% 2.66/1.43 ! [A6: $tType,A7: $tType] :
% 2.66/1.43 ( ( ord @ A7 @ ( type2 @ A7 ) )
% 2.66/1.43 => ( ord @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 2.66/1.43 ! [A6: $tType] : ( order @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 2.66/1.43 ! [A6: $tType] : ( ord @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.66/1.43 linorder @ $o @ ( type2 @ $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 2.66/1.43 order @ $o @ ( type2 @ $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 2.66/1.43 ord @ $o @ ( type2 @ $o ) ).
% 2.66/1.43
% 2.66/1.43 thf(help_If_3_1_T,axiom,
% 2.66/1.43 ! [P: $o] :
% 2.66/1.43 ( ( P = $true )
% 2.66/1.43 | ( P = $false ) ) ).
% 2.66/1.43
% 2.66/1.43 thf(help_If_2_1_T,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Y: A] :
% 2.66/1.43 ( ( if @ A @ $false @ X @ Y )
% 2.66/1.43 = Y ) ).
% 2.66/1.43
% 2.66/1.43 thf(help_If_1_1_T,axiom,
% 2.66/1.43 ! [A: $tType,X: A,Y: A] :
% 2.66/1.43 ( ( if @ A @ $true @ X @ Y )
% 2.66/1.43 = X ) ).
% 2.66/1.43
% 2.66/1.43 thf(conj_0,conjecture,
% 2.66/1.43 ! [X3: a] :
% 2.66/1.43 ( ( member @ a @ X3 @ ( set2 @ a @ ( rBT_Im380146495e_keys @ a @ b @ t2 ) ) )
% 2.66/1.43 => ( less @ k @ X3 ) ) ).
% 2.66/1.43 ------------------------
% 2.66/1.45 % (17037)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/18Mi)
% 2.66/1.45 % (17031)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/183Mi)
% 2.66/1.45 % (17032)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_16703 for (2999ds/4Mi)
% 2.66/1.46 % (17032)Instruction limit reached!
% 2.66/1.46 % (17032)------------------------------
% 2.66/1.46 % (17032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.46 % (17032)Termination reason: Unknown
% 2.66/1.46 % (17032)Termination phase: shuffling
% 2.66/1.46
% 2.66/1.46 % (17032)Memory used [KB]: 1407
% 2.66/1.46 % (17032)Time elapsed: 0.003 s
% 2.66/1.46 % (17032)Instructions burned: 5 (million)
% 2.66/1.46 % (17032)------------------------------
% 2.66/1.46 % (17032)------------------------------
% 2.66/1.46 % (17037)Instruction limit reached!
% 2.66/1.46 % (17037)------------------------------
% 2.66/1.46 % (17037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.46 % (17037)Termination reason: Unknown
% 2.66/1.46 % (17037)Termination phase: shuffling
% 2.66/1.46
% 2.66/1.46 % (17037)Memory used [KB]: 1663
% 2.66/1.46 % (17037)Time elapsed: 0.008 s
% 2.66/1.46 % (17037)Instructions burned: 19 (million)
% 2.66/1.46 % (17037)------------------------------
% 2.66/1.46 % (17037)------------------------------
% 2.66/1.46 % (17033)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_16703 for (2999ds/27Mi)
% 2.66/1.46 % (17034)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/2Mi)
% 2.66/1.46 % (17035)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_16703 for (2999ds/2Mi)
% 2.66/1.46 % (17036)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_16703 for (2999ds/275Mi)
% 2.66/1.46 % (17034)Instruction limit reached!
% 2.66/1.46 % (17034)------------------------------
% 2.66/1.46 % (17034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.46 % (17034)Termination reason: Unknown
% 2.66/1.46 % (17034)Termination phase: shuffling
% 2.66/1.46
% 2.66/1.46 % (17034)Memory used [KB]: 1407
% 2.66/1.46 % (17034)Time elapsed: 0.004 s
% 2.66/1.46 % (17034)Instructions burned: 3 (million)
% 2.66/1.46 % (17034)------------------------------
% 2.66/1.46 % (17034)------------------------------
% 2.66/1.46 % (17035)Instruction limit reached!
% 2.66/1.46 % (17035)------------------------------
% 2.66/1.46 % (17035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.46 % (17035)Termination reason: Unknown
% 2.66/1.46 % (17035)Termination phase: shuffling
% 2.66/1.46
% 2.66/1.46 % (17035)Memory used [KB]: 1407
% 2.66/1.46 % (17035)Time elapsed: 0.004 s
% 2.66/1.46 % (17035)Instructions burned: 3 (million)
% 2.66/1.46 % (17035)------------------------------
% 2.66/1.46 % (17035)------------------------------
% 2.66/1.47 % (17038)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/3Mi)
% 2.66/1.47 % (17038)Instruction limit reached!
