%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT234^1 : 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 08:45:14 AM UTC 2026
% Result : Theorem 2.97s 1.67s
% Output : Refutation 2.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT234^1 : 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 06:12:55 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : DAT234^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Data Structures
% 0.19/0.45 % Problem : Red-black trees 740
% 0.19/0.45 % Version : [Bla16] axioms : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.19/0.45 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bla16]
% 0.19/0.45 % Names : rbt_impl__740.p [Bla16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.33 v9.1.0, 0.00 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 319 ( 138 unt; 57 typ; 0 def)
% 0.19/0.45 % Number of atoms : 757 ( 232 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 13 ( 2 avg)
% 0.19/0.45 % Number of connectives : 7045 ( 95 ~; 13 |; 56 &;6606 @)
% 0.19/0.45 % ( 0 <=>; 275 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 30 ( 10 avg)
% 0.19/0.45 % Number of types : 4 ( 3 usr)
% 0.19/0.45 % Number of type conns : 341 ( 341 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 55 ( 54 usr; 13 con; 0-7 aty)
% 0.19/0.45 % Number of variables : 1699 ( 23 ^;1599 !; 24 ?;1699 :)
% 0.19/0.45 % ( 53 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.45 % 2016-07-13 14:42:42.561
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 %----Could-be-implicit typings (9)
% 0.19/0.45 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 0.19/0.45 rBT_Im1923302023_color: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 0.19/0.45 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Product__Type_Oprod,type,
% 0.19/0.45 product_prod: $tType > $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Option_Ooption,type,
% 0.19/0.45 option: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_List_Olist,type,
% 0.19/0.45 list: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Set_Oset,type,
% 0.19/0.45 set: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_itself,type,
% 0.19/0.45 itself: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_b,type,
% 0.19/0.45 b: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_a,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 %----Explicit typings (48)
% 0.19/0.45 thf(sy_cl_HOL_Otype,type,
% 0.19/0.45 type:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.45 ord:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.45 order:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Olist_OCons,type,
% 0.19/0.45 cons:
% 0.19/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Olist_ONil,type,
% 0.19/0.45 nil:
% 0.19/0.45 !>[A: $tType] : ( list @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Olist_Oset,type,
% 0.19/0.45 set2:
% 0.19/0.45 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Oord_Olexordp,type,
% 0.19/0.45 lexordp:
% 0.19/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.19/0.45 lexordp_eq:
% 0.19/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Map_Omap__of,type,
% 0.19/0.45 map_of:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( list @ ( product_prod @ A @ B ) ) > A > ( option @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Option_Ooption_ONone,type,
% 0.19/0.45 none:
% 0.19/0.45 !>[A: $tType] : ( option @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.45 ord_less:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oorder_Ostrict__mono,type,
% 0.19/0.45 strict_mono:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Pure_Otype,type,
% 0.19/0.45 type2:
% 0.19/0.45 !>[A: $tType] : ( itself @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance,type,
% 0.19/0.45 rBT_Im1648453169alance:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance__left,type,
% 0.19/0.45 rBT_Im1278323832e_left:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance__right,type,
% 0.19/0.45 rBT_Im1053358987_right:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 0.19/0.45 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 0.19/0.45 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocombine,type,
% 0.19/0.45 rBT_Im1591839508ombine:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries,type,
% 0.19/0.45 rBT_Im954575269ntries:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Ois__rbt,type,
% 0.19/0.45 rBT_Im862805236is_rbt:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 0.19/0.45 rBT_Im1259024060reater:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__ins,type,
% 0.19/0.45 rBT_Im1756508336bt_ins:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert,type,
% 0.19/0.45 rBT_Im852463031insert:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert__with,type,
% 0.19/0.45 rBT_Im241132701t_with:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert__with__key,type,
% 0.19/0.45 rBT_Im627674146th_key:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 0.19/0.45 rBT_Im2075124343t_less:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup,type,
% 0.19/0.45 rBT_Im35466040lookup:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > A > ( option @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 0.19/0.45 rBT_Im759614907sorted:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Opaint,type,
% 0.19/0.45 rBT_Im945281971_paint:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 0.19/0.45 rBT_Im480247531Branch:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 0.19/0.45 rBT_Im418718756_Empty:
% 0.19/0.45 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set_OCollect,type,
% 0.19/0.45 collect:
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set__Interval_Oord_OgreaterThan,type,
% 0.19/0.45 set_greaterThan:
% 0.19/0.45 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set__Interval_Oord_OlessThan,type,
% 0.19/0.45 set_lessThan:
% 0.19/0.45 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member,type,
% 0.19/0.45 member:
% 0.19/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_a____,type,
% 0.19/0.45 a2: rBT_Im246033960le_rbt @ a @ b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_b____,type,
% 0.19/0.45 b2: rBT_Im246033960le_rbt @ a @ b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_c____,type,
% 0.19/0.45 c: rBT_Im246033960le_rbt @ a @ b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_d____,type,
% 0.19/0.45 d: rBT_Im246033960le_rbt @ a @ b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_k,type,
% 0.19/0.45 k: a ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_l,type,
% 0.19/0.45 l: rBT_Im246033960le_rbt @ a @ b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_less,type,
% 0.19/0.45 less: a > a > $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_r,type,
% 0.19/0.45 r: rBT_Im246033960le_rbt @ a @ b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_v____,type,
% 0.19/0.45 v: b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_w____,type,
% 0.19/0.45 w: b ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_x____,type,
% 0.19/0.45 x: a ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_y____,type,
% 0.19/0.45 y: a ).
% 0.19/0.45
% 0.19/0.45 %----Relevant facts (255)
% 0.19/0.45 thf(fact_0_local_Oantisym__conv3,axiom,
% 0.19/0.45 ! [Y: a,X: a] :
% 0.19/0.45 ( ~ ( less @ Y @ X )
% 0.19/0.45 => ( ( ~ ( less @ X @ Y ) )
% 0.19/0.45 = ( X = Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.antisym_conv3
% 0.19/0.45 thf(fact_1_local_Odual__order_Oasym,axiom,
% 0.19/0.45 ! [B2: a,A2: a] :
% 0.19/0.45 ( ( less @ B2 @ A2 )
% 0.19/0.45 => ~ ( less @ A2 @ B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.dual_order.asym
% 0.19/0.45 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 0.19/0.45 ! [B2: a,A2: a] :
% 0.19/0.45 ( ( less @ B2 @ A2 )
% 0.19/0.45 => ( A2 != B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.dual_order.strict_implies_not_eq
% 0.19/0.45 thf(fact_3_local_Odual__order_Ostrict__trans,axiom,
% 0.19/0.45 ! [B2: a,A2: a,C: a] :
% 0.19/0.45 ( ( less @ B2 @ A2 )
% 0.19/0.45 => ( ( less @ C @ B2 )
% 0.19/0.45 => ( less @ C @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.dual_order.strict_trans
% 0.19/0.45 thf(fact_4_local_Oless__asym,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ~ ( less @ Y @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_asym
% 0.19/0.45 thf(fact_5_local_Oless__asym_H,axiom,
% 0.19/0.45 ! [A2: a,B2: a] :
% 0.19/0.45 ( ( less @ A2 @ B2 )
% 0.19/0.45 => ~ ( less @ B2 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_asym'
% 0.19/0.45 thf(fact_6_local_Oless__imp__neq,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ( X != Y ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_imp_neq
% 0.19/0.45 thf(fact_7_local_Oless__imp__not__eq,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ( X != Y ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_imp_not_eq
% 0.19/0.45 thf(fact_8_local_Oless__imp__not__eq2,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ( Y != X ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_imp_not_eq2
% 0.19/0.45 thf(fact_9_local_Oless__imp__not__less,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ~ ( less @ Y @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_imp_not_less
% 0.19/0.45 thf(fact_10_local_Oless__imp__triv,axiom,
% 0.19/0.45 ! [X: a,Y: a,P: $o] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ( ( less @ Y @ X )
% 0.19/0.45 => P ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_imp_triv
% 0.19/0.45 thf(fact_11_local_Oless__irrefl,axiom,
% 0.19/0.45 ! [X: a] :
% 0.19/0.45 ~ ( less @ X @ X ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_irrefl
% 0.19/0.45 thf(fact_12_local_Oless__linear,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 | ( X = Y )
% 0.19/0.45 | ( less @ Y @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_linear
% 0.19/0.45 thf(fact_13_local_Oless__not__sym,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ~ ( less @ Y @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_not_sym
% 0.19/0.45 thf(fact_14_local_Oless__trans,axiom,
% 0.19/0.45 ! [X: a,Y: a,Z: a] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ( ( less @ Y @ Z )
% 0.19/0.45 => ( less @ X @ Z ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.less_trans
% 0.19/0.45 thf(fact_15_local_Olinorder__cases,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ~ ( less @ X @ Y )
% 0.19/0.45 => ( ( X != Y )
% 0.19/0.45 => ( less @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.linorder_cases
% 0.19/0.45 thf(fact_16_local_OneqE,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( X != Y )
% 0.19/0.45 => ( ~ ( less @ X @ Y )
% 0.19/0.45 => ( less @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.neqE
% 0.19/0.45 thf(fact_17_local_Oneq__iff,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( X != Y )
% 0.19/0.45 = ( ( less @ X @ Y )
% 0.19/0.45 | ( less @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.neq_iff
% 0.19/0.45 thf(fact_18_local_Onot__less__iff__gr__or__eq,axiom,
% 0.19/0.45 ! [X: a,Y: a] :
% 0.19/0.45 ( ( ~ ( less @ X @ Y ) )
% 0.19/0.45 = ( ( less @ Y @ X )
% 0.19/0.45 | ( X = Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.not_less_iff_gr_or_eq
% 0.19/0.45 thf(fact_19_local_Oord__eq__less__trans,axiom,
% 0.19/0.45 ! [A2: a,B2: a,C: a] :
% 0.19/0.45 ( ( A2 = B2 )
% 0.19/0.45 => ( ( less @ B2 @ C )
% 0.19/0.45 => ( less @ A2 @ C ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.ord_eq_less_trans
% 0.19/0.45 thf(fact_20_local_Oord__less__eq__trans,axiom,
% 0.19/0.45 ! [A2: a,B2: a,C: a] :
% 0.19/0.45 ( ( less @ A2 @ B2 )
% 0.19/0.45 => ( ( B2 = C )
% 0.19/0.45 => ( less @ A2 @ C ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.ord_less_eq_trans
% 0.19/0.45 thf(fact_21_local_Oorder_Oasym,axiom,
% 0.19/0.45 ! [A2: a,B2: a] :
% 0.19/0.45 ( ( less @ A2 @ B2 )
% 0.19/0.45 => ~ ( less @ B2 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.order.asym
% 0.19/0.45 thf(fact_22_local_Oorder_Oirrefl,axiom,
% 0.19/0.45 ! [A2: a] :
% 0.19/0.45 ~ ( less @ A2 @ A2 ) ).
% 0.19/0.45
% 0.19/0.45 % local.order.irrefl
% 0.19/0.45 thf(fact_23_local_Oorder_Ostrict__implies__not__eq,axiom,
% 0.19/0.45 ! [A2: a,B2: a] :
% 0.19/0.45 ( ( less @ A2 @ B2 )
% 0.19/0.45 => ( A2 != B2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.order.strict_implies_not_eq
% 0.19/0.45 thf(fact_24_local_Oorder_Ostrict__trans,axiom,
% 0.19/0.45 ! [A2: a,B2: a,C: a] :
% 0.19/0.45 ( ( less @ A2 @ B2 )
% 0.19/0.45 => ( ( less @ B2 @ C )
% 0.19/0.45 => ( less @ A2 @ C ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.order.strict_trans
% 0.19/0.45 thf(fact_25_local_Orbt__greater__trans,axiom,
% 0.19/0.45 ! [C2: $tType,X: a,Y: a,T: rBT_Im246033960le_rbt @ a @ C2] :
% 0.19/0.45 ( ( less @ X @ Y )
% 0.19/0.45 => ( ( rBT_Im1259024060reater @ a @ C2 @ less @ Y @ T )
% 0.19/0.45 => ( rBT_Im1259024060reater @ a @ C2 @ less @ X @ T ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.rbt_greater_trans
% 0.19/0.45 thf(fact_26__092_060open_062x_A_060_Ay_A_092_060and_062_Ay_A_092_060guillemotleft_062_124_Ad_092_060close_062,axiom,
% 0.19/0.45 ( ( less @ x @ y )
% 0.19/0.45 & ( rBT_Im1259024060reater @ a @ b @ less @ y @ d ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>x < y \<and> y \<guillemotleft>| d\<close>
% 0.19/0.45 thf(fact_27_local_Ostrict__mono__eq,axiom,
% 0.19/0.45 ! [B: $tType] :
% 0.19/0.45 ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.45 ( ( strict_mono @ a @ B @ less @ F )
% 0.19/0.45 => ( ( ( F @ X )
% 0.19/0.45 = ( F @ Y ) )
% 0.19/0.45 = ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.strict_mono_eq
% 0.19/0.45 thf(fact_28_assms_I4_J,axiom,
% 0.19/0.45 rBT_Im1259024060reater @ a @ b @ less @ k @ r ).
% 0.19/0.45
% 0.19/0.45 % assms(4)
% 0.19/0.45 thf(fact_29_combine__rbt__greater,axiom,
% 0.19/0.45 ! [B: $tType,K: a,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.45 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ L )
% 0.19/0.45 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.19/0.45 => ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im1591839508ombine @ a @ B @ L @ R ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % combine_rbt_greater
% 0.19/0.45 thf(fact_30__092_060open_062x_A_092_060guillemotleft_062_124_Ac_092_060close_062,axiom,
% 0.19/0.45 rBT_Im1259024060reater @ a @ b @ less @ x @ c ).
% 0.19/0.45
% 0.19/0.45 % \<open>x \<guillemotleft>| c\<close>
% 0.19/0.45 thf(fact_31_local_Obalance__right__rbt__greater,axiom,
% 0.19/0.45 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 0.19/0.45 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ A2 )
% 0.19/0.45 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ B2 )
% 0.19/0.45 => ( ( less @ K @ X )
% 0.19/0.45 => ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im1053358987_right @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.balance_right_rbt_greater
% 0.19/0.45 thf(fact_32_local_Obalance__left__rbt__greater,axiom,
% 0.19/0.45 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 0.19/0.45 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ A2 )
% 0.19/0.45 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ B2 )
% 0.19/0.45 => ( ( less @ K @ X )
% 0.19/0.45 => ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im1278323832e_left @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.balance_left_rbt_greater
% 0.19/0.45 thf(fact_33_assms_I2_J,axiom,
% 0.19/0.45 rBT_Im759614907sorted @ a @ b @ less @ r ).
% 0.19/0.45
% 0.19/0.45 % assms(2)
% 0.19/0.45 thf(fact_34_assms_I1_J,axiom,
% 0.19/0.45 rBT_Im759614907sorted @ a @ b @ less @ l ).
% 0.19/0.45
% 0.19/0.45 % assms(1)
% 0.19/0.45 thf(fact_35__092_060open_062x_A_060_Ak_A_092_060and_062_Ak_A_092_060guillemotleft_062_124_Ac_092_060close_062,axiom,
% 0.19/0.45 ( ( less @ x @ k )
% 0.19/0.45 & ( rBT_Im1259024060reater @ a @ b @ less @ k @ c ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>x < k \<and> k \<guillemotleft>| c\<close>
% 0.19/0.45 thf(fact_36_local_Orbt__less__trans,axiom,
% 0.19/0.45 ! [C2: $tType,X: a,T: rBT_Im246033960le_rbt @ a @ C2,Y: a] :
% 0.19/0.45 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ X @ T )
% 0.19/0.45 => ( ( less @ X @ Y )
% 0.19/0.45 => ( rBT_Im2075124343t_less @ a @ C2 @ less @ Y @ T ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.rbt_less_trans
% 0.19/0.45 thf(fact_37_local_Olexordp__eq__antisym,axiom,
% 0.19/0.45 ! [Xs: list @ a,Ys: list @ a] :
% 0.19/0.45 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.19/0.45 => ( ( lexordp_eq @ a @ less @ Ys @ Xs )
% 0.19/0.45 => ( Xs = Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.lexordp_eq_antisym
% 0.19/0.45 thf(fact_38_local_Olexordp__eq__linear,axiom,
% 0.19/0.45 ! [Xs: list @ a,Ys: list @ a] :
% 0.19/0.45 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.19/0.45 | ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.lexordp_eq_linear
% 0.19/0.45 thf(fact_39_local_Olexordp__eq__refl,axiom,
% 0.19/0.45 ! [Xs: list @ a] : ( lexordp_eq @ a @ less @ Xs @ Xs ) ).
% 0.19/0.45
% 0.19/0.45 % local.lexordp_eq_refl
% 0.19/0.45 thf(fact_40_local_Olexordp__eq__trans,axiom,
% 0.19/0.45 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 0.19/0.45 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.19/0.45 => ( ( lexordp_eq @ a @ less @ Ys @ Zs )
% 0.19/0.45 => ( lexordp_eq @ a @ less @ Xs @ Zs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.lexordp_eq_trans
% 0.19/0.45 thf(fact_41_assms_I3_J,axiom,
% 0.19/0.45 rBT_Im2075124343t_less @ a @ b @ less @ k @ l ).
% 0.19/0.45
% 0.19/0.45 % assms(3)
% 0.19/0.45 thf(fact_42_combine__rbt__less,axiom,
% 0.19/0.45 ! [B: $tType,K: a,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.45 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.19/0.45 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ R )
% 0.19/0.45 => ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im1591839508ombine @ a @ B @ L @ R ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % combine_rbt_less
% 0.19/0.45 thf(fact_43_local_Obalance__left__rbt__less,axiom,
% 0.19/0.45 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 0.19/0.45 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ A2 )
% 0.19/0.45 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ B2 )
% 0.19/0.45 => ( ( less @ X @ K )
% 0.19/0.45 => ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im1278323832e_left @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.balance_left_rbt_less
% 0.19/0.45 thf(fact_44_local_Obalance__right__rbt__less,axiom,
% 0.19/0.45 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 0.19/0.45 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ A2 )
% 0.19/0.45 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ B2 )
% 0.19/0.45 => ( ( less @ X @ K )
% 0.19/0.45 => ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im1053358987_right @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.balance_right_rbt_less
% 0.19/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.19/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.19/0.45 = ( P @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % mem_Collect_eq
% 0.19/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.45 ! [A: $tType,A3: set @ A] :
% 0.19/0.45 ( ( collect @ A
% 0.19/0.45 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.19/0.45 = A3 ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mem_eq
% 0.19/0.45 thf(fact_47_Collect__cong,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( P @ X3 )
% 0.19/0.45 = ( Q @ X3 ) )
% 0.19/0.45 => ( ( collect @ A @ P )
% 0.19/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_cong
% 0.19/0.45 thf(fact_48_ext,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( F @ X3 )
% 0.19/0.45 = ( G @ X3 ) )
% 0.19/0.45 => ( F = G ) ) ).
% 0.19/0.45
% 0.19/0.45 % ext
% 0.19/0.45 thf(fact_49_local_Obalance__left__rbt__sorted,axiom,
% 0.19/0.45 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 0.19/0.45 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.19/0.45 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 0.19/0.45 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.19/0.45 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.19/0.45 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1278323832e_left @ a @ B @ L @ K @ V @ R ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.balance_left_rbt_sorted
% 0.19/0.45 thf(fact_50_local_Obalance__right__rbt__sorted,axiom,
% 0.19/0.45 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 0.19/0.45 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.19/0.45 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 0.19/0.45 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.19/0.45 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.19/0.45 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1053358987_right @ a @ B @ L @ K @ V @ R ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.balance_right_rbt_sorted
% 0.19/0.45 thf(fact_51_local_Orbt__insertw__rbt__sorted,axiom,
% 0.19/0.45 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: B > B > B,K: a,V: B] :
% 0.19/0.45 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.19/0.45 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im241132701t_with @ a @ B @ less @ F @ K @ V @ T ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.rbt_insertw_rbt_sorted
% 0.19/0.45 thf(fact_52_local_Orbt__insert__rbt__sorted,axiom,
% 0.19/0.45 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 0.19/0.45 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.19/0.45 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im852463031insert @ a @ B @ less @ K @ V @ T ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % local.rbt_insert_rbt_sorted
% 0.19/0.45 thf(fact_53_local_Orbt__insertwk__rbt__sorted,axiom,
% 0.19/0.45 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: a > B > B > B,K: a,X: B] :
% 0.19/0.45 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.19/0.45 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im627674146th_key @ a @ B @ less @ F @ K @ X @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insertwk_rbt_sorted
% 0.19/0.46 thf(fact_54_local_Ois__rbt__rbt__sorted,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 0.19/0.46 => ( rBT_Im759614907sorted @ a @ B @ less @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.is_rbt_rbt_sorted
% 0.19/0.46 thf(fact_55__C2_C,axiom,
% 0.19/0.46 rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ).
% 0.19/0.46
% 0.19/0.46 % "2"
% 0.19/0.46 thf(fact_56__C3_C,axiom,
% 0.19/0.46 rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ).
% 0.19/0.46
% 0.19/0.46 % "3"
% 0.19/0.46 thf(fact_57__092_060open_062k_A_060_Ay_A_092_060and_062_Ab_A_124_092_060guillemotleft_062_Ak_092_060close_062,axiom,
% 0.19/0.46 ( ( less @ k @ y )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % \<open>k < y \<and> b |\<guillemotleft> k\<close>
% 0.19/0.46 thf(fact_58__092_060open_062b_A_124_092_060guillemotleft_062_Ay_092_060close_062,axiom,
% 0.19/0.46 rBT_Im2075124343t_less @ a @ b @ less @ y @ b2 ).
% 0.19/0.46
% 0.19/0.46 % \<open>b |\<guillemotleft> y\<close>
% 0.19/0.46 thf(fact_59_local_Opaint__rbt__sorted,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,C: rBT_Im1923302023_color] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.19/0.46 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.paint_rbt_sorted
% 0.19/0.46 thf(fact_60_local_Orbt__sorted_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,K: a,V: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ C @ L @ K @ V @ R ) )
% 0.19/0.46 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.19/0.46 & ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.19/0.46 & ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.19/0.46 & ( rBT_Im759614907sorted @ a @ B @ less @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_sorted.simps(2)
% 0.19/0.46 thf(fact_61_local_Obalance__rbt__sorted,axiom,
% 0.19/0.46 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.19/0.46 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 0.19/0.46 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.19/0.46 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.19/0.46 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1648453169alance @ a @ B @ L @ K @ V @ R ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.balance_rbt_sorted
% 0.19/0.46 thf(fact_62_local_Orbt__insertwk__is__rbt,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: a > B > B > B,K: a,X: B] :
% 0.19/0.46 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 0.19/0.46 => ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im627674146th_key @ a @ B @ less @ F @ K @ X @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insertwk_is_rbt
% 0.19/0.46 thf(fact_63_local_Orbt__insert__is__rbt,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 0.19/0.46 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 0.19/0.46 => ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im852463031insert @ a @ B @ less @ K @ V @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insert_is_rbt
% 0.19/0.46 thf(fact_64_local_Orbt__insertw__is__rbt,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: B > B > B,K: a,V: B] :
% 0.19/0.46 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 0.19/0.46 => ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im241132701t_with @ a @ B @ less @ F @ K @ V @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insertw_is_rbt
% 0.19/0.46 thf(fact_65_rbt_Oinject,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: 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] :
% 0.19/0.46 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 )
% 0.19/0.46 & ( X23 = Y23 )
% 0.19/0.46 & ( X24 = Y24 )
% 0.19/0.46 & ( X25 = Y25 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rbt.inject
% 0.19/0.46 thf(fact_66_local_Orbt__greater__simps_I2_J,axiom,
% 0.19/0.46 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.19/0.46 = ( ( less @ K @ Kt )
% 0.19/0.46 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Lt )
% 0.19/0.46 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_greater_simps(2)
% 0.19/0.46 thf(fact_67_local_Orbt__less__simps_I2_J,axiom,
% 0.19/0.46 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.19/0.46 = ( ( less @ Kt @ K )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Lt )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_less_simps(2)
% 0.19/0.46 thf(fact_68_local_Obalance__rbt__greater,axiom,
% 0.19/0.46 ! [B: $tType,V: a,A2: rBT_Im246033960le_rbt @ a @ B,K: a,X: B,B2: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ ( rBT_Im1648453169alance @ a @ B @ A2 @ K @ X @ B2 ) )
% 0.19/0.46 = ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ A2 )
% 0.19/0.46 & ( rBT_Im1259024060reater @ a @ B @ less @ V @ B2 )
% 0.19/0.46 & ( less @ V @ K ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.balance_rbt_greater
% 0.19/0.46 thf(fact_69_local_Obalance__rbt__less,axiom,
% 0.19/0.46 ! [B: $tType,V: a,A2: rBT_Im246033960le_rbt @ a @ B,K: a,X: B,B2: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ ( rBT_Im1648453169alance @ a @ B @ A2 @ K @ X @ B2 ) )
% 0.19/0.46 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ A2 )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ a @ B @ less @ V @ B2 )
% 0.19/0.46 & ( less @ K @ V ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.balance_rbt_less
% 0.19/0.46 thf(fact_70_local_Opaint__rbt__greater,axiom,
% 0.19/0.46 ! [B: $tType,V: a,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) )
% 0.19/0.46 = ( rBT_Im1259024060reater @ a @ B @ less @ V @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.paint_rbt_greater
% 0.19/0.46 thf(fact_71_local_Opaint__rbt__less,axiom,
% 0.19/0.46 ! [B: $tType,V: a,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) )
% 0.19/0.46 = ( rBT_Im2075124343t_less @ a @ B @ less @ V @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.paint_rbt_less
% 0.19/0.46 thf(fact_72_Empty,axiom,
% 0.19/0.46 ( ( rBT_Im1591839508ombine @ a @ b @ b2 @ c )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ a @ b ) ) ).
% 0.19/0.46
% 0.19/0.46 % Empty
% 0.19/0.46 thf(fact_73_paint_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,C: rBT_Im1923302023_color,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im945281971_paint @ A @ B @ C @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ K @ V @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V @ R ) ) ).
% 0.19/0.46
% 0.19/0.46 % paint.simps(2)
% 0.19/0.46 thf(fact_74_ord_Orbt__greater__simps_I2_J,axiom,
% 0.19/0.46 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.19/0.46 = ( ( Less @ K @ Kt )
% 0.19/0.46 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Lt )
% 0.19/0.46 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_greater_simps(2)
% 0.19/0.46 thf(fact_75_ord_Orbt__less__simps_I2_J,axiom,
% 0.19/0.46 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 0.19/0.46 = ( ( Less @ Kt @ K )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Lt )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_less_simps(2)
% 0.19/0.46 thf(fact_76_ord_Obalance__rbt__greater,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ A @ B @ Less @ V @ ( rBT_Im1648453169alance @ A @ B @ A2 @ K @ X @ B2 ) )
% 0.19/0.46 = ( ( rBT_Im1259024060reater @ A @ B @ Less @ V @ A2 )
% 0.19/0.46 & ( rBT_Im1259024060reater @ A @ B @ Less @ V @ B2 )
% 0.19/0.46 & ( Less @ V @ K ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.balance_rbt_greater
% 0.19/0.46 thf(fact_77_ord_Obalance__rbt__less,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ ( rBT_Im1648453169alance @ A @ B @ A2 @ K @ X @ B2 ) )
% 0.19/0.46 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ A2 )
% 0.19/0.46 & ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ B2 )
% 0.19/0.46 & ( Less @ K @ V ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.balance_rbt_less
% 0.19/0.46 thf(fact_78_ord_Opaint__rbt__sorted,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,T: rBT_Im246033960le_rbt @ A @ B,C: rBT_Im1923302023_color] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ A @ B @ Less @ T )
% 0.19/0.46 => ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.paint_rbt_sorted
% 0.19/0.46 thf(fact_79_ord_Opaint__rbt__greater,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ A @ B @ Less @ V @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) )
% 0.19/0.46 = ( rBT_Im1259024060reater @ A @ B @ Less @ V @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.paint_rbt_greater
% 0.19/0.46 thf(fact_80_ord_Opaint__rbt__less,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) )
% 0.19/0.46 = ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.paint_rbt_less
% 0.19/0.46 thf(fact_81_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V @ R ) )
% 0.19/0.46 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ L )
% 0.19/0.46 & ( rBT_Im1259024060reater @ A @ B @ Less @ K @ R )
% 0.19/0.46 & ( rBT_Im759614907sorted @ A @ B @ Less @ L )
% 0.19/0.46 & ( rBT_Im759614907sorted @ A @ B @ Less @ R ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_sorted.simps(2)
% 0.19/0.46 thf(fact_82_ord_Ois__rbt__rbt__sorted,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im862805236is_rbt @ A @ B @ Less @ T )
% 0.19/0.46 => ( rBT_Im759614907sorted @ A @ B @ Less @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.is_rbt_rbt_sorted
% 0.19/0.46 thf(fact_83__C4_Ohyps_C,axiom,
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ b @ less @ b2 )
% 0.19/0.46 => ( ( rBT_Im759614907sorted @ a @ b @ less @ c )
% 0.19/0.46 => ( ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 )
% 0.19/0.46 => ( ( rBT_Im1259024060reater @ a @ b @ less @ k @ c )
% 0.19/0.46 => ( rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % "4.hyps"
% 0.19/0.46 thf(fact_84_local_Oins__rbt__sorted,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: a > B > B > B,K: a,X: B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.19/0.46 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ X @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.ins_rbt_sorted
% 0.19/0.46 thf(fact_85_local_Ostrict__monoD,axiom,
% 0.19/0.46 ! [B: $tType] :
% 0.19/0.46 ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.46 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.46 ( ( strict_mono @ a @ B @ less @ F )
% 0.19/0.46 => ( ( less @ X @ Y )
% 0.19/0.46 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.strict_monoD