% 2.66/1.47 % (17038)------------------------------
% 2.66/1.47 % (17038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.47 % (17038)Termination reason: Unknown
% 2.66/1.47 % (17038)Termination phase: shuffling
% 2.66/1.47
% 2.66/1.47 % (17038)Memory used [KB]: 1407
% 2.66/1.47 % (17038)Time elapsed: 0.003 s
% 2.66/1.47 % (17038)Instructions burned: 3 (million)
% 2.66/1.47 % (17038)------------------------------
% 2.66/1.47 % (17038)------------------------------
% 2.66/1.47 % (17039)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_16703 for (2999ds/37Mi)
% 2.66/1.48 % (17042)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_16703 for (2999ds/1041Mi)
% 2.66/1.48 % (17033)Instruction limit reached!
% 2.66/1.48 % (17033)------------------------------
% 2.66/1.48 % (17033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.48 % (17033)Termination reason: Unknown
% 2.66/1.48 % (17033)Termination phase: shuffling
% 2.66/1.48
% 2.66/1.48 % (17033)Memory used [KB]: 1791
% 2.66/1.48 % (17033)Time elapsed: 0.019 s
% 2.66/1.48 % (17033)Instructions burned: 27 (million)
% 2.66/1.48 % (17033)------------------------------
% 2.66/1.48 % (17033)------------------------------
% 2.66/1.48 % (17040)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_16703 for (2999ds/15Mi)
% 2.66/1.48 % (17041)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_16703 for (2999ds/3Mi)
% 2.66/1.48 % (17039)Instruction limit reached!
% 2.66/1.48 % (17039)------------------------------
% 2.66/1.48 % (17039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.48 % (17039)Termination reason: Unknown
% 2.66/1.48 % (17039)Termination phase: shuffling
% 2.66/1.48
% 2.66/1.48 % (17039)Memory used [KB]: 2174
% 2.66/1.48 % (17039)Time elapsed: 0.013 s
% 2.66/1.48 % (17039)Instructions burned: 40 (million)
% 2.66/1.48 % (17039)------------------------------
% 2.66/1.48 % (17039)------------------------------
% 2.66/1.48 % (17041)Instruction limit reached!
% 2.66/1.48 % (17041)------------------------------
% 2.66/1.48 % (17041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.48 % (17041)Termination reason: Unknown
% 2.66/1.48 % (17041)Termination phase: shuffling
% 2.66/1.48
% 2.66/1.48 % (17041)Memory used [KB]: 1407
% 2.66/1.48 % (17041)Time elapsed: 0.004 s
% 2.66/1.48 % (17041)Instructions burned: 3 (million)
% 2.66/1.48 % (17041)------------------------------
% 2.66/1.48 % (17041)------------------------------
% 2.66/1.49 % (17040)Instruction limit reached!
% 2.66/1.49 % (17040)------------------------------
% 2.66/1.49 % (17040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.49 % (17040)Termination reason: Unknown
% 2.66/1.49 % (17040)Termination phase: shuffling
% 2.66/1.49
% 2.66/1.49 % (17040)Memory used [KB]: 1663
% 2.66/1.49 % (17040)Time elapsed: 0.012 s
% 2.66/1.49 % (17040)Instructions burned: 16 (million)
% 2.66/1.49 % (17040)------------------------------
% 2.66/1.49 % (17040)------------------------------
% 2.66/1.49 % (17044)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/16Mi)
% 2.66/1.50 % (17043)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/7Mi)
% 2.66/1.50 % (17044)Instruction limit reached!
% 2.66/1.50 % (17044)------------------------------
% 2.66/1.50 % (17044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.50 % (17044)Termination reason: Unknown
% 2.66/1.50 % (17044)Termination phase: shuffling
% 2.66/1.50
% 2.66/1.50 % (17044)Memory used [KB]: 1663
% 2.66/1.50 % (17044)Time elapsed: 0.006 s
% 2.66/1.50 % (17044)Instructions burned: 16 (million)
% 2.66/1.50 % (17044)------------------------------
% 2.66/1.50 % (17044)------------------------------
% 2.70/1.50 % (17045)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_16703 for (2999ds/3Mi)
% 2.70/1.50 % (17043)Instruction limit reached!