% 0.19/0.46 thf(fact_86_local_Ostrict__monoI,axiom,
% 0.19/0.46 ! [B: $tType] :
% 0.19/0.46 ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.46 => ! [F: a > B] :
% 0.19/0.46 ( ! [X3: a,Y2: a] :
% 0.19/0.46 ( ( less @ X3 @ Y2 )
% 0.19/0.46 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.46 => ( strict_mono @ a @ B @ less @ F ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.strict_monoI
% 0.19/0.46 thf(fact_87_local_Ostrict__mono__def,axiom,
% 0.19/0.46 ! [B: $tType] :
% 0.19/0.46 ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.46 => ! [F: a > B] :
% 0.19/0.46 ( ( strict_mono @ a @ B @ less @ F )
% 0.19/0.46 = ( ! [X2: a,Y3: a] :
% 0.19/0.46 ( ( less @ X2 @ Y3 )
% 0.19/0.46 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.strict_mono_def
% 0.19/0.46 thf(fact_88_local_Ostrict__mono__less,axiom,
% 0.19/0.46 ! [B: $tType] :
% 0.19/0.46 ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.46 => ! [F: a > B,X: a,Y: a] :
% 0.19/0.46 ( ( strict_mono @ a @ B @ less @ F )
% 0.19/0.46 => ( ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) )
% 0.19/0.46 = ( less @ X @ Y ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.strict_mono_less
% 0.19/0.46 thf(fact_89_local_Olexordp__eq_ONil,axiom,
% 0.19/0.46 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq.Nil
% 0.19/0.46 thf(fact_90_local_Orbt__sorted_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType] : ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_sorted.simps(1)
% 0.19/0.46 thf(fact_91_local_OEmpty__is__rbt,axiom,
% 0.19/0.46 ! [B: $tType] : ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.Empty_is_rbt
% 0.19/0.46 thf(fact_92_local_Orbt__insert__def,axiom,
% 0.19/0.46 ! [B: $tType] :
% 0.19/0.46 ( ( rBT_Im852463031insert @ a @ B @ less )
% 0.19/0.46 = ( rBT_Im627674146th_key @ a @ B @ less
% 0.19/0.46 @ ^ [Uu2: a,Uv: B,Nv: B] : Nv ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insert_def
% 0.19/0.46 thf(fact_93_local_Orbt__insertw__def,axiom,
% 0.19/0.46 ! [B: $tType,F: B > B > B] :
% 0.19/0.46 ( ( rBT_Im241132701t_with @ a @ B @ less @ F )
% 0.19/0.46 = ( rBT_Im627674146th_key @ a @ B @ less
% 0.19/0.46 @ ^ [Uu2: a] : F ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insertw_def
% 0.19/0.46 thf(fact_94_local_Olexordp__eq__simps_I1_J,axiom,
% 0.19/0.46 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq_simps(1)
% 0.19/0.46 thf(fact_95_local_Olexordp__eq__simps_I2_J,axiom,
% 0.19/0.46 ! [Xs: list @ a] :
% 0.19/0.46 ( ( lexordp_eq @ a @ less @ Xs @ ( nil @ a ) )
% 0.19/0.46 = ( Xs
% 0.19/0.46 = ( nil @ a ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq_simps(2)
% 0.19/0.46 thf(fact_96_local_Oins__rbt__greater,axiom,
% 0.19/0.46 ! [B: $tType,V: a,F: a > B > B > B,K: a,X: B,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ X @ T ) )
% 0.19/0.46 = ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ T )
% 0.19/0.46 & ( less @ V @ K ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.ins_rbt_greater
% 0.19/0.46 thf(fact_97_local_Oins__rbt__less,axiom,
% 0.19/0.46 ! [B: $tType,V: a,F: a > B > B > B,K: a,X: B,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ X @ T ) )
% 0.19/0.46 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ T )
% 0.19/0.46 & ( less @ K @ V ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.ins_rbt_less
% 0.19/0.46 thf(fact_98_local_Orbt__greater__simps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,K: a] : ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_greater_simps(1)
% 0.19/0.46 thf(fact_99_local_Orbt__less__simps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,K: a] : ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_less_simps(1)
% 0.19/0.46 thf(fact_100_rbt_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im418718756_Empty @ A @ B )
% 0.19/0.46 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 0.19/0.46
% 0.19/0.46 % rbt.distinct(1)
% 0.19/0.46 thf(fact_101_rbt_Oinduct,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 => ( ! [X1: rBT_Im1923302023_color,X26: rBT_Im246033960le_rbt @ A @ B,X32: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( P @ X26 )
% 0.19/0.46 => ( ( P @ X5 )
% 0.19/0.46 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X26 @ X32 @ X4 @ X5 ) ) ) )
% 0.19/0.46 => ( P @ Rbt ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rbt.induct
% 0.19/0.46 thf(fact_102_rbt_Oexhaust,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( Y
% 0.19/0.46 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rbt.exhaust
% 0.19/0.46 thf(fact_103_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_sorted.simps(1)
% 0.19/0.46 thf(fact_104_ord_Orbt__greater__simps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_greater_simps(1)
% 0.19/0.46 thf(fact_105_ord_Orbt__less__simps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_less_simps(1)
% 0.19/0.46 thf(fact_106_ord_Orbt__insert__def,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( rBT_Im852463031insert @ A @ B )
% 0.19/0.46 = ( ^ [Less2: A > A > $o] :
% 0.19/0.46 ( rBT_Im627674146th_key @ A @ B @ Less2
% 0.19/0.46 @ ^ [Uu2: A,Uv: B,Nv: B] : Nv ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_insert_def
% 0.19/0.46 thf(fact_107_ord_Orbt__insertw__def,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( rBT_Im241132701t_with @ A @ B )
% 0.19/0.46 = ( ^ [Less2: A > A > $o,F2: B > B > B] :
% 0.19/0.46 ( rBT_Im627674146th_key @ A @ B @ Less2
% 0.19/0.46 @ ^ [Uu2: A] : F2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_insertw_def
% 0.19/0.46 thf(fact_108_paint_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,C: rBT_Im1923302023_color] :
% 0.19/0.46 ( ( rBT_Im945281971_paint @ A @ B @ C @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % paint.simps(1)
% 0.19/0.46 thf(fact_109_balance__left_Osimps_I6_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(6)
% 0.19/0.46 thf(fact_110_combine_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ X )
% 0.19/0.46 = X ) ).
% 0.19/0.46
% 0.19/0.46 % combine.simps(1)
% 0.19/0.46 thf(fact_111_balance__right_Osimps_I6_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(6)
% 0.19/0.46 thf(fact_112_ord_OEmpty__is__rbt,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im862805236is_rbt @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.Empty_is_rbt
% 0.19/0.46 thf(fact_113_combine_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ Va @ Vb @ Vc @ Vd ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ V @ Va @ Vb @ Vc @ Vd ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.simps(2)
% 0.19/0.46 thf(fact_114__C4_Oprems_C_I4_J,axiom,
% 0.19/0.46 rBT_Im1259024060reater @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ) ).
% 0.19/0.46
% 0.19/0.46 % "4.prems"(4)
% 0.19/0.46 thf(fact_115__C4_Oprems_C_I2_J,axiom,
% 0.19/0.46 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ) ).
% 0.19/0.46
% 0.19/0.46 % "4.prems"(2)
% 0.19/0.46 thf(fact_116_local_OgreaterThan__def,axiom,
% 0.19/0.46 ! [L: a] :
% 0.19/0.46 ( ( set_greaterThan @ a @ less @ L )
% 0.19/0.46 = ( collect @ a @ ( less @ L ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.greaterThan_def
% 0.19/0.46 thf(fact_117_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.19/0.46 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 0.19/0.46 = ( Xs
% 0.19/0.46 = ( nil @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq_simps(2)
% 0.19/0.46 thf(fact_118_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq_simps(1)
% 0.19/0.46 thf(fact_119__C4_Oprems_C_I3_J,axiom,
% 0.19/0.46 rBT_Im2075124343t_less @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ) ).
% 0.19/0.46
% 0.19/0.46 % "4.prems"(3)
% 0.19/0.46 thf(fact_120_local_Orbt__ins_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,K: a,X: a,F: a > B > B > B,V: B,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( ( less @ K @ X )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ a @ B @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 0.19/0.46 & ( ~ ( less @ K @ X )
% 0.19/0.46 => ( ( ( less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ a @ B @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ R ) ) ) )
% 0.19/0.46 & ( ~ ( less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_ins.simps(2)
% 0.19/0.46 thf(fact_121_local_Orbt__insert__with__key__def,axiom,
% 0.19/0.46 ! [B: $tType,F: a > B > B > B,K: a,V: B,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im627674146th_key @ a @ B @ less @ F @ K @ V @ T )
% 0.19/0.46 = ( rBT_Im945281971_paint @ a @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_insert_with_key_def
% 0.19/0.46 thf(fact_122__C4_Oprems_C_I1_J,axiom,
% 0.19/0.46 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ) ).
% 0.19/0.46
% 0.19/0.46 % "4.prems"(1)
% 0.19/0.46 thf(fact_123_local_OgreaterThan__iff,axiom,
% 0.19/0.46 ! [I: a,K: a] :
% 0.19/0.46 ( ( member @ a @ I @ ( set_greaterThan @ a @ less @ K ) )
% 0.19/0.46 = ( less @ K @ I ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.greaterThan_iff
% 0.19/0.46 thf(fact_124_balance_Osimps_I23_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(23)
% 0.19/0.46 thf(fact_125_balance_Osimps_I27_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(27)
% 0.19/0.46 thf(fact_126_balance_Osimps_I29_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vi: rBT_Im246033960le_rbt @ A @ B,Vn: A,Vo: B,Vp: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(29)
% 0.19/0.46 thf(fact_127_balance_Osimps_I39_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(39)
% 0.19/0.46 thf(fact_128_balance_Osimps_I43_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(43)
% 0.19/0.46 thf(fact_129_balance_Osimps_I45_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vn: A,Vo: B,Vp: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(45)
% 0.19/0.46 thf(fact_130_balance_Osimps_I14_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(14)
% 0.19/0.46 thf(fact_131_balance_Osimps_I15_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(15)
% 0.19/0.46 thf(fact_132_balance_Osimps_I16_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(16)
% 0.19/0.46 thf(fact_133_balance_Osimps_I17_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Vb: A,Vc: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(17)
% 0.19/0.46 thf(fact_134_balance_Osimps_I18_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(18)
% 0.19/0.46 thf(fact_135_balance_Osimps_I19_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(19)
% 0.19/0.46 thf(fact_136_balance_Osimps_I20_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Vb: A,Vc: B,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(20)
% 0.19/0.46 thf(fact_137_balance_Osimps_I21_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Ve: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(21)
% 0.19/0.46 thf(fact_138_balance_Osimps_I22_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(22)
% 0.19/0.46 thf(fact_139_balance_Osimps_I24_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(24)
% 0.19/0.46 thf(fact_140_balance_Osimps_I25_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vf: A,Vg: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(25)
% 0.19/0.46 thf(fact_141_balance_Osimps_I26_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(26)
% 0.19/0.46 thf(fact_142_balance_Osimps_I28_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vf: A,Vg: B,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(28)
% 0.19/0.46 thf(fact_143_balance_Osimps_I32_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(32)
% 0.19/0.46 thf(fact_144_balance_Osimps_I33_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vb: A,Vc: B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(33)
% 0.19/0.46 thf(fact_145_balance_Osimps_I34_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vb: A,Vc: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(34)
% 0.19/0.46 thf(fact_146_balance_Osimps_I35_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(35)
% 0.19/0.46 thf(fact_147_balance_Osimps_I36_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(36)
% 0.19/0.46 thf(fact_148_balance_Osimps_I37_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(37)
% 0.19/0.46 thf(fact_149_balance_Osimps_I40_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(40)
% 0.19/0.46 thf(fact_150_balance_Osimps_I41_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: A,Vg: B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(41)
% 0.19/0.46 thf(fact_151_balance_Osimps_I42_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: A,Vg: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(42)
% 0.19/0.46 thf(fact_152_balance_Osimps_I44_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(44)
% 0.19/0.46 thf(fact_153_balance__left_Osimps_I9_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(9)
% 0.19/0.46 thf(fact_154_balance__right_Osimps_I9_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(9)
% 0.19/0.46 thf(fact_155_ord_Orbt__ins_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,K: A,X: A,F: A > B > B > B,V: B,L: rBT_Im246033960le_rbt @ A @ B,Y: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( ( Less @ K @ X )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 0.19/0.46 & ( ~ ( Less @ K @ X )
% 0.19/0.46 => ( ( ( Less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ A @ B @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ R ) ) ) )
% 0.19/0.46 & ( ~ ( Less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_ins.simps(2)
% 0.19/0.46 thf(fact_156_ord_Olexordp__eq__refl,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq_refl
% 0.19/0.46 thf(fact_157_ord_Orbt__insert__with__key__def,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( rBT_Im627674146th_key @ A @ B )
% 0.19/0.46 = ( ^ [Less2: A > A > $o,F2: A > B > B > B,K2: A,V2: B,T2: rBT_Im246033960le_rbt @ A @ B] : ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ A @ B @ Less2 @ F2 @ K2 @ V2 @ T2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_insert_with_key_def
% 0.19/0.46 thf(fact_158_ord_Olexordp__eq_ONil,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq.Nil
% 0.19/0.46 thf(fact_159_local_OlessThan__def,axiom,
% 0.19/0.46 ! [U: a] :
% 0.19/0.46 ( ( set_lessThan @ a @ less @ U )
% 0.19/0.46 = ( collect @ a
% 0.19/0.46 @ ^ [X2: a] : ( less @ X2 @ U ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lessThan_def
% 0.19/0.46 thf(fact_160_local_Orbt__ins_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,F: a > B > B > B,K: a,V: B] :
% 0.19/0.46 ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im418718756_Empty @ a @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ a @ B ) @ K @ V @ ( rBT_Im418718756_Empty @ a @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_ins.simps(1)
% 0.19/0.46 thf(fact_161_local_Orbt__ins_Oinduct,axiom,
% 0.19/0.46 ! [B: $tType,P: ( a > B > B > B ) > a > B > ( rBT_Im246033960le_rbt @ a @ B ) > $o,A0: a > B > B > B,A1: a,A22: B,A32: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ! [F3: a > B > B > B,K3: a,V3: B] : ( P @ F3 @ K3 @ V3 @ ( rBT_Im418718756_Empty @ a @ B ) )
% 0.19/0.46 => ( ! [F3: a > B > B > B,K3: a,V3: B,L2: rBT_Im246033960le_rbt @ a @ B,X3: a,Y2: B,R2: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( ( less @ K3 @ X3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 0.19/0.46 => ( ( ~ ( less @ K3 @ X3 )
% 0.19/0.46 => ( ( less @ X3 @ K3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 0.19/0.46 => ( ! [F3: a > B > B > B,K3: a,V3: B,L2: rBT_Im246033960le_rbt @ a @ B,X3: a,Y2: B,R2: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( ( less @ K3 @ X3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 0.19/0.46 => ( ( ~ ( less @ K3 @ X3 )
% 0.19/0.46 => ( ( less @ X3 @ K3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_ins.induct
% 0.19/0.46 thf(fact_162_local_Orbt__lookup__balance,axiom,
% 0.19/0.46 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B,X: a] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 0.19/0.46 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 0.19/0.46 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 0.19/0.46 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 0.19/0.46 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im1648453169alance @ a @ B @ L @ K @ V @ R ) @ X )
% 0.19/0.46 = ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ K @ V @ R ) @ X ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_lookup_balance
% 0.19/0.46 thf(fact_163_local_Orbt__ins_Osimps_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,K: a,X: a,F: a > B > B > B,V: B,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( ( less @ K @ X )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 0.19/0.46 & ( ~ ( less @ K @ X )
% 0.19/0.46 => ( ( ( less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ R ) ) ) )
% 0.19/0.46 & ( ~ ( less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_ins.simps(3)
% 0.19/0.46 thf(fact_164_local_OlessThan__iff,axiom,
% 0.19/0.46 ! [I: a,K: a] :
% 0.19/0.46 ( ( member @ a @ I @ ( set_lessThan @ a @ less @ K ) )
% 0.19/0.46 = ( less @ I @ K ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lessThan_iff
% 0.19/0.46 thf(fact_165_local_Opaint__rbt__lookup,axiom,
% 0.19/0.46 ! [B: $tType,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) )
% 0.19/0.46 = ( rBT_Im35466040lookup @ a @ B @ less @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.paint_rbt_lookup
% 0.19/0.46 thf(fact_166_color_Oexhaust,axiom,
% 0.19/0.46 ! [Y: rBT_Im1923302023_color] :
% 0.19/0.46 ( ( Y != rBT_Impl_Mirabelle_R )
% 0.19/0.46 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 0.19/0.46
% 0.19/0.46 % color.exhaust
% 0.19/0.46 thf(fact_167_color_Oinduct,axiom,
% 0.19/0.46 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 0.19/0.46 ( ( P @ rBT_Impl_Mirabelle_R )
% 0.19/0.46 => ( ( P @ rBT_Impl_Mirabelle_B )
% 0.19/0.46 => ( P @ Color ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % color.induct
% 0.19/0.46 thf(fact_168_color_Odistinct_I1_J,axiom,
% 0.19/0.46 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 0.19/0.46
% 0.19/0.46 % color.distinct(1)
% 0.19/0.46 thf(fact_169_ord_Orbt__ins_Osimps_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,K: A,X: A,F: A > B > B > B,V: B,L: rBT_Im246033960le_rbt @ A @ B,Y: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( ( Less @ K @ X )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 0.19/0.46 & ( ~ ( Less @ K @ X )
% 0.19/0.46 => ( ( ( Less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ R ) ) ) )
% 0.19/0.46 & ( ~ ( Less @ X @ K )
% 0.19/0.46 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_ins.simps(3)
% 0.19/0.46 thf(fact_170_ord_Opaint__rbt__lookup,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) )
% 0.19/0.46 = ( rBT_Im35466040lookup @ A @ B @ Less @ T ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.paint_rbt_lookup
% 0.19/0.46 thf(fact_171_rbt__cases,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( T
% 0.19/0.46 != ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 => ( ! [L2: rBT_Im246033960le_rbt @ A @ B,K3: A,V3: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( T
% 0.19/0.46 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ K3 @ V3 @ R2 ) )
% 0.19/0.46 => ~ ! [L2: rBT_Im246033960le_rbt @ A @ B,K3: A,V3: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( T
% 0.19/0.46 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ K3 @ V3 @ R2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % rbt_cases
% 0.19/0.46 thf(fact_172_combine_Oinduct,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o,A0: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ! [X1: rBT_Im246033960le_rbt @ A @ B] : ( P @ ( rBT_Im418718756_Empty @ A @ B ) @ X1 )
% 0.19/0.46 => ( ! [V3: rBT_Im1923302023_color,Va2: rBT_Im246033960le_rbt @ A @ B,Vb2: A,Vc2: B,Vd2: rBT_Im246033960le_rbt @ A @ B] : ( P @ ( rBT_Im480247531Branch @ A @ B @ V3 @ Va2 @ Vb2 @ Vc2 @ Vd2 ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 => ( ! [A4: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,B3: rBT_Im246033960le_rbt @ A @ B,C3: rBT_Im246033960le_rbt @ A @ B,S2: A,Y2: B,D: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( P @ B3 @ C3 )
% 0.19/0.46 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A4 @ K3 @ X3 @ B3 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C3 @ S2 @ Y2 @ D ) ) )
% 0.19/0.46 => ( ! [A4: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,B3: rBT_Im246033960le_rbt @ A @ B,C3: rBT_Im246033960le_rbt @ A @ B,S2: A,Y2: B,D: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( P @ B3 @ C3 )
% 0.19/0.46 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A4 @ K3 @ X3 @ B3 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C3 @ S2 @ Y2 @ D ) ) )
% 0.19/0.46 => ( ! [Va2: rBT_Im246033960le_rbt @ A @ B,Vb2: A,Vc2: B,Vd2: rBT_Im246033960le_rbt @ A @ B,B3: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,C3: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) @ B3 )
% 0.19/0.46 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B3 @ K3 @ X3 @ C3 ) ) )
% 0.19/0.46 => ( ! [A4: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,B3: rBT_Im246033960le_rbt @ A @ B,Va2: rBT_Im246033960le_rbt @ A @ B,Vb2: A,Vc2: B,Vd2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( P @ B3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) )
% 0.19/0.46 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A4 @ K3 @ X3 @ B3 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.induct
% 0.19/0.46 thf(fact_173_ord_Orbt__ins_Oinduct,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,P: ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > $o,Less: A > A > $o,A0: A > B > B > B,A1: A,A22: B,A32: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ! [F3: A > B > B > B,K3: A,V3: B] : ( P @ F3 @ K3 @ V3 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( ( Less @ K3 @ X3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 0.19/0.46 => ( ( ~ ( Less @ K3 @ X3 )
% 0.19/0.46 => ( ( Less @ X3 @ K3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 0.19/0.46 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( ( Less @ K3 @ X3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 0.19/0.46 => ( ( ~ ( Less @ K3 @ X3 )
% 0.19/0.46 => ( ( Less @ X3 @ K3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_ins.induct
% 0.19/0.46 thf(fact_174_balance_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,D2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C @ Y @ Z @ D2 ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ D2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(1)
% 0.19/0.46 thf(fact_175_balance_Osimps_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ W @ X @ B2 ) @ S @ T @ C ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(3)
% 0.19/0.46 thf(fact_176_balance_Osimps_I7_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(7)
% 0.19/0.46 thf(fact_177_balance_Osimps_I9_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,D2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C @ Y @ Z @ D2 ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ D2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(9)
% 0.19/0.46 thf(fact_178_balance_Osimps_I13_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(13)
% 0.19/0.46 thf(fact_179_balance__left_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ S @ Y @ C )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ K @ X @ B2 ) @ S @ Y @ C ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(1)
% 0.19/0.46 thf(fact_180_ord_Orbt__ins_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o,F: A > B > B > B,K: A,V: B] :
% 0.19/0.46 ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ V @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_ins.simps(1)
% 0.19/0.46 thf(fact_181_balance__left_Osimps_I7_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(7)
% 0.19/0.46 thf(fact_182_balance__left_Osimps_I8_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ Vh ) @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(8)
% 0.19/0.46 thf(fact_183_balance__right_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ Y @ C ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ B2 @ S @ Y @ C ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(1)
% 0.19/0.46 thf(fact_184_combine_Osimps_I5_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,B2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ K @ X @ C ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ B2 ) @ K @ X @ C ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.simps(5)
% 0.19/0.46 thf(fact_185_combine_Osimps_I6_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im1591839508ombine @ A @ B @ B2 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % combine.simps(6)
% 0.19/0.46 thf(fact_186_balance__right_Osimps_I7_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,K: A,X: B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Va @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(7)
% 0.19/0.46 thf(fact_187_balance__right_Osimps_I8_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,K: A,X: B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Va @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ Vh ) ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(8)
% 0.19/0.46 thf(fact_188_ord__class_Orbt__ins_Oinduct,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.46 => ! [P: ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > $o,A0: A > B > B > B,A1: A,A22: B,A32: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ! [F3: A > B > B > B,K3: A,V3: B] : ( P @ F3 @ K3 @ V3 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( ( ord_less @ A @ K3 @ X3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 0.19/0.46 => ( ( ~ ( ord_less @ A @ K3 @ X3 )
% 0.19/0.46 => ( ( ord_less @ A @ X3 @ K3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 0.19/0.46 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( ( ord_less @ A @ K3 @ X3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 0.19/0.46 => ( ( ~ ( ord_less @ A @ K3 @ X3 )
% 0.19/0.46 => ( ( ord_less @ A @ X3 @ K3 )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 0.19/0.46 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord_class.rbt_ins.induct
% 0.19/0.46 thf(fact_189_balance_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ W @ X @ B2 ) @ S @ T @ C ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(2)
% 0.19/0.46 thf(fact_190_balance_Osimps_I4_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(4)
% 0.19/0.46 thf(fact_191_balance_Osimps_I5_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(5)
% 0.19/0.46 thf(fact_192_balance_Osimps_I6_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(6)
% 0.19/0.46 thf(fact_193_balance_Osimps_I8_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,D2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C @ Y @ Z @ D2 ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ D2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(8)
% 0.19/0.46 thf(fact_194_balance_Osimps_I10_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(10)
% 0.19/0.46 thf(fact_195_balance_Osimps_I11_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(11)
% 0.19/0.46 thf(fact_196_balance_Osimps_I12_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 0.19/0.46 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance.simps(12)
% 0.19/0.46 thf(fact_197_balance__left_Osimps_I11_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Vi @ Vj @ Vk @ Vl ) @ Vf @ Vg @ Vh ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(11)
% 0.19/0.46 thf(fact_198_balance__left_Osimps_I10_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ Vh ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(10)
% 0.19/0.46 thf(fact_199_balance__right_Osimps_I11_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Vi @ Vj @ Vk @ Vl ) ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(11)
% 0.19/0.46 thf(fact_200_balance__right_Osimps_I10_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,K: A,X: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(10)
% 0.19/0.46 thf(fact_201_balance__left_Osimps_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ S @ Y @ B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(3)
% 0.19/0.46 thf(fact_202_balance__right_Osimps_I3_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(3)
% 0.19/0.46 thf(fact_203_balance__left_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ S @ Y @ B2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(2)
% 0.19/0.46 thf(fact_204_balance__right_Osimps_I2_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(2)
% 0.19/0.46 thf(fact_205_balance__left_Osimps_I5_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) @ T @ Z @ C ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ A2 ) @ S @ Y @ ( rBT_Im1648453169alance @ A @ B @ B2 @ T @ Z @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ C ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(5)
% 0.19/0.46 thf(fact_206_balance__right_Osimps_I5_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ B2 @ S @ Y @ C ) ) @ T @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ A2 ) @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ T @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(5)
% 0.19/0.46 thf(fact_207_balance__left_Osimps_I4_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) @ T @ Z @ C ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ A2 ) @ S @ Y @ ( rBT_Im1648453169alance @ A @ B @ B2 @ T @ Z @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ C ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_left.simps(4)
% 0.19/0.46 thf(fact_208_balance__right_Osimps_I4_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B] :
% 0.19/0.46 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ B2 @ S @ Y @ C ) ) @ T @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ A2 ) @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ T @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % balance_right.simps(4)
% 0.19/0.46 thf(fact_209_local_Oentries__rbt__lookup,axiom,
% 0.19/0.46 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.19/0.46 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.19/0.46 => ( ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 0.19/0.46 = ( rBT_Im954575269ntries @ a @ B @ T22 ) )
% 0.19/0.46 = ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 0.19/0.46 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.entries_rbt_lookup
% 0.19/0.46 thf(fact_210_local_Oentries__eqI,axiom,
% 0.19/0.46 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.19/0.46 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.19/0.46 => ( ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 0.19/0.46 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) )
% 0.19/0.46 => ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 0.19/0.46 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.entries_eqI
% 0.19/0.46 thf(fact_211_local_Orbt__lookup_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,K: a] :
% 0.19/0.46 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) @ K )
% 0.19/0.46 = ( none @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_lookup.simps(1)
% 0.19/0.46 thf(fact_212_local_Orbt__lookup__Empty,axiom,
% 0.19/0.46 ! [B: $tType] :
% 0.19/0.46 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) )
% 0.19/0.46 = ( ^ [X2: a] : ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_lookup_Empty
% 0.19/0.46 thf(fact_213_local_Orbt__lookup__rbt__greater,axiom,
% 0.19/0.46 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 0.19/0.46 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.19/0.46 = ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_lookup_rbt_greater
% 0.19/0.46 thf(fact_214_local_Orbt__lookup__rbt__less,axiom,
% 0.19/0.46 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 0.19/0.46 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 0.19/0.46 = ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.rbt_lookup_rbt_less
% 0.19/0.46 thf(fact_215_entries_Osimps_I1_J,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType] :
% 0.19/0.46 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % entries.simps(1)
% 0.19/0.46 thf(fact_216_ord_Orbt__lookup__Empty,axiom,
% 0.19/0.46 ! [B: $tType,A: $tType,Less: A > A > $o] :
% 0.19/0.46 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) )
% 0.19/0.46 = ( ^ [X2: A] : ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_lookup_Empty
% 0.19/0.46 thf(fact_217_ord_Orbt__lookup_Osimps_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Less: A > A > $o,K: A] :
% 0.19/0.46 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) @ K )
% 0.19/0.46 = ( none @ B ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_lookup.simps(1)
% 0.19/0.46 thf(fact_218_ord_Orbt__lookup__rbt__greater,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im1259024060reater @ A @ B @ Less @ K @ T )
% 0.19/0.46 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 0.19/0.46 = ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_lookup_rbt_greater
% 0.19/0.46 thf(fact_219_ord_Orbt__lookup__rbt__less,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 0.19/0.46 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ T )
% 0.19/0.46 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 0.19/0.46 = ( none @ B ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.rbt_lookup_rbt_less
% 0.19/0.46 thf(fact_220_local_Omap__of__entries,axiom,
% 0.19/0.46 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 0.19/0.46 => ( ( map_of @ a @ B @ ( rBT_Im954575269ntries @ a @ B @ T ) )
% 0.19/0.46 = ( rBT_Im35466040lookup @ a @ B @ less @ T ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.map_of_entries