% 2.70/1.50 % (17043)------------------------------
% 2.70/1.50 % (17043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.50 % (17043)Termination reason: Unknown
% 2.70/1.50 % (17043)Termination phase: shuffling
% 2.70/1.50
% 2.70/1.50 % (17043)Memory used [KB]: 1535
% 2.70/1.50 % (17043)Time elapsed: 0.007 s
% 2.70/1.50 % (17043)Instructions burned: 8 (million)
% 2.70/1.50 % (17043)------------------------------
% 2.70/1.50 % (17043)------------------------------
% 2.70/1.50 % (17045)Instruction limit reached!
% 2.70/1.50 % (17045)------------------------------
% 2.70/1.50 % (17045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.50 % (17045)Termination reason: Unknown
% 2.70/1.50 % (17045)Termination phase: shuffling
% 2.70/1.50
% 2.70/1.50 % (17045)Memory used [KB]: 1407
% 2.70/1.50 % (17045)Time elapsed: 0.004 s
% 2.70/1.50 % (17045)Instructions burned: 3 (million)
% 2.70/1.50 % (17045)------------------------------
% 2.70/1.50 % (17045)------------------------------
% 2.70/1.51 % (17047)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/7Mi)
% 2.70/1.51 % (17047)Instruction limit reached!
% 2.70/1.51 % (17047)------------------------------
% 2.70/1.51 % (17047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.51 % (17047)Termination reason: Unknown
% 2.70/1.51 % (17047)Termination phase: shuffling
% 2.70/1.51
% 2.70/1.51 % (17047)Memory used [KB]: 1535
% 2.70/1.51 % (17047)Time elapsed: 0.004 s
% 2.70/1.51 % (17047)Instructions burned: 9 (million)
% 2.70/1.51 % (17047)------------------------------
% 2.70/1.51 % (17047)------------------------------
% 2.70/1.51 % (17046)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_16703 for (2999ds/3Mi)
% 2.70/1.51 % (17046)Instruction limit reached!
% 2.70/1.51 % (17046)------------------------------
% 2.70/1.51 % (17046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.51 % (17046)Termination reason: Unknown
% 2.70/1.51 % (17046)Termination phase: shuffling
% 2.70/1.51
% 2.70/1.51 % (17046)Memory used [KB]: 1407
% 2.70/1.51 % (17046)Time elapsed: 0.004 s
% 2.70/1.51 % (17046)Instructions burned: 3 (million)
% 2.70/1.51 % (17046)------------------------------
% 2.70/1.51 % (17046)------------------------------
% 2.70/1.51 % (17031)Instruction limit reached!
% 2.70/1.51 % (17031)------------------------------
% 2.70/1.51 % (17031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.51 % (17031)Termination reason: Unknown
% 2.70/1.51 % (17031)Termination phase: Saturation
% 2.70/1.51
% 2.70/1.51 % (17031)Memory used [KB]: 7291
% 2.70/1.51 % (17031)Time elapsed: 0.058 s
% 2.70/1.51 % (17031)Instructions burned: 184 (million)
% 2.70/1.51 % (17031)------------------------------
% 2.70/1.51 % (17031)------------------------------
% 2.70/1.52 % (17048)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/3Mi)
% 2.70/1.52 % (17050)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/18Mi)
% 2.70/1.52 % (17048)Instruction limit reached!
% 2.70/1.52 % (17048)------------------------------
% 2.70/1.52 % (17048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.52 % (17048)Termination reason: Unknown
% 2.70/1.52 % (17048)Termination phase: shuffling
% 2.70/1.52
% 2.70/1.52 % (17048)Memory used [KB]: 1407
% 2.70/1.52 % (17048)Time elapsed: 0.004 s
% 2.70/1.52 % (17048)Instructions burned: 5 (million)
% 2.70/1.52 % (17048)------------------------------
% 2.70/1.52 % (17048)------------------------------
% 2.70/1.52 % (17049)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/4Mi)
% 2.70/1.52 % (17052)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/6Mi)
% 2.70/1.52 % (17049)Instruction limit reached!
% 2.70/1.52 % (17049)------------------------------
% 2.70/1.52 % (17049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.52 % (17049)Termination reason: Unknown
% 2.70/1.52 % (17049)Termination phase: shuffling
% 2.70/1.52
% 2.70/1.52 % (17049)Memory used [KB]: 1407
% 2.70/1.52 % (17049)Time elapsed: 0.005 s
% 2.70/1.52 % (17049)Instructions burned: 5 (million)
% 2.70/1.52 % (17049)------------------------------
% 2.70/1.52 % (17049)------------------------------
% 2.70/1.52 % (17052)Instruction limit reached!