% 0.19/0.46 thf(fact_221_local_Olexordp__eq_Ocases,axiom,
% 0.19/0.46 ! [A1: list @ a,A22: list @ a] :
% 0.19/0.46 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 0.19/0.46 => ( ( ( A1
% 0.19/0.46 = ( nil @ a ) )
% 0.19/0.46 => ! [Ys2: list @ a] : ( A22 != Ys2 ) )
% 0.19/0.46 => ( ! [X3: a] :
% 0.19/0.46 ( ? [Xs2: list @ a] :
% 0.19/0.46 ( A1
% 0.19/0.46 = ( cons @ a @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Y2: a] :
% 0.19/0.46 ( ? [Ys2: list @ a] :
% 0.19/0.46 ( A22
% 0.19/0.46 = ( cons @ a @ Y2 @ Ys2 ) )
% 0.19/0.46 => ~ ( less @ X3 @ Y2 ) ) )
% 0.19/0.46 => ~ ! [X3: a,Y2: a,Xs2: list @ a] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons @ a @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Ys2: list @ a] :
% 0.19/0.46 ( ( A22
% 0.19/0.46 = ( cons @ a @ Y2 @ Ys2 ) )
% 0.19/0.46 => ( ~ ( less @ X3 @ Y2 )
% 0.19/0.46 => ( ~ ( less @ Y2 @ X3 )
% 0.19/0.46 => ~ ( lexordp_eq @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq.cases
% 0.19/0.46 thf(fact_222_local_Olexordp__eq_OCons__eq,axiom,
% 0.19/0.46 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.19/0.46 ( ~ ( less @ X @ Y )
% 0.19/0.46 => ( ~ ( less @ Y @ X )
% 0.19/0.46 => ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 0.19/0.46 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq.Cons_eq
% 0.19/0.46 thf(fact_223_local_Olexordp__eq_OCons,axiom,
% 0.19/0.46 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 0.19/0.46 ( ( less @ X @ Y )
% 0.19/0.46 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq.Cons
% 0.19/0.46 thf(fact_224_list_Oinject,axiom,
% 0.19/0.46 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.19/0.46 ( ( ( cons @ A @ X21 @ X22 )
% 0.19/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.19/0.46 = ( ( X21 = Y21 )
% 0.19/0.46 & ( X22 = Y22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inject
% 0.19/0.46 thf(fact_225_local_Olexordp__eq_Osimps,axiom,
% 0.19/0.46 ! [A1: list @ a,A22: list @ a] :
% 0.19/0.46 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 0.19/0.46 = ( ? [Ys3: list @ a] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( nil @ a ) )
% 0.19/0.46 & ( A22 = Ys3 ) )
% 0.19/0.46 | ? [X2: a,Y3: a,Xs3: list @ a,Ys3: list @ a] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons @ a @ X2 @ Xs3 ) )
% 0.19/0.46 & ( A22
% 0.19/0.46 = ( cons @ a @ Y3 @ Ys3 ) )
% 0.19/0.46 & ( less @ X2 @ Y3 ) )
% 0.19/0.46 | ? [X2: a,Y3: a,Xs3: list @ a,Ys3: list @ a] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons @ a @ X2 @ Xs3 ) )
% 0.19/0.46 & ( A22
% 0.19/0.46 = ( cons @ a @ Y3 @ Ys3 ) )
% 0.19/0.46 & ~ ( less @ X2 @ Y3 )
% 0.19/0.46 & ~ ( less @ Y3 @ X2 )
% 0.19/0.46 & ( lexordp_eq @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq.simps
% 0.19/0.46 thf(fact_226_local_Olexordp__eq_Oinducts,axiom,
% 0.19/0.46 ! [X12: list @ a,X27: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.19/0.46 ( ( lexordp_eq @ a @ less @ X12 @ X27 )
% 0.19/0.46 => ( ! [X1: list @ a] : ( P @ ( nil @ a ) @ X1 )
% 0.19/0.46 => ( ! [X3: a,Y2: a,Xs2: list @ a,Ys2: list @ a] :
% 0.19/0.46 ( ( less @ X3 @ Y2 )
% 0.19/0.46 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y2 @ Ys2 ) ) )
% 0.19/0.46 => ( ! [X3: a,Y2: a,Xs2: list @ a,Ys2: list @ a] :
% 0.19/0.46 ( ~ ( less @ X3 @ Y2 )
% 0.19/0.46 => ( ~ ( less @ Y2 @ X3 )
% 0.19/0.46 => ( ( lexordp_eq @ a @ less @ Xs2 @ Ys2 )
% 0.19/0.46 => ( ( P @ Xs2 @ Ys2 )
% 0.19/0.46 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y2 @ Ys2 ) ) ) ) ) )
% 0.19/0.46 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq.inducts
% 0.19/0.46 thf(fact_227_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.19/0.46 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.19/0.46 = ( ( Less @ X @ Y )
% 0.19/0.46 | ( ~ ( Less @ Y @ X )
% 0.19/0.46 & ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq_simps(4)
% 0.19/0.46 thf(fact_228_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 0.19/0.46 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq_simps(3)
% 0.19/0.46 thf(fact_229_local_Olexordp__eq__simps_I4_J,axiom,
% 0.19/0.46 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 0.19/0.46 ( ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 0.19/0.46 = ( ( less @ X @ Y )
% 0.19/0.46 | ( ~ ( less @ Y @ X )
% 0.19/0.46 & ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq_simps(4)
% 0.19/0.46 thf(fact_230_local_Olexordp__eq__simps_I3_J,axiom,
% 0.19/0.46 ! [X: a,Xs: list @ a] :
% 0.19/0.46 ~ ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( nil @ a ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_eq_simps(3)
% 0.19/0.46 thf(fact_231_ord_Olexordp__eq_Ocases,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.19/0.46 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 0.19/0.46 => ( ( ( A1
% 0.19/0.46 = ( nil @ A ) )
% 0.19/0.46 => ! [Ys2: list @ A] : ( A22 != Ys2 ) )
% 0.19/0.46 => ( ! [X3: A] :
% 0.19/0.46 ( ? [Xs2: list @ A] :
% 0.19/0.46 ( A1
% 0.19/0.46 = ( cons @ A @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Y2: A] :
% 0.19/0.46 ( ? [Ys2: list @ A] :
% 0.19/0.46 ( A22
% 0.19/0.46 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.19/0.46 => ~ ( Less @ X3 @ Y2 ) ) )
% 0.19/0.46 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.19/0.46 ( ( A1
% 0.19/0.46 = ( cons @ A @ X3 @ Xs2 ) )
% 0.19/0.46 => ! [Ys2: list @ A] :
% 0.19/0.46 ( ( A22
% 0.19/0.46 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.19/0.46 => ( ~ ( Less @ X3 @ Y2 )
% 0.19/0.46 => ( ~ ( Less @ Y2 @ X3 )
% 0.19/0.46 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq.cases
% 0.19/0.46 thf(fact_232_ord_Olexordp__eq_Osimps,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( lexordp_eq @ A )
% 0.19/0.46 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.19/0.46 ( ? [Ys3: list @ A] :
% 0.19/0.46 ( ( A12
% 0.19/0.46 = ( nil @ A ) )
% 0.19/0.46 & ( A23 = Ys3 ) )
% 0.19/0.46 | ? [X2: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 0.19/0.46 ( ( A12
% 0.19/0.46 = ( cons @ A @ X2 @ Xs3 ) )
% 0.19/0.46 & ( A23
% 0.19/0.46 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.19/0.46 & ( Less2 @ X2 @ Y3 ) )
% 0.19/0.46 | ? [X2: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 0.19/0.46 ( ( A12
% 0.19/0.46 = ( cons @ A @ X2 @ Xs3 ) )
% 0.19/0.46 & ( A23
% 0.19/0.46 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.19/0.46 & ~ ( Less2 @ X2 @ Y3 )
% 0.19/0.46 & ~ ( Less2 @ Y3 @ X2 )
% 0.19/0.46 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq.simps
% 0.19/0.46 thf(fact_233_ord_Olexordp__eq_Oinducts,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,X12: list @ A,X27: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.19/0.46 ( ( lexordp_eq @ A @ Less @ X12 @ X27 )
% 0.19/0.46 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.19/0.46 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.19/0.46 ( ( Less @ X3 @ Y2 )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.19/0.46 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.19/0.46 ( ~ ( Less @ X3 @ Y2 )
% 0.19/0.46 => ( ~ ( Less @ Y2 @ X3 )
% 0.19/0.46 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 )
% 0.19/0.46 => ( ( P @ Xs2 @ Ys2 )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) )
% 0.19/0.46 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq.inducts
% 0.19/0.46 thf(fact_234_list_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.19/0.46 ( ( nil @ A )
% 0.19/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.distinct(1)
% 0.19/0.46 thf(fact_235_list_OdiscI,axiom,
% 0.19/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.19/0.46 ( ( List
% 0.19/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.19/0.46 => ( List
% 0.19/0.46 != ( nil @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.discI
% 0.19/0.46 thf(fact_236_list_Oexhaust,axiom,
% 0.19/0.46 ! [A: $tType,Y: list @ A] :
% 0.19/0.46 ( ( Y
% 0.19/0.46 != ( nil @ A ) )
% 0.19/0.46 => ~ ! [X212: A,X222: list @ A] :
% 0.19/0.46 ( Y
% 0.19/0.46 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.exhaust
% 0.19/0.46 thf(fact_237_list_Oinducts,axiom,
% 0.19/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.19/0.46 ( ( P @ ( nil @ A ) )
% 0.19/0.46 => ( ! [X1: A,X26: list @ A] :
% 0.19/0.46 ( ( P @ X26 )
% 0.19/0.46 => ( P @ ( cons @ A @ X1 @ X26 ) ) )
% 0.19/0.46 => ( P @ List ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.inducts
% 0.19/0.46 thf(fact_238_neq__Nil__conv,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 != ( nil @ A ) )
% 0.19/0.46 = ( ? [Y3: A,Ys3: list @ A] :
% 0.19/0.46 ( Xs
% 0.19/0.46 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % neq_Nil_conv
% 0.19/0.46 thf(fact_239_list__induct2_H,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.19/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.19/0.46 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 0.19/0.46 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 0.19/0.46 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.19/0.46 ( ( P @ Xs2 @ Ys2 )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 0.19/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list_induct2'
% 0.19/0.46 thf(fact_240_splice_Oinduct,axiom,
% 0.19/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.19/0.46 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.19/0.46 => ( ! [V3: A,Va2: list @ A] : ( P @ ( cons @ A @ V3 @ Va2 ) @ ( nil @ A ) )
% 0.19/0.46 => ( ! [X3: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.19/0.46 ( ( P @ Xs2 @ Ys2 )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.19/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % splice.induct
% 0.19/0.46 thf(fact_241_transpose_Ocases,axiom,
% 0.19/0.46 ! [A: $tType,X: list @ ( list @ A )] :
% 0.19/0.46 ( ( X
% 0.19/0.46 != ( nil @ ( list @ A ) ) )
% 0.19/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.19/0.46 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % transpose.cases
% 0.19/0.46 thf(fact_242_remdups__adj_Ocases,axiom,
% 0.19/0.46 ! [A: $tType,X: list @ A] :
% 0.19/0.46 ( ( X
% 0.19/0.46 != ( nil @ A ) )
% 0.19/0.46 => ( ! [X3: A] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.19/0.46 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.19/0.46 ( X
% 0.19/0.46 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % remdups_adj.cases
% 0.19/0.46 thf(fact_243_remdups__adj_Oinduct,axiom,
% 0.19/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.19/0.46 ( ( P @ ( nil @ A ) )
% 0.19/0.46 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.19/0.46 => ( ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.19/0.46 ( ( ( X3 = Y2 )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.19/0.46 => ( ( ( X3 != Y2 )
% 0.19/0.46 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.19/0.46 => ( P @ A0 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % remdups_adj.induct
% 0.19/0.46 thf(fact_244_list__nonempty__induct,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 != ( nil @ A ) )
% 0.19/0.46 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.19/0.46 => ( ! [X3: A,Xs2: list @ A] :
% 0.19/0.46 ( ( Xs2
% 0.19/0.46 != ( nil @ A ) )
% 0.19/0.46 => ( ( P @ Xs2 )
% 0.19/0.46 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 0.19/0.46 => ( P @ Xs ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list_nonempty_induct
% 0.19/0.46 thf(fact_245_map__tailrec__rev_Oinduct,axiom,
% 0.19/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.19/0.46 ( ! [F3: A > B,X1: list @ B] : ( P @ F3 @ ( nil @ A ) @ X1 )
% 0.19/0.46 => ( ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.19/0.46 ( ( P @ F3 @ As @ ( cons @ B @ ( F3 @ A4 ) @ Bs ) )
% 0.19/0.46 => ( P @ F3 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.19/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % map_tailrec_rev.induct
% 0.19/0.46 thf(fact_246_not__Cons__self2,axiom,
% 0.19/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.19/0.46 ( ( cons @ A @ X @ Xs )
% 0.19/0.46 != Xs ) ).
% 0.19/0.46
% 0.19/0.46 % not_Cons_self2
% 0.19/0.46 thf(fact_247_ord_Olexordp__eq_OCons,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.19/0.46 ( ( Less @ X @ Y )
% 0.19/0.46 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq.Cons
% 0.19/0.46 thf(fact_248_ord_Olexordp__eq_OCons__eq,axiom,
% 0.19/0.46 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.19/0.46 ( ~ ( Less @ X @ Y )
% 0.19/0.46 => ( ~ ( Less @ Y @ X )
% 0.19/0.46 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys )
% 0.19/0.46 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ord.lexordp_eq.Cons_eq
% 0.19/0.46 thf(fact_249_local_Oset__entries__inject,axiom,
% 0.19/0.46 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 0.19/0.46 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 0.19/0.46 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 0.19/0.46 => ( ( ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T1 ) )
% 0.19/0.46 = ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T22 ) ) )
% 0.19/0.46 = ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 0.19/0.46 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.set_entries_inject
% 0.19/0.46 thf(fact_250_local_Olexordp__induct,axiom,
% 0.19/0.46 ! [Xs: list @ a,Ys: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 0.19/0.46 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.19/0.46 => ( ! [Y2: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y2 @ Ys2 ) )
% 0.19/0.46 => ( ! [X3: a,Xs2: list @ a,Y2: a,Ys2: list @ a] :
% 0.19/0.46 ( ( less @ X3 @ Y2 )
% 0.19/0.46 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y2 @ Ys2 ) ) )
% 0.19/0.46 => ( ! [X3: a,Xs2: list @ a,Ys2: list @ a] :
% 0.19/0.46 ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 0.19/0.46 => ( ( P @ Xs2 @ Ys2 )
% 0.19/0.46 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ X3 @ Ys2 ) ) ) )
% 0.19/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_induct
% 0.19/0.46 thf(fact_251_local_Olexordp__antisym,axiom,
% 0.19/0.46 ! [Xs: list @ a,Ys: list @ a] :
% 0.19/0.46 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.19/0.46 => ~ ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_antisym
% 0.19/0.46 thf(fact_252_local_Olexordp__irreflexive,axiom,
% 0.19/0.46 ! [Xs: list @ a] :
% 0.19/0.46 ( ! [X3: a] :
% 0.19/0.46 ~ ( less @ X3 @ X3 )
% 0.19/0.46 => ~ ( lexordp @ a @ less @ Xs @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_irreflexive
% 0.19/0.46 thf(fact_253_local_Olexordp__irreflexive_H,axiom,
% 0.19/0.46 ! [Xs: list @ a] :
% 0.19/0.46 ~ ( lexordp @ a @ less @ Xs @ Xs ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_irreflexive'
% 0.19/0.46 thf(fact_254_local_Olexordp__linear,axiom,
% 0.19/0.46 ! [Xs: list @ a,Ys: list @ a] :
% 0.19/0.46 ( ( lexordp @ a @ less @ Xs @ Ys )
% 0.19/0.46 | ( Xs = Ys )
% 0.19/0.46 | ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % local.lexordp_linear
% 0.19/0.46
% 0.19/0.46 %----Type constructors (6)
% 0.19/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.46 ! [A5: $tType,A6: $tType] :
% 0.19/0.46 ( ( order @ A6 @ ( type2 @ A6 ) )
% 0.19/0.46 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.19/0.46 ! [A5: $tType,A6: $tType] :
% 0.19/0.46 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 0.19/0.46 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 0.19/0.46 ! [A5: $tType] : ( order @ ( set @ A5 ) @ ( type2 @ ( set @ A5 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.19/0.46 ! [A5: $tType] : ( ord @ ( set @ A5 ) @ ( type2 @ ( set @ A5 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 0.19/0.46 order @ $o @ ( type2 @ $o ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.19/0.46 ord @ $o @ ( type2 @ $o ) ).
% 0.19/0.46
% 0.19/0.46 %----Conjectures (1)
% 0.19/0.46 thf(conj_0,conjecture,
% 0.19/0.46 rBT_Im1259024060reater @ a @ b @ less @ x @ d ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 2.85/1.53 ---- Embedded in THF ---
% 2.85/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.85/1.53 %%% Generated on Tue Feb 24 06:12:56 EST 2026
% 2.85/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.85/1.53 %%% Logic specification used:
% 2.85/1.53 %%% thf(spec, logic, $$dhol).
% 2.85/1.53
% 2.85/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.F0zMB7Y9hR/DTF2DTF19201.p
% 2.85/1.53 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor, type, rBT_Im1923302023_color: $tType).
% 2.85/1.53 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt, type, rBT_Im246033960le_rbt: ($tType > ($tType > $tType))).
% 2.85/1.53 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.85/1.53 thf(ty_t_Option_Ooption, type, option: ($tType > $tType)).
% 2.85/1.53 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.85/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.85/1.53 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.85/1.53 thf(ty_tf_b, type, b: $tType).
% 2.85/1.53 thf(ty_tf_a, type, a: $tType).