% 2.70/1.52 % (17052)------------------------------
% 2.70/1.52 % (17052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.52 % (17052)Termination reason: Unknown
% 2.70/1.52 % (17052)Termination phase: shuffling
% 2.70/1.52
% 2.70/1.52 % (17052)Memory used [KB]: 1407
% 2.70/1.52 % (17052)Time elapsed: 0.004 s
% 2.70/1.52 % (17052)Instructions burned: 6 (million)
% 2.70/1.52 % (17052)------------------------------
% 2.70/1.52 % (17052)------------------------------
% 2.70/1.52 % (17050)Instruction limit reached!
% 2.70/1.52 % (17050)------------------------------
% 2.70/1.52 % (17050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.52 % (17050)Termination reason: Unknown
% 2.70/1.52 % (17050)Termination phase: shuffling
% 2.70/1.52
% 2.70/1.52 % (17050)Memory used [KB]: 1791
% 2.70/1.52 % (17050)Time elapsed: 0.008 s
% 2.70/1.52 % (17050)Instructions burned: 20 (million)
% 2.70/1.52 % (17050)------------------------------
% 2.70/1.52 % (17050)------------------------------
% 2.70/1.53 % (17051)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/710Mi)
% 2.70/1.53 % (17053)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_16703 for (2999ds/902Mi)
% 2.70/1.53 % (17055)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/5Mi)
% 2.70/1.53 % (17056)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_16703 for (2999ds/6Mi)
% 2.70/1.54 % (17055)Instruction limit reached!
% 2.70/1.54 % (17055)------------------------------
% 2.70/1.54 % (17055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.54 % (17055)Termination reason: Unknown
% 2.70/1.54 % (17055)Termination phase: shuffling
% 2.70/1.54
% 2.70/1.54 % (17055)Memory used [KB]: 1535
% 2.70/1.54 % (17055)Time elapsed: 0.004 s
% 2.70/1.54 % (17055)Instructions burned: 7 (million)
% 2.70/1.54 % (17055)------------------------------
% 2.70/1.54 % (17055)------------------------------
% 2.70/1.54 % (17056)Instruction limit reached!
% 2.70/1.54 % (17056)------------------------------
% 2.70/1.54 % (17056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.54 % (17056)Termination reason: Unknown
% 2.70/1.54 % (17056)Termination phase: shuffling
% 2.70/1.54
% 2.70/1.54 % (17056)Memory used [KB]: 1535
% 2.70/1.54 % (17056)Time elapsed: 0.003 s
% 2.70/1.54 % (17056)Instructions burned: 7 (million)
% 2.70/1.54 % (17056)------------------------------
% 2.70/1.54 % (17056)------------------------------
% 2.70/1.54 % (17054)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_16703 for (2999ds/21Mi)
% 2.70/1.55 % (17058)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_16703 for (2999ds/779Mi)
% 2.70/1.55 % (17057)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16703 for (2999ds/377Mi)
% 2.70/1.55 % (17054)Instruction limit reached!
% 2.70/1.55 % (17054)------------------------------
% 2.70/1.55 % (17054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.55 % (17054)Termination reason: Unknown
% 2.70/1.55 % (17054)Termination phase: shuffling
% 2.70/1.55
% 2.70/1.55 % (17054)Memory used [KB]: 1791
% 2.70/1.55 % (17054)Time elapsed: 0.015 s
% 2.70/1.55 % (17054)Instructions burned: 21 (million)
% 2.70/1.55 % (17054)------------------------------
% 2.70/1.55 % (17054)------------------------------
% 2.70/1.56 % (17036)Instruction limit reached!
% 2.70/1.56 % (17036)------------------------------
% 2.70/1.56 % (17036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.56 % (17036)Termination reason: Unknown
% 2.70/1.56 % (17036)Termination phase: Saturation
% 2.70/1.56
% 2.70/1.56 % (17036)Memory used [KB]: 7291
% 2.70/1.56 % (17036)Time elapsed: 0.100 s
% 2.70/1.56 % (17036)Instructions burned: 277 (million)
% 2.70/1.56 % (17036)------------------------------
% 2.70/1.56 % (17036)------------------------------
% 2.70/1.57 % (17060)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16703 for (2998ds/879Mi)
% 2.70/1.57 % (17059)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_16703 for (2998ds/19Mi)
% 2.70/1.58 % (17059)Instruction limit reached!