% 2.85/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.85/1.53 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.85/1.53 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.85/1.53 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.85/1.53 thf(sy_c_List_Oord_Olexordp, type, lexordp: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.85/1.53 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.85/1.53 thf(sy_c_Map_Omap__of, type, map_of: (!> [A:$tType,B:$tType]: (((list @ ((product_prod @ A) @ B)) > (A > (option @ B)))))).
% 2.85/1.53 thf(sy_c_Option_Ooption_ONone, type, none: (!> [A:$tType]: ((option @ A)))).
% 2.85/1.53 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.85/1.53 thf(sy_c_Orderings_Oorder_Ostrict__mono, type, strict_mono: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > $o))))).
% 2.85/1.53 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance, type, rBT_Im1648453169alance: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B)))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance__left, type, rBT_Im1278323832e_left: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B)))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance__right, type, rBT_Im1053358987_right: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B)))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocombine, type, rBT_Im1591839508ombine: (!> [A:$tType,B:$tType]: ((((rBT_Im246033960le_rbt @ A) @ B) > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B)))))).
% 2.85/1.53 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)))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Ois__rbt, type, rBT_Im862805236is_rbt: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater, type, rBT_Im1259024060reater: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__ins, type, rBT_Im1756508336bt_ins: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > (B > (B > B))) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert, type, rBT_Im852463031insert: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B)))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert__with, type, rBT_Im241132701t_with: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((B > (B > B)) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert__with__key, type, rBT_Im627674146th_key: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > (B > (B > B))) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less, type, rBT_Im2075124343t_less: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (A > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup, type, rBT_Im35466040lookup: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (option @ B))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted, type, rBT_Im759614907sorted: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > (((rBT_Im246033960le_rbt @ A) @ B) > $o))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Opaint, type, rBT_Im945281971_paint: (!> [A:$tType,B:$tType]: ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B)))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch, type, rBT_Im480247531Branch: (!> [A:$tType,B:$tType]: ((rBT_Im1923302023_color > (((rBT_Im246033960le_rbt @ A) @ B) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > ((rBT_Im246033960le_rbt @ A) @ B))))))))).
% 2.85/1.53 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty, type, rBT_Im418718756_Empty: (!> [A:$tType,B:$tType]: (((rBT_Im246033960le_rbt @ A) @ B)))).
% 2.85/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.85/1.53 thf(sy_c_Set__Interval_Oord_OgreaterThan, type, set_greaterThan: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.85/1.53 thf(sy_c_Set__Interval_Oord_OlessThan, type, set_lessThan: (!> [A:$tType]: (((A > (A > $o)) > (A > (set @ A)))))).
% 2.85/1.53 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.85/1.53 thf(sy_v_a____, type, a2: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.85/1.53 thf(sy_v_b____, type, b2: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.85/1.53 thf(sy_v_c____, type, c: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.85/1.53 thf(sy_v_d____, type, d: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.85/1.53 thf(sy_v_k, type, k: a).
% 2.85/1.53 thf(sy_v_l, type, l: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.85/1.53 thf(sy_v_less, type, less: (a > (a > $o))).
% 2.85/1.53 thf(sy_v_r, type, r: ((rBT_Im246033960le_rbt @ a) @ b)).
% 2.85/1.53 thf(sy_v_v____, type, v: b).
% 2.85/1.53 thf(sy_v_w____, type, w: b).
% 2.85/1.53 thf(sy_v_x____, type, x: a).
% 2.85/1.53 thf(sy_v_y____, type, y: a).
% 2.85/1.53 thf(fact_0_local_Oantisym__conv3, axiom, (! [Y:a,X:a]: (((~ (((less @ Y) @ X))) => ((~ (((less @ X) @ Y))) = (X = Y)))))).
% 2.85/1.53 thf(fact_1_local_Odual__order_Oasym, axiom, (! [B2:a,A2:a]: ((((less @ B2) @ A2) => (~ (((less @ A2) @ B2))))))).
% 2.85/1.53 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq, axiom, (! [B2:a,A2:a]: ((((less @ B2) @ A2) => (A2 != B2))))).
% 2.85/1.53 thf(fact_3_local_Odual__order_Ostrict__trans, axiom, (! [B2:a,A2:a,C:a]: ((((less @ B2) @ A2) => (((less @ C) @ B2) => ((less @ C) @ A2)))))).
% 2.85/1.53 thf(fact_4_local_Oless__asym, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.85/1.53 thf(fact_5_local_Oless__asym_H, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (~ (((less @ B2) @ A2))))))).
% 2.85/1.53 thf(fact_6_local_Oless__imp__neq, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (X != Y))))).
% 2.85/1.53 thf(fact_7_local_Oless__imp__not__eq, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (X != Y))))).
% 2.85/1.53 thf(fact_8_local_Oless__imp__not__eq2, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (Y != X))))).
% 2.85/1.53 thf(fact_9_local_Oless__imp__not__less, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.85/1.53 thf(fact_10_local_Oless__imp__triv, axiom, (! [X:a,Y:a,P:$o]: ((((less @ X) @ Y) => (((less @ Y) @ X) => P))))).
% 2.85/1.53 thf(fact_11_local_Oless__irrefl, axiom, (! [X:a]: ((~ (((less @ X) @ X)))))).
% 2.85/1.53 thf(fact_12_local_Oless__linear, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) | ((X = Y) | ((less @ Y) @ X)))))).
% 2.85/1.53 thf(fact_13_local_Oless__not__sym, axiom, (! [X:a,Y:a]: ((((less @ X) @ Y) => (~ (((less @ Y) @ X))))))).
% 2.85/1.53 thf(fact_14_local_Oless__trans, axiom, (! [X:a,Y:a,Z:a]: ((((less @ X) @ Y) => (((less @ Y) @ Z) => ((less @ X) @ Z)))))).
% 2.85/1.53 thf(fact_15_local_Olinorder__cases, axiom, (! [X:a,Y:a]: (((~ (((less @ X) @ Y))) => ((X != Y) => ((less @ Y) @ X)))))).
% 2.85/1.53 thf(fact_16_local_OneqE, axiom, (! [X:a,Y:a]: (((X != Y) => ((~ (((less @ X) @ Y))) => ((less @ Y) @ X)))))).
% 2.85/1.53 thf(fact_17_local_Oneq__iff, axiom, (! [X:a,Y:a]: (((X != Y) = (((less @ X) @ Y) | ((less @ Y) @ X)))))).
% 2.85/1.53 thf(fact_18_local_Onot__less__iff__gr__or__eq, axiom, (! [X:a,Y:a]: (((~ (((less @ X) @ Y))) = (((less @ Y) @ X) | (X = Y)))))).
% 2.85/1.53 thf(fact_19_local_Oord__eq__less__trans, axiom, (! [A2:a,B2:a,C:a]: (((A2 = B2) => (((less @ B2) @ C) => ((less @ A2) @ C)))))).
% 2.85/1.53 thf(fact_20_local_Oord__less__eq__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less @ A2) @ B2) => ((B2 = C) => ((less @ A2) @ C)))))).
% 2.85/1.53 thf(fact_21_local_Oorder_Oasym, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (~ (((less @ B2) @ A2))))))).
% 2.85/1.53 thf(fact_22_local_Oorder_Oirrefl, axiom, (! [A2:a]: ((~ (((less @ A2) @ A2)))))).
% 2.85/1.53 thf(fact_23_local_Oorder_Ostrict__implies__not__eq, axiom, (! [A2:a,B2:a]: ((((less @ A2) @ B2) => (A2 != B2))))).
% 2.85/1.53 thf(fact_24_local_Oorder_Ostrict__trans, axiom, (! [A2:a,B2:a,C:a]: ((((less @ A2) @ B2) => (((less @ B2) @ C) => ((less @ A2) @ C)))))).
% 2.85/1.53 thf(fact_25_local_Orbt__greater__trans, axiom, (! [C2:$tType,X:a,Y:a,T:((rBT_Im246033960le_rbt @ a) @ C2)]: ((((less @ X) @ Y) => ((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ Y) @ T) => (((((rBT_Im1259024060reater @ a) @ C2) @ less) @ X) @ T)))))).
% 2.85/1.53 thf(fact_26__092_060open_062x_A_060_Ay_A_092_060and_062_Ay_A_092_060guillemotleft_062_124_Ad_092_060close_062, axiom, (((less @ x) @ y) & (((((rBT_Im1259024060reater @ a) @ b) @ less) @ y) @ d))).
% 2.85/1.53 thf(fact_27_local_Ostrict__mono__eq, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => (((F @ X) = (F @ Y)) = (X = Y))))))))).
% 2.85/1.53 thf(fact_28_assms_I4_J, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ k) @ r)).
% 2.85/1.53 thf(fact_29_combine__rbt__greater, axiom, (! [B:$tType,K:a,L:((rBT_Im246033960le_rbt @ a) @ B),R:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ L) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) => (((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ ((((rBT_Im1591839508ombine @ a) @ B) @ L) @ R))))))).
% 2.85/1.53 thf(fact_30__092_060open_062x_A_092_060guillemotleft_062_124_Ac_092_060close_062, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ x) @ c)).
% 2.85/1.53 thf(fact_31_local_Obalance__right__rbt__greater, axiom, (! [B:$tType,K:a,A2:((rBT_Im246033960le_rbt @ a) @ B),B2:((rBT_Im246033960le_rbt @ a) @ B),X:a,T:B]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ A2) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ B2) => (((less @ K) @ X) => (((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ ((((((rBT_Im1053358987_right @ a) @ B) @ A2) @ X) @ T) @ B2)))))))).
% 2.85/1.53 thf(fact_32_local_Obalance__left__rbt__greater, axiom, (! [B:$tType,K:a,A2:((rBT_Im246033960le_rbt @ a) @ B),B2:((rBT_Im246033960le_rbt @ a) @ B),X:a,T:B]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ A2) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ B2) => (((less @ K) @ X) => (((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ ((((((rBT_Im1278323832e_left @ a) @ B) @ A2) @ X) @ T) @ B2)))))))).
% 2.85/1.53 thf(fact_33_assms_I2_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ r)).
% 2.85/1.53 thf(fact_34_assms_I1_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ l)).
% 2.85/1.53 thf(fact_35__092_060open_062x_A_060_Ak_A_092_060and_062_Ak_A_092_060guillemotleft_062_124_Ac_092_060close_062, axiom, (((less @ x) @ k) & (((((rBT_Im1259024060reater @ a) @ b) @ less) @ k) @ c))).
% 2.85/1.53 thf(fact_36_local_Orbt__less__trans, axiom, (! [C2:$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)))))).
% 2.85/1.53 thf(fact_37_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)))))).
% 2.85/1.53 thf(fact_38_local_Olexordp__eq__linear, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ Ys) | ((((lexordp_eq @ a) @ less) @ Ys) @ Xs))))).
% 2.85/1.53 thf(fact_39_local_Olexordp__eq__refl, axiom, (! [Xs:(list @ a)]: (((((lexordp_eq @ a) @ less) @ Xs) @ Xs)))).
% 2.85/1.53 thf(fact_40_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)))))).
% 2.85/1.53 thf(fact_41_assms_I3_J, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ k) @ l)).
% 2.85/1.53 thf(fact_42_combine__rbt__less, axiom, (! [B:$tType,K:a,L:((rBT_Im246033960le_rbt @ a) @ B),R:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ R) => (((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ ((((rBT_Im1591839508ombine @ a) @ B) @ L) @ R))))))).
% 2.85/1.53 thf(fact_43_local_Obalance__left__rbt__less, axiom, (! [B:$tType,K:a,A2:((rBT_Im246033960le_rbt @ a) @ B),B2:((rBT_Im246033960le_rbt @ a) @ B),X:a,T:B]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ A2) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ B2) => (((less @ X) @ K) => (((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ ((((((rBT_Im1278323832e_left @ a) @ B) @ A2) @ X) @ T) @ B2)))))))).
% 2.85/1.53 thf(fact_44_local_Obalance__right__rbt__less, axiom, (! [B:$tType,K:a,A2:((rBT_Im246033960le_rbt @ a) @ B),B2:((rBT_Im246033960le_rbt @ a) @ B),X:a,T:B]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ A2) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ B2) => (((less @ X) @ K) => (((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ ((((((rBT_Im1053358987_right @ a) @ B) @ A2) @ X) @ T) @ B2)))))))).
% 2.85/1.53 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.85/1.53 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 2.85/1.53 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.85/1.53 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.85/1.53 thf(fact_49_local_Obalance__left__rbt__sorted, axiom, (! [B:$tType,L:((rBT_Im246033960le_rbt @ a) @ B),R:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ R) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((((((rBT_Im1278323832e_left @ a) @ B) @ L) @ K) @ V) @ R))))))))).
% 2.85/1.53 thf(fact_50_local_Obalance__right__rbt__sorted, axiom, (! [B:$tType,L:((rBT_Im246033960le_rbt @ a) @ B),R:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ R) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((((((rBT_Im1053358987_right @ a) @ B) @ L) @ K) @ V) @ R))))))))).
% 2.85/1.53 thf(fact_51_local_Orbt__insertw__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),F:(B > (B > B)),K:a,V:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ (((((((rBT_Im241132701t_with @ a) @ B) @ less) @ F) @ K) @ V) @ T)))))).
% 2.85/1.53 thf(fact_52_local_Orbt__insert__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((((((rBT_Im852463031insert @ a) @ B) @ less) @ K) @ V) @ T)))))).
% 2.85/1.53 thf(fact_53_local_Orbt__insertwk__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),F:(a > (B > (B > B))),K:a,X:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ (((((((rBT_Im627674146th_key @ a) @ B) @ less) @ F) @ K) @ X) @ T)))))).
% 2.85/1.53 thf(fact_54_local_Ois__rbt__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ T))))).
% 2.85/1.53 thf(fact_55__C2_C, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ x) @ ((((rBT_Im1591839508ombine @ a) @ b) @ b2) @ c))).
% 2.85/1.53 thf(fact_56__C3_C, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ y) @ ((((rBT_Im1591839508ombine @ a) @ b) @ b2) @ c))).
% 2.85/1.53 thf(fact_57__092_060open_062k_A_060_Ay_A_092_060and_062_Ab_A_124_092_060guillemotleft_062_Ak_092_060close_062, axiom, (((less @ k) @ y) & (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ k) @ b2))).
% 2.85/1.53 thf(fact_58__092_060open_062b_A_124_092_060guillemotleft_062_Ay_092_060close_062, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ y) @ b2)).
% 2.85/1.53 thf(fact_59_local_Opaint__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),C:rBT_Im1923302023_color]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((((rBT_Im945281971_paint @ a) @ B) @ C) @ T)))))).
% 2.85/1.53 thf(fact_60_local_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ C) @ L) @ K) @ V) @ R)) = ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) & ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) & (((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) & ((((rBT_Im759614907sorted @ a) @ B) @ less) @ R)))))))).
% 2.85/1.53 thf(fact_61_local_Obalance__rbt__sorted, axiom, (! [B:$tType,L:((rBT_Im246033960le_rbt @ a) @ B),R:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ R) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((((((rBT_Im1648453169alance @ a) @ B) @ L) @ K) @ V) @ R))))))))).
% 2.85/1.53 thf(fact_62_local_Orbt__insertwk__is__rbt, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),F:(a > (B > (B > B))),K:a,X:B]: ((((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ T) => ((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ (((((((rBT_Im627674146th_key @ a) @ B) @ less) @ F) @ K) @ X) @ T)))))).
% 2.85/1.53 thf(fact_63_local_Orbt__insert__is__rbt, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B]: ((((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ T) => ((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ ((((((rBT_Im852463031insert @ a) @ B) @ less) @ K) @ V) @ T)))))).