% 2.70/1.58 % (17059)------------------------------
% 2.70/1.58 % (17059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.58 % (17059)Termination reason: Unknown
% 2.70/1.58 % (17059)Termination phase: shuffling
% 2.70/1.58
% 2.70/1.58 % (17059)Memory used [KB]: 1663
% 2.70/1.58 % (17059)Time elapsed: 0.009 s
% 2.70/1.58 % (17059)Instructions burned: 19 (million)
% 2.70/1.58 % (17059)------------------------------
% 2.70/1.58 % (17059)------------------------------
% 2.70/1.59 % (17061)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16703 for (2998ds/17Mi)
% 2.70/1.59 % (17061)Instruction limit reached!
% 2.70/1.59 % (17061)------------------------------
% 2.70/1.59 % (17061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.59 % (17061)Termination reason: Unknown
% 2.70/1.59 % (17061)Termination phase: shuffling
% 2.70/1.59
% 2.70/1.59 % (17061)Memory used [KB]: 1791
% 2.70/1.59 % (17061)Time elapsed: 0.008 s
% 2.70/1.59 % (17061)Instructions burned: 18 (million)
% 2.70/1.59 % (17061)------------------------------
% 2.70/1.59 % (17061)------------------------------
% 2.70/1.60 % (17062)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16703 for (2998ds/3Mi)
% 2.70/1.60 % (17062)Instruction limit reached!
% 2.70/1.60 % (17062)------------------------------
% 2.70/1.60 % (17062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.60 % (17062)Termination reason: Unknown
% 2.70/1.60 % (17062)Termination phase: shuffling
% 2.70/1.60
% 2.70/1.60 % (17062)Memory used [KB]: 1407
% 2.70/1.60 % (17062)Time elapsed: 0.003 s
% 2.70/1.60 % (17062)Instructions burned: 3 (million)
% 2.70/1.60 % (17062)------------------------------
% 2.70/1.60 % (17062)------------------------------
% 2.70/1.61 % (17063)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16703 for (2998ds/30Mi)
% 2.70/1.62 % (17060)First to succeed.
% 2.70/1.62 % (17060)Refutation found. Thanks to Tanya!
% 2.70/1.62 % SZS status Theorem for DTF2THF_16703
% 2.70/1.62 % SZS output start Proof for DTF2THF_16703
% 2.70/1.62 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.70/1.62 thf(type_def_7, type, set: ($tType) > $tType).
% 2.70/1.62 thf(type_def_8, type, list: ($tType) > $tType).
% 2.70/1.62 thf(type_def_9, type, option: ($tType) > $tType).
% 2.70/1.62 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 2.70/1.62 thf(type_def_11, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 2.70/1.62 thf(type_def_12, type, rBT_Im1923302023_color: $tType).
% 2.70/1.62 thf(type_def_13, type, a: $tType).
% 2.70/1.62 thf(type_def_14, type, b: $tType).
% 2.70/1.62 thf(func_def_0, type, rBT_Im1923302023_color: $tType).
% 2.70/1.62 thf(func_def_1, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 2.70/1.62 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 2.70/1.62 thf(func_def_3, type, option: ($tType) > $tType).
% 2.70/1.62 thf(func_def_4, type, list: ($tType) > $tType).
% 2.70/1.62 thf(func_def_5, type, set: ($tType) > $tType).
% 2.70/1.62 thf(func_def_6, type, itself: ($tType) > $tType).
% 2.70/1.62 thf(func_def_7, type, b: $tType).
% 2.70/1.62 thf(func_def_8, type, a: $tType).
% 2.70/1.62 thf(func_def_9, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.70/1.62 thf(func_def_10, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.70/1.62 thf(func_def_11, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.70/1.62 thf(func_def_12, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.70/1.62 thf(func_def_13, type, inj_on: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > $o)).
% 2.70/1.62 thf(func_def_14, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 2.70/1.62 thf(func_def_15, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_16, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 2.70/1.62 thf(func_def_17, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_18, type, distinct: !>[X0: $tType]:(list @ X0 > $o)).
% 2.70/1.62 thf(func_def_19, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_20, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 2.70/1.62 thf(func_def_21, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_22, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.70/1.62 thf(func_def_23, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 2.70/1.62 thf(func_def_24, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 2.70/1.62 thf(func_def_25, type, lexordp: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 2.70/1.62 thf(func_def_26, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 2.70/1.62 thf(func_def_27, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.70/1.62 thf(func_def_28, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_29, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.70/1.62 thf(func_def_30, type, union: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_31, type, dom: !>[X0: $tType, X1: $tType]:((X0 > option @ X1) > set @ X0)).
% 2.70/1.62 thf(func_def_32, type, map_of: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > X0 > option @ X1)).
% 2.70/1.62 thf(func_def_33, type, none: !>[X0: $tType]:(option @ X0)).
% 2.70/1.62 thf(func_def_34, type, some: !>[X0: $tType]:(X0 > option @ X0)).
% 2.70/1.62 thf(func_def_35, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.70/1.62 thf(func_def_36, type, strict_mono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 2.70/1.62 thf(func_def_37, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.70/1.62 thf(func_def_38, type, rBT_Im954575269ntries: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > list @ product_prod @ X0 @ X1)).
% 2.70/1.62 thf(func_def_39, type, rBT_Im380146495e_keys: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > list @ X0)).
% 2.70/1.62 thf(func_def_40, type, rBT_Im1259024060reater: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.70/1.62 thf(func_def_41, type, rBT_Im2075124343t_less: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.70/1.62 thf(func_def_42, type, rBT_Im35466040lookup: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > X0 > option @ X1)).
% 2.70/1.62 thf(func_def_43, type, rBT_Im759614907sorted: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.70/1.62 thf(func_def_44, type, rBT_Im1332541288reater: !>[X0: $tType, X1: $tType]:(X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.70/1.62 thf(func_def_45, type, rBT_Im903026891t_less: !>[X0: $tType, X1: $tType]:(X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.70/1.62 thf(func_def_46, type, rBT_Im1183586831sorted: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.70/1.62 thf(func_def_47, type, rBT_Im480247531Branch: !>[X0: $tType, X1: $tType]:(rBT_Im1923302023_color > rBT_Im246033960le_rbt @ X0 @ X1 > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.70/1.62 thf(func_def_48, type, rBT_Im418718756_Empty: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.70/1.62 thf(func_def_49, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.70/1.62 thf(func_def_50, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 2.70/1.62 thf(func_def_51, type, set_greaterThan: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.70/1.62 thf(func_def_52, type, set_lessThan: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.70/1.62 thf(func_def_53, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.70/1.62 thf(func_def_54, type, c: rBT_Im1923302023_color).
% 2.70/1.62 thf(func_def_55, type, k: a).
% 2.70/1.62 thf(func_def_56, type, less: a > a > $o).
% 2.70/1.62 thf(func_def_57, type, t1: rBT_Im246033960le_rbt @ a @ b).
% 2.70/1.62 thf(func_def_58, type, t2: rBT_Im246033960le_rbt @ a @ b).
% 2.70/1.62 thf(func_def_59, type, v: b).
% 2.70/1.62 thf(func_def_78, type, sK0: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_79, type, sK1: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_80, type, sK2: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_81, type, sK3: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_82, type, sK4: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_83, type, sK5: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_84, type, sK6: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_85, type, sK7: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_86, type, sK8: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_87, type, sK9: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_88, type, sK10: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_89, type, sK11: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_90, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > list @ X0) > (X1 > list @ X0) > list @ X1 > X1)).
% 2.70/1.62 thf(func_def_91, type, sK13: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_92, type, sK14: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_93, type, sK15: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_94, type, sK16: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_95, type, sK17: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_96, type, sK18: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_97, type, sK19: a).
% 2.70/1.62 thf(func_def_98, type, sK20: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 2.70/1.62 thf(func_def_99, type, sK21: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_100, type, sK22: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_101, type, sK23: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_102, type, sK24: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_103, type, sK25: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.70/1.62 thf(func_def_104, type, sK26: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_105, type, sK27: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 2.70/1.62 thf(func_def_106, type, sK28: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_107, type, sK29: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_108, type, sK30: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_109, type, sK31: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_111, type, sK33: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_112, type, sK34: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_113, type, sK35: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_114, type, sK36: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_115, type, sK37: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 2.70/1.62 thf(func_def_116, type, sK38: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_117, type, sK39: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 2.70/1.62 thf(func_def_118, type, sK40: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_119, type, sK41: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_120, type, sK42: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_121, type, sK43: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_122, type, sK44: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_123, type, sK45: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_124, type, sK46: !>[X0: $tType]:(list @ X0 > X0)).
% 2.70/1.62 thf(func_def_125, type, sK47: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.70/1.62 thf(func_def_126, type, sK48: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_127, type, sK49: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 2.70/1.62 thf(func_def_128, type, sK50: !>[X0: $tType]:(list @ X0 > (X0 > $o) > list @ X0)).
% 2.70/1.62 thf(func_def_129, type, sK51: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 2.70/1.62 thf(func_def_130, type, sK52: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_131, type, sK53: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 2.70/1.62 thf(func_def_132, type, ph54: !>[X0: $tType]:(X0)).
% 2.70/1.62 thf(f1178,plain,(
% 2.70/1.62 $false),
% 2.70/1.62 inference(subsumption_resolution,[status(thm)],[f1177,f881])).