% 2.85/1.53 thf(fact_64_local_Orbt__insertw__is__rbt, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),F:(B > (B > B)),K:a,V:B]: ((((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ T) => ((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ (((((((rBT_Im241132701t_with @ a) @ B) @ less) @ F) @ K) @ V) @ T)))))).
% 2.85/1.53 thf(fact_65_rbt_Oinject, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B),Y21:rBT_Im1923302023_color,Y22:((rBT_Im246033960le_rbt @ A) @ B),Y23:A,Y24:B,Y25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25) = (((((((rBT_Im480247531Branch @ A) @ B) @ Y21) @ Y22) @ Y23) @ Y24) @ Y25)) = ((X21 = Y21) & ((X22 = Y22) & ((X23 = Y23) & ((X24 = Y24) & (X25 = Y25))))))))).
% 2.85/1.53 thf(fact_66_local_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,K:a,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ a) @ C2),Kt:a,V:C2,Rt:((rBT_Im246033960le_rbt @ a) @ C2)]: (((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ (((((((rBT_Im480247531Branch @ a) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((less @ K) @ Kt) & ((((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ Lt) & (((((rBT_Im1259024060reater @ a) @ C2) @ less) @ K) @ Rt))))))).
% 2.85/1.53 thf(fact_67_local_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,K:a,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ a) @ C2),Kt:a,V:C2,Rt:((rBT_Im246033960le_rbt @ a) @ C2)]: (((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ (((((((rBT_Im480247531Branch @ a) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((less @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ a) @ C2) @ less) @ K) @ Rt))))))).
% 2.85/1.53 thf(fact_68_local_Obalance__rbt__greater, axiom, (! [B:$tType,V:a,A2:((rBT_Im246033960le_rbt @ a) @ B),K:a,X:B,B2:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ ((((((rBT_Im1648453169alance @ a) @ B) @ A2) @ K) @ X) @ B2)) = ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ A2) & ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ B2) & ((less @ V) @ K))))))).
% 2.85/1.53 thf(fact_69_local_Obalance__rbt__less, axiom, (! [B:$tType,V:a,A2:((rBT_Im246033960le_rbt @ a) @ B),K:a,X:B,B2:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ ((((((rBT_Im1648453169alance @ a) @ B) @ A2) @ K) @ X) @ B2)) = ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ A2) & ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ B2) & ((less @ K) @ V))))))).
% 2.85/1.53 thf(fact_70_local_Opaint__rbt__greater, axiom, (! [B:$tType,V:a,C:rBT_Im1923302023_color,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ ((((rBT_Im945281971_paint @ a) @ B) @ C) @ T)) = (((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ T))))).
% 2.85/1.53 thf(fact_71_local_Opaint__rbt__less, axiom, (! [B:$tType,V:a,C:rBT_Im1923302023_color,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ ((((rBT_Im945281971_paint @ a) @ B) @ C) @ T)) = (((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ T))))).
% 2.85/1.53 thf(fact_72_Empty, axiom, (((((rBT_Im1591839508ombine @ a) @ b) @ b2) @ c) = ((rBT_Im418718756_Empty @ a) @ b))).
% 2.85/1.53 thf(fact_73_paint_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,C:rBT_Im1923302023_color,Uu:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im945281971_paint @ A) @ B) @ C) @ (((((((rBT_Im480247531Branch @ A) @ B) @ Uu) @ L) @ K) @ V) @ R)) = (((((((rBT_Im480247531Branch @ A) @ B) @ C) @ L) @ K) @ V) @ R))))).
% 2.85/1.53 thf(fact_74_ord_Orbt__greater__simps_I2_J, axiom, (! [C2:$tType,A:$tType,Less:(A > (A > $o)),K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((((rBT_Im1259024060reater @ A) @ C2) @ Less) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((Less @ K) @ Kt) & ((((((rBT_Im1259024060reater @ A) @ C2) @ Less) @ K) @ Lt) & (((((rBT_Im1259024060reater @ A) @ C2) @ Less) @ K) @ Rt))))))).
% 2.85/1.53 thf(fact_75_ord_Orbt__less__simps_I2_J, axiom, (! [C2:$tType,A:$tType,Less:(A > (A > $o)),K:A,C:rBT_Im1923302023_color,Lt:((rBT_Im246033960le_rbt @ A) @ C2),Kt:A,V:C2,Rt:((rBT_Im246033960le_rbt @ A) @ C2)]: (((((((rBT_Im2075124343t_less @ A) @ C2) @ Less) @ K) @ (((((((rBT_Im480247531Branch @ A) @ C2) @ C) @ Lt) @ Kt) @ V) @ Rt)) = (((Less @ Kt) @ K) & ((((((rBT_Im2075124343t_less @ A) @ C2) @ Less) @ K) @ Lt) & (((((rBT_Im2075124343t_less @ A) @ C2) @ Less) @ K) @ Rt))))))).
% 2.85/1.53 thf(fact_76_ord_Obalance__rbt__greater, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),V:A,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ V) @ ((((((rBT_Im1648453169alance @ A) @ B) @ A2) @ K) @ X) @ B2)) = ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ V) @ A2) & ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ V) @ B2) & ((Less @ V) @ K))))))).
% 2.85/1.53 thf(fact_77_ord_Obalance__rbt__less, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),V:A,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ V) @ ((((((rBT_Im1648453169alance @ A) @ B) @ A2) @ K) @ X) @ B2)) = ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ V) @ A2) & ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ V) @ B2) & ((Less @ K) @ V))))))).
% 2.85/1.53 thf(fact_78_ord_Opaint__rbt__sorted, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),T:((rBT_Im246033960le_rbt @ A) @ B),C:rBT_Im1923302023_color]: ((((((rBT_Im759614907sorted @ A) @ B) @ Less) @ T) => ((((rBT_Im759614907sorted @ A) @ B) @ Less) @ ((((rBT_Im945281971_paint @ A) @ B) @ C) @ T)))))).
% 2.85/1.53 thf(fact_79_ord_Opaint__rbt__greater, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),V:A,C:rBT_Im1923302023_color,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ V) @ ((((rBT_Im945281971_paint @ A) @ B) @ C) @ T)) = (((((rBT_Im1259024060reater @ A) @ B) @ Less) @ V) @ T))))).
% 2.85/1.53 thf(fact_80_ord_Opaint__rbt__less, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),V:A,C:rBT_Im1923302023_color,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ V) @ ((((rBT_Im945281971_paint @ A) @ B) @ C) @ T)) = (((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ V) @ T))))).
% 2.85/1.53 thf(fact_81_ord_Orbt__sorted_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),C:rBT_Im1923302023_color,L:((rBT_Im246033960le_rbt @ A) @ B),K:A,V:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im759614907sorted @ A) @ B) @ Less) @ (((((((rBT_Im480247531Branch @ A) @ B) @ C) @ L) @ K) @ V) @ R)) = ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ L) & ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ R) & (((((rBT_Im759614907sorted @ A) @ B) @ Less) @ L) & ((((rBT_Im759614907sorted @ A) @ B) @ Less) @ R)))))))).
% 2.85/1.53 thf(fact_82_ord_Ois__rbt__rbt__sorted, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),T:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im862805236is_rbt @ A) @ B) @ Less) @ T) => ((((rBT_Im759614907sorted @ A) @ B) @ Less) @ T))))).
% 2.85/1.53 thf(fact_83__C4_Ohyps_C, axiom, (((((rBT_Im759614907sorted @ a) @ b) @ less) @ b2) => (((((rBT_Im759614907sorted @ a) @ b) @ less) @ c) => ((((((rBT_Im2075124343t_less @ a) @ b) @ less) @ k) @ b2) => ((((((rBT_Im1259024060reater @ a) @ b) @ less) @ k) @ c) => ((((rBT_Im759614907sorted @ a) @ b) @ less) @ ((((rBT_Im1591839508ombine @ a) @ b) @ b2) @ c))))))).
% 2.85/1.53 thf(fact_84_local_Oins__rbt__sorted, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B),F:(a > (B > (B > B))),K:a,X:B]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((rBT_Im759614907sorted @ a) @ B) @ less) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ X) @ T)))))).
% 2.85/1.53 thf(fact_85_local_Ostrict__monoD, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B),X:a,Y:a]: ((((((strict_mono @ a) @ B) @ less) @ F) => (((less @ X) @ Y) => (((ord_less @ B) @ (F @ X)) @ (F @ Y)))))))))).
% 2.85/1.53 thf(fact_86_local_Ostrict__monoI, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B)]: (((! [X3:a,Y2:a]: ((((less @ X3) @ Y2) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y2))))) => ((((strict_mono @ a) @ B) @ less) @ F)))))))).
% 2.85/1.53 thf(fact_87_local_Ostrict__mono__def, axiom, (! [B:$tType]: ((((order @ B) @ (type2 @ B)) => (! [F:(a > B)]: ((((((strict_mono @ a) @ B) @ less) @ F) = (! [X2:a,Y3:a]: ((((less @ X2) @ Y3) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y3)))))))))))).
% 2.85/1.53 thf(fact_88_local_Ostrict__mono__less, axiom, (! [B:$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))))))))).
% 2.85/1.53 thf(fact_89_local_Olexordp__eq_ONil, axiom, (! [Ys:(list @ a)]: (((((lexordp_eq @ a) @ less) @ (nil @ a)) @ Ys)))).
% 2.85/1.53 thf(fact_90_local_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType]: (((((rBT_Im759614907sorted @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.85/1.53 thf(fact_91_local_OEmpty__is__rbt, axiom, (! [B:$tType]: (((((rBT_Im862805236is_rbt @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.85/1.53 thf(fact_92_local_Orbt__insert__def, axiom, (! [B:$tType]: (((((rBT_Im852463031insert @ a) @ B) @ less) = ((((rBT_Im627674146th_key @ a) @ B) @ less) @ (^ [Uu2:a,Uv:B,Nv:B]: (Nv))))))).
% 2.85/1.53 thf(fact_93_local_Orbt__insertw__def, axiom, (! [B:$tType,F:(B > (B > B))]: ((((((rBT_Im241132701t_with @ a) @ B) @ less) @ F) = ((((rBT_Im627674146th_key @ a) @ B) @ less) @ (^ [Uu2:a]: (F))))))).
% 2.85/1.53 thf(fact_94_local_Olexordp__eq__simps_I1_J, axiom, (! [Ys:(list @ a)]: (((((lexordp_eq @ a) @ less) @ (nil @ a)) @ Ys)))).
% 2.85/1.53 thf(fact_95_local_Olexordp__eq__simps_I2_J, axiom, (! [Xs:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ Xs) @ (nil @ a)) = (Xs = (nil @ a)))))).
% 2.85/1.53 thf(fact_96_local_Oins__rbt__greater, axiom, (! [B:$tType,V:a,F:(a > (B > (B > B))),K:a,X:B,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ X) @ T)) = ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ V) @ T) & ((less @ V) @ K)))))).
% 2.85/1.53 thf(fact_97_local_Oins__rbt__less, axiom, (! [B:$tType,V:a,F:(a > (B > (B > B))),K:a,X:B,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ X) @ T)) = ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ V) @ T) & ((less @ K) @ V)))))).
% 2.85/1.53 thf(fact_98_local_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,K:a]: ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.85/1.53 thf(fact_99_local_Orbt__less__simps_I1_J, axiom, (! [B:$tType,K:a]: ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ ((rBT_Im418718756_Empty @ a) @ B))))).
% 2.85/1.53 thf(fact_100_rbt_Odistinct_I1_J, axiom, (! [B:$tType,A:$tType,X21:rBT_Im1923302023_color,X22:((rBT_Im246033960le_rbt @ A) @ B),X23:A,X24:B,X25:((rBT_Im246033960le_rbt @ A) @ B)]: ((((rBT_Im418718756_Empty @ A) @ B) != (((((((rBT_Im480247531Branch @ A) @ B) @ X21) @ X22) @ X23) @ X24) @ X25))))).
% 2.85/1.53 thf(fact_101_rbt_Oinduct, axiom, (! [B:$tType,A:$tType,P:(((rBT_Im246033960le_rbt @ A) @ B) > $o),Rbt:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ ((rBT_Im418718756_Empty @ A) @ B)) => ((! [X1:rBT_Im1923302023_color,X26:((rBT_Im246033960le_rbt @ A) @ B),X32:A,X4:B,X5:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ X26) => ((P @ X5) => (P @ (((((((rBT_Im480247531Branch @ A) @ B) @ X1) @ X26) @ X32) @ X4) @ X5)))))) => (P @ Rbt)))))).
% 2.85/1.53 thf(fact_102_rbt_Oexhaust, axiom, (! [B:$tType,A:$tType,Y:((rBT_Im246033960le_rbt @ A) @ B)]: (((Y != ((rBT_Im418718756_Empty @ A) @ B)) => (~ ((! [X212:rBT_Im1923302023_color,X222:((rBT_Im246033960le_rbt @ A) @ B),X232:A,X242:B,X252:((rBT_Im246033960le_rbt @ A) @ B)]: ((Y != (((((((rBT_Im480247531Branch @ A) @ B) @ X212) @ X222) @ X232) @ X242) @ X252)))))))))).
% 2.85/1.53 thf(fact_103_ord_Orbt__sorted_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: (((((rBT_Im759614907sorted @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_104_ord_Orbt__greater__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A]: ((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_105_ord_Orbt__less__simps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A]: ((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_106_ord_Orbt__insert__def, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im852463031insert @ A) @ B) = (^ [Less2:(A > (A > $o))]: (((((rBT_Im627674146th_key @ A) @ B) @ Less2) @ (^ [Uu2:A,Uv:B,Nv:B]: (Nv))))))))).
% 2.85/1.53 thf(fact_107_ord_Orbt__insertw__def, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im241132701t_with @ A) @ B) = (^ [Less2:(A > (A > $o)),F2:(B > (B > B))]: (((((rBT_Im627674146th_key @ A) @ B) @ Less2) @ (^ [Uu2:A]: (F2))))))))).
% 2.85/1.53 thf(fact_108_paint_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,C:rBT_Im1923302023_color]: ((((((rBT_Im945281971_paint @ A) @ B) @ C) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_109_balance__left_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,K:A,X:B]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_110_combine_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,X:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im1591839508ombine @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ X) = X)))).
% 2.85/1.53 thf(fact_111_balance__right_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,K:A,X:B]: ((((((((rBT_Im1053358987_right @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_112_ord_OEmpty__is__rbt, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: (((((rBT_Im862805236is_rbt @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_113_combine_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im1591839508ombine @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ Va) @ Vb) @ Vc) @ Vd)) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ Va) @ Vb) @ Vc) @ Vd))))).
% 2.85/1.53 thf(fact_114__C4_Oprems_C_I4_J, axiom, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ k) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ c) @ y) @ w) @ d))).
% 2.85/1.53 thf(fact_115__C4_Oprems_C_I2_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ c) @ y) @ w) @ d))).
% 2.85/1.53 thf(fact_116_local_OgreaterThan__def, axiom, (! [L:a]: (((((set_greaterThan @ a) @ less) @ L) = ((collect @ a) @ (less @ L)))))).
% 2.85/1.53 thf(fact_117_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.85/1.53 thf(fact_118_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys)))).
% 2.85/1.53 thf(fact_119__C4_Oprems_C_I3_J, axiom, (((((rBT_Im2075124343t_less @ a) @ b) @ less) @ k) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ a2) @ x) @ v) @ b2))).