% 2.70/1.62 thf(f881,plain,(
% 2.70/1.62 ((less @ k @ sK19) != $true)),
% 2.70/1.62 inference(cnf_transformation,[status(thm)],[f809])).
% 2.70/1.62 thf(f809,plain,(
% 2.70/1.62 ((member @ a @ sK19 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) = $true) & ((less @ k @ sK19) != $true)),
% 2.70/1.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f777,f808])).
% 2.70/1.62 thf(f808,plain,(
% 2.70/1.62 ? [X0 : a] : (($true = (member @ a @ X0 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2)))) & ($true != (less @ k @ X0))) => (((member @ a @ sK19 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) = $true) & ((less @ k @ sK19) != $true))),
% 2.70/1.62 introduced(definition,[],[choice_axiom])).
% 2.70/1.62 thf(f777,plain,(
% 2.70/1.62 ? [X0 : a] : (($true = (member @ a @ X0 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2)))) & ($true != (less @ k @ X0)))),
% 2.70/1.62 inference(ennf_transformation,[status(thm)],[f394])).
% 2.70/1.62 thf(f394,plain,(
% 2.70/1.62 ~! [X0 : a] : (($true = (member @ a @ X0 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2)))) => ($true = (less @ k @ X0)))),
% 2.70/1.62 inference(fool_elimination,[status(thm)],[f393])).
% 2.70/1.62 thf(f393,plain,(
% 2.70/1.62 ~! [X0 : a] : ((member @ a @ X0 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) => (less @ k @ X0))),
% 2.70/1.62 inference(rectify,[status(thm)],[f267])).
% 2.70/1.62 thf(f267,negated_conjecture,(
% 2.70/1.62 ~! [X20 : a] : ((member @ a @ X20 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) => (less @ k @ X20))),
% 2.70/1.62 inference(negated_conjecture,[status(cth)],[f266])).
% 2.70/1.62 thf(f266,conjecture,(
% 2.70/1.62 ! [X20 : a] : ((member @ a @ X20 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) => (less @ k @ X20))),
% 2.70/1.62 file('/export/starexec/sandbox/tmp/tmp.oBDkFFmvot/DTF2THF_16703.p',conj_0)).
% 2.70/1.62 thf(f1177,plain,(
% 2.70/1.62 ((less @ k @ sK19) = $true)),
% 2.70/1.62 inference(trivial_inequality_removal,[status(thm)],[f1175])).
% 2.70/1.62 thf(f1175,plain,(
% 2.70/1.62 ($false = $true) | ((less @ k @ sK19) = $true)),
% 2.70/1.62 inference(superposition,[status(thm)],[f882,f965])).
% 2.70/1.62 thf(f965,plain,(
% 2.70/1.62 ( ! [X1 : a] : (($false = (member @ a @ X1 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2)))) | ($true = (less @ k @ X1))) )),
% 2.70/1.62 inference(binary_proxy_clausification,[status(thm)],[f964])).
% 2.70/1.62 thf(f964,plain,(
% 2.70/1.62 ( ! [X1 : a] : (($true = ((member @ a @ X1 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) => (less @ k @ X1)))) )),
% 2.70/1.62 inference(beta_eta_normalization,[status(thm)],[f963])).
% 2.70/1.62 thf(f963,plain,(
% 2.70/1.62 ( ! [X1 : a] : ((((^[Y0 : a]: ((member @ a @ Y0 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) => (less @ k @ Y0))) @ X1) = $true)) )),
% 2.70/1.62 inference(pi_clausification,[status(thm)],[f962])).
% 2.70/1.62 thf(f962,plain,(
% 2.70/1.62 ((!! @ a @ (^[Y0 : a]: ((member @ a @ Y0 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) => (less @ k @ Y0)))) = $true)),
% 2.70/1.62 inference(beta_eta_normalization,[status(thm)],[f927])).
% 2.70/1.62 thf(f927,plain,(
% 2.70/1.62 ($true = ((^[Y0 : a > a > $o]: ((^[Y1 : a]: ((^[Y2 : rBT_Im246033960le_rbt @ a @ b]: (!! @ a @ (^[Y3 : a]: ((member @ a @ Y3 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ Y2))) => (Y0 @ Y1 @ Y3))))))))) @ less @ k @ t2))),
% 2.70/1.62 inference(definition_unfolding,[status(thm)],[f860,f847])).