% 2.85/1.53 thf(fact_120_local_Orbt__ins_Osimps_I2_J, axiom, (! [B:$tType,K:a,X:a,F:(a > (B > (B > B))),V:B,L:((rBT_Im246033960le_rbt @ a) @ B),Y:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: (((((less @ K) @ X) => ((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ Y) @ R)) = ((((((rBT_Im1648453169alance @ a) @ B) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ L)) @ X) @ Y) @ R))) & ((~ (((less @ K) @ X))) => ((((less @ X) @ K) => ((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ Y) @ R)) = ((((((rBT_Im1648453169alance @ a) @ B) @ L) @ X) @ Y) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ R)))) & ((~ (((less @ X) @ K))) => ((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ (((F @ K) @ Y) @ V)) @ R))))))))).
% 2.85/1.53 thf(fact_121_local_Orbt__insert__with__key__def, axiom, (! [B:$tType,F:(a > (B > (B > B))),K:a,V:B,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((((rBT_Im627674146th_key @ a) @ B) @ less) @ F) @ K) @ V) @ T) = ((((rBT_Im945281971_paint @ a) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ T)))))).
% 2.85/1.53 thf(fact_122__C4_Oprems_C_I1_J, axiom, ((((rBT_Im759614907sorted @ a) @ b) @ less) @ (((((((rBT_Im480247531Branch @ a) @ b) @ rBT_Impl_Mirabelle_B) @ a2) @ x) @ v) @ b2))).
% 2.85/1.53 thf(fact_123_local_OgreaterThan__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_greaterThan @ a) @ less) @ K)) = ((less @ K) @ I))))).
% 2.85/1.53 thf(fact_124_balance_Osimps_I23_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)))))).
% 2.85/1.53 thf(fact_125_balance_Osimps_I27_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vj:((rBT_Im246033960le_rbt @ A) @ B),Vk:A,Vl:B,Vm:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm))))))).
% 2.85/1.53 thf(fact_126_balance_Osimps_I29_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,V:rBT_Im1923302023_color,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vn:A,Vo:B,Vp:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vj:((rBT_Im246033960le_rbt @ A) @ B),Vk:A,Vl:B,Vm:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vn) @ Vo) @ Vp)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vn) @ Vo) @ Vp)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm))))))).
% 2.85/1.53 thf(fact_127_balance_Osimps_I39_J, axiom, (! [B:$tType,A:$tType,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_128_balance_Osimps_I43_J, axiom, (! [B:$tType,A:$tType,Vj:((rBT_Im246033960le_rbt @ A) @ B),Vk:A,Vl:B,Vm:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm)) @ Vf) @ Vg) @ Vh)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm)) @ Vf) @ Vg) @ Vh)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_129_balance_Osimps_I45_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vj:((rBT_Im246033960le_rbt @ A) @ B),Vk:A,Vl:B,Vm:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vn:A,Vo:B,Vp:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vn) @ Vo) @ Vp))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vn) @ Vo) @ Vp))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_130_balance_Osimps_I14_J, axiom, (! [B:$tType,A:$tType,S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_131_balance_Osimps_I15_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_132_balance_Osimps_I16_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_133_balance_Osimps_I17_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,V:rBT_Im1923302023_color,Vb:A,Vc:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_134_balance_Osimps_I18_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,V:rBT_Im1923302023_color,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_135_balance_Osimps_I19_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vf:((rBT_Im246033960le_rbt @ A) @ B),Vg:A,Vh:B,Vi:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi))))))).
% 2.85/1.53 thf(fact_136_balance_Osimps_I20_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,V:rBT_Im1923302023_color,Vb:A,Vc:B,Vf:((rBT_Im246033960le_rbt @ A) @ B),Vg:A,Vh:B,Vi:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi))))))).
% 2.85/1.53 thf(fact_137_balance_Osimps_I21_J, axiom, (! [B:$tType,A:$tType,S:A,T:B,V:rBT_Im1923302023_color,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vj:A,Vk:B,Vl:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vf:((rBT_Im246033960le_rbt @ A) @ B),Vg:A,Vh:B,Vi:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vj) @ Vk) @ Vl)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vj) @ Vk) @ Vl)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi))))))).
% 2.85/1.53 thf(fact_138_balance_Osimps_I22_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_139_balance_Osimps_I24_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_140_balance_Osimps_I25_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,V:rBT_Im1923302023_color,Vf:A,Vg:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_141_balance_Osimps_I26_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,V:rBT_Im1923302023_color,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vj:A,Vk:B,Vl:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vj) @ Vk) @ Vl)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vj) @ Vk) @ Vl)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_142_balance_Osimps_I28_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,V:rBT_Im1923302023_color,Vf:A,Vg:B,Vj:((rBT_Im246033960le_rbt @ A) @ B),Vk:A,Vl:B,Vm:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm))))))).
% 2.85/1.53 thf(fact_143_balance_Osimps_I32_J, axiom, (! [B:$tType,A:$tType,Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_144_balance_Osimps_I33_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vb:A,Vc:B,S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_145_balance_Osimps_I34_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vb:A,Vc:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_146_balance_Osimps_I35_J, axiom, (! [B:$tType,A:$tType,Vf:((rBT_Im246033960le_rbt @ A) @ B),Vg:A,Vh:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi)) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi)) @ Vb) @ Vc) @ Vd)) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_147_balance_Osimps_I36_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vf:((rBT_Im246033960le_rbt @ A) @ B),Vg:A,Vh:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi)) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_148_balance_Osimps_I37_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vf:((rBT_Im246033960le_rbt @ A) @ B),Vg:A,Vh:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vj:A,Vk:B,Vl:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vj) @ Vk) @ Vl))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vf) @ Vg) @ Vh) @ Vi)) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vj) @ Vk) @ Vl))) @ S) @ T) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_149_balance_Osimps_I40_J, axiom, (! [B:$tType,A:$tType,Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ Vh)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ Vh)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_150_balance_Osimps_I41_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vf:A,Vg:B,S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_151_balance_Osimps_I42_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vf:A,Vg:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vj:A,Vk:B,Vl:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vj) @ Vk) @ Vl))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vi) @ Vj) @ Vk) @ Vl))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_152_balance_Osimps_I44_J, axiom, (! [B:$tType,A:$tType,V:rBT_Im1923302023_color,Vj:((rBT_Im246033960le_rbt @ A) @ B),Vk:A,Vl:B,Vm:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,S:A,T:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Vj) @ Vk) @ Vl) @ Vm)) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_153_balance__left_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_154_balance__right_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,K:A,X:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1053358987_right @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_155_ord_Orbt__ins_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A,X:A,F:(A > (B > (B > B))),V:B,L:((rBT_Im246033960le_rbt @ A) @ B),Y:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((Less @ K) @ X) => ((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ Y) @ R)) = ((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ L)) @ X) @ Y) @ R))) & ((~ (((Less @ K) @ X))) => ((((Less @ X) @ K) => ((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ Y) @ R)) = ((((((rBT_Im1648453169alance @ A) @ B) @ L) @ X) @ Y) @ (((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ R)))) & ((~ (((Less @ X) @ K))) => ((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ X) @ (((F @ K) @ Y) @ V)) @ R))))))))).
% 2.85/1.53 thf(fact_156_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ Xs) @ Xs)))).
% 2.85/1.53 thf(fact_157_ord_Orbt__insert__with__key__def, axiom, (! [B:$tType,A:$tType]: ((((rBT_Im627674146th_key @ A) @ B) = (^ [Less2:(A > (A > $o)),F2:(A > (B > (B > B))),K2:A,V2:B,T2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((rBT_Im945281971_paint @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less2) @ F2) @ K2) @ V2) @ T2)))))))).
% 2.85/1.53 thf(fact_158_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys)))).
% 2.85/1.53 thf(fact_159_local_OlessThan__def, axiom, (! [U:a]: (((((set_lessThan @ a) @ less) @ U) = ((collect @ a) @ (^ [X2:a]: (((less @ X2) @ U)))))))).
% 2.85/1.53 thf(fact_160_local_Orbt__ins_Osimps_I1_J, axiom, (! [B:$tType,F:(a > (B > (B > B))),K:a,V:B]: (((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ ((rBT_Im418718756_Empty @ a) @ B)) = (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ ((rBT_Im418718756_Empty @ a) @ B)) @ K) @ V) @ ((rBT_Im418718756_Empty @ a) @ B)))))).
% 2.85/1.53 thf(fact_161_local_Orbt__ins_Oinduct, axiom, (! [B:$tType,P:((a > (B > (B > B))) > (a > (B > (((rBT_Im246033960le_rbt @ a) @ B) > $o)))),A0:(a > (B > (B > B))),A1:a,A22:B,A32:((rBT_Im246033960le_rbt @ a) @ B)]: (((! [F3:(a > (B > (B > B))),K3:a,V3:B]: (((((P @ F3) @ K3) @ V3) @ ((rBT_Im418718756_Empty @ a) @ B)))) => ((! [F3:(a > (B > (B > B))),K3:a,V3:B,L2:((rBT_Im246033960le_rbt @ a) @ B),X3:a,Y2:B,R2:((rBT_Im246033960le_rbt @ a) @ B)]: (((((less @ K3) @ X3) => ((((P @ F3) @ K3) @ V3) @ L2)) => (((~ (((less @ K3) @ X3))) => (((less @ X3) @ K3) => ((((P @ F3) @ K3) @ V3) @ R2))) => ((((P @ F3) @ K3) @ V3) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_B) @ L2) @ X3) @ Y2) @ R2)))))) => ((! [F3:(a > (B > (B > B))),K3:a,V3:B,L2:((rBT_Im246033960le_rbt @ a) @ B),X3:a,Y2:B,R2:((rBT_Im246033960le_rbt @ a) @ B)]: (((((less @ K3) @ X3) => ((((P @ F3) @ K3) @ V3) @ L2)) => (((~ (((less @ K3) @ X3))) => (((less @ X3) @ K3) => ((((P @ F3) @ K3) @ V3) @ R2))) => ((((P @ F3) @ K3) @ V3) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ L2) @ X3) @ Y2) @ R2)))))) => ((((P @ A0) @ A1) @ A22) @ A32))))))).
% 2.85/1.53 thf(fact_162_local_Orbt__lookup__balance, axiom, (! [B:$tType,L:((rBT_Im246033960le_rbt @ a) @ B),R:((rBT_Im246033960le_rbt @ a) @ B),K:a,V:B,X:a]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ L) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ R) => ((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ L) => ((((((rBT_Im1259024060reater @ a) @ B) @ less) @ K) @ R) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((((((rBT_Im1648453169alance @ a) @ B) @ L) @ K) @ V) @ R)) @ X) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_B) @ L) @ K) @ V) @ R)) @ X))))))))).
% 2.85/1.53 thf(fact_163_local_Orbt__ins_Osimps_I3_J, axiom, (! [B:$tType,K:a,X:a,F:(a > (B > (B > B))),V:B,L:((rBT_Im246033960le_rbt @ a) @ B),Y:B,R:((rBT_Im246033960le_rbt @ a) @ B)]: (((((less @ K) @ X) => ((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ L)) @ X) @ Y) @ R))) & ((~ (((less @ K) @ X))) => ((((less @ X) @ K) => ((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ (((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ R)))) & ((~ (((less @ X) @ K))) => ((((((((rBT_Im1756508336bt_ins @ a) @ B) @ less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ a) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ (((F @ K) @ Y) @ V)) @ R))))))))).
% 2.85/1.53 thf(fact_164_local_OlessThan__iff, axiom, (! [I:a,K:a]: (((((member @ a) @ I) @ (((set_lessThan @ a) @ less) @ K)) = ((less @ I) @ K))))).
% 2.85/1.53 thf(fact_165_local_Opaint__rbt__lookup, axiom, (! [B:$tType,C:rBT_Im1923302023_color,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((((rBT_Im945281971_paint @ a) @ B) @ C) @ T)) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T))))).
% 2.85/1.53 thf(fact_166_color_Oexhaust, axiom, (! [Y:rBT_Im1923302023_color]: (((Y != rBT_Impl_Mirabelle_R) => (Y = rBT_Impl_Mirabelle_B))))).
% 2.85/1.53 thf(fact_167_color_Oinduct, axiom, (! [P:(rBT_Im1923302023_color > $o),Color:rBT_Im1923302023_color]: (((P @ rBT_Impl_Mirabelle_R) => ((P @ rBT_Impl_Mirabelle_B) => (P @ Color)))))).
% 2.85/1.53 thf(fact_168_color_Odistinct_I1_J, axiom, (rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B)).
% 2.85/1.53 thf(fact_169_ord_Orbt__ins_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),K:A,X:A,F:(A > (B > (B > B))),V:B,L:((rBT_Im246033960le_rbt @ A) @ B),Y:B,R:((rBT_Im246033960le_rbt @ A) @ B)]: (((((Less @ K) @ X) => ((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ L)) @ X) @ Y) @ R))) & ((~ (((Less @ K) @ X))) => ((((Less @ X) @ K) => ((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ (((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ R)))) & ((~ (((Less @ X) @ K))) => ((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ Y) @ R)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L) @ X) @ (((F @ K) @ Y) @ V)) @ R))))))))).
% 2.85/1.53 thf(fact_170_ord_Opaint__rbt__lookup, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),C:rBT_Im1923302023_color,T:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ ((((rBT_Im945281971_paint @ A) @ B) @ C) @ T)) = ((((rBT_Im35466040lookup @ A) @ B) @ Less) @ T))))).
% 2.85/1.53 thf(fact_171_rbt__cases, axiom, (! [B:$tType,A:$tType,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((T != ((rBT_Im418718756_Empty @ A) @ B)) => ((! [L2:((rBT_Im246033960le_rbt @ A) @ B),K3:A,V3:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((T != (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L2) @ K3) @ V3) @ R2)))) => (~ ((! [L2:((rBT_Im246033960le_rbt @ A) @ B),K3:A,V3:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((T != (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L2) @ K3) @ V3) @ R2))))))))))).
% 2.85/1.53 thf(fact_172_combine_Oinduct, axiom, (! [B:$tType,A:$tType,P:(((rBT_Im246033960le_rbt @ A) @ B) > (((rBT_Im246033960le_rbt @ A) @ B) > $o)),A0:((rBT_Im246033960le_rbt @ A) @ B),A1:((rBT_Im246033960le_rbt @ A) @ B)]: (((! [X1:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ ((rBT_Im418718756_Empty @ A) @ B)) @ X1))) => ((! [V3:rBT_Im1923302023_color,Va2:((rBT_Im246033960le_rbt @ A) @ B),Vb2:A,Vc2:B,Vd2:((rBT_Im246033960le_rbt @ A) @ B)]: (((P @ (((((((rBT_Im480247531Branch @ A) @ B) @ V3) @ Va2) @ Vb2) @ Vc2) @ Vd2)) @ ((rBT_Im418718756_Empty @ A) @ B)))) => ((! [A4:((rBT_Im246033960le_rbt @ A) @ B),K3:A,X3:B,B3:((rBT_Im246033960le_rbt @ A) @ B),C3:((rBT_Im246033960le_rbt @ A) @ B),S2:A,Y2:B,D:((rBT_Im246033960le_rbt @ A) @ B)]: ((((P @ B3) @ C3) => ((P @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A4) @ K3) @ X3) @ B3)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ C3) @ S2) @ Y2) @ D))))) => ((! [A4:((rBT_Im246033960le_rbt @ A) @ B),K3:A,X3:B,B3:((rBT_Im246033960le_rbt @ A) @ B),C3:((rBT_Im246033960le_rbt @ A) @ B),S2:A,Y2:B,D:((rBT_Im246033960le_rbt @ A) @ B)]: ((((P @ B3) @ C3) => ((P @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A4) @ K3) @ X3) @ B3)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C3) @ S2) @ Y2) @