% 2.70/1.62 thf(f847,plain,(
% 2.70/1.62 ( ! [X1 : $tType,X0 : $tType] : (((^[Y0 : X1 > X1 > $o]: ((^[Y1 : X1]: ((^[Y2 : rBT_Im246033960le_rbt @ X1 @ X0]: (!! @ X1 @ (^[Y3 : X1]: ((member @ X1 @ Y3 @ (set2 @ X1 @ (rBT_Im380146495e_keys @ X1 @ X0 @ Y2))) => (Y0 @ Y1 @ Y3))))))))) = rBT_Im1259024060reater @ X1 @ X0)) )),
% 2.70/1.62 inference(cnf_transformation,[status(thm)],[f644])).
% 2.70/1.62 thf(f644,plain,(
% 2.70/1.62 ! [X0 : $tType,X1 : $tType] : ((^[Y0 : X1 > X1 > $o]: ((^[Y1 : X1]: ((^[Y2 : rBT_Im246033960le_rbt @ X1 @ X0]: (!! @ X1 @ (^[Y3 : X1]: ((member @ X1 @ Y3 @ (set2 @ X1 @ (rBT_Im380146495e_keys @ X1 @ X0 @ Y2))) => (Y0 @ Y1 @ Y3))))))))) = rBT_Im1259024060reater @ X1 @ X0)),
% 2.70/1.62 inference(fool_elimination,[status(thm)],[f643])).
% 2.70/1.62 thf(f643,plain,(
% 2.70/1.62 ! [X0 : $tType,X1 : $tType] : ((^[X2 : X1 > X1 > $o, X3 : X1, X4 : rBT_Im246033960le_rbt @ X1 @ X0] : (! [X5 : X1] : ((member @ X1 @ X5 @ (set2 @ X1 @ (rBT_Im380146495e_keys @ X1 @ X0 @ X4))) => (X2 @ X3 @ X5)))) = rBT_Im1259024060reater @ X1 @ X0)),
% 2.70/1.62 inference(rectify,[status(thm)],[f31])).
% 2.70/1.62 thf(f31,axiom,(
% 2.70/1.62 ! [X1 : $tType,X0 : $tType] : ((^[X14 : X0 > X0 > $o, X15 : X0, X16 : rBT_Im246033960le_rbt @ X0 @ X1] : (! [X11 : X0] : ((member @ X0 @ X11 @ (set2 @ X0 @ (rBT_Im380146495e_keys @ X0 @ X1 @ X16))) => (X14 @ X15 @ X11)))) = rBT_Im1259024060reater @ X0 @ X1)),
% 2.70/1.62 file('/export/starexec/sandbox/tmp/tmp.oBDkFFmvot/DTF2THF_16703.p',fact_30_ord_Orbt__greater__prop)).
% 2.70/1.62 thf(f860,plain,(
% 2.70/1.62 ((rBT_Im1259024060reater @ a @ b @ less @ k @ t2) = $true)),
% 2.70/1.62 inference(cnf_transformation,[status(thm)],[f608])).
% 2.70/1.62 thf(f608,plain,(
% 2.70/1.62 ((rBT_Im1259024060reater @ a @ b @ less @ k @ t2) = $true)),
% 2.70/1.62 inference(fool_elimination,[status(thm)],[f607])).
% 2.70/1.62 thf(f607,plain,(
% 2.70/1.62 (rBT_Im1259024060reater @ a @ b @ less @ k @ t2)),
% 2.70/1.62 inference(rectify,[status(thm)],[f28])).
% 2.70/1.62 thf(f28,axiom,(
% 2.70/1.62 (rBT_Im1259024060reater @ a @ b @ less @ k @ t2)),
% 2.70/1.62 file('/export/starexec/sandbox/tmp/tmp.oBDkFFmvot/DTF2THF_16703.p',fact_27__092_060open_062k_A_092_060guillemotleft_062_124_At2_092_060close_062)).
% 2.70/1.62 thf(f882,plain,(
% 2.70/1.62 ((member @ a @ sK19 @ (set2 @ a @ (rBT_Im380146495e_keys @ a @ b @ t2))) = $true)),
% 2.70/1.62 inference(cnf_transformation,[status(thm)],[f809])).
% 2.70/1.62 % SZS output end Proof for DTF2THF_16703
% 2.70/1.62 % (17060)------------------------------
% 2.70/1.62 % (17060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.70/1.62 % (17060)Termination reason: Refutation
% 2.70/1.62
% 2.70/1.62 % (17060)Memory used [KB]: 7036
% 2.70/1.62 % (17060)Time elapsed: 0.048 s
% 2.70/1.62 % (17060)Instructions burned: 147 (million)
% 2.70/1.62 % (17060)------------------------------
% 2.70/1.62 % (17060)------------------------------
% 2.70/1.62 % (17030)Success in time 0.171 s
%------------------------------------------------------------------------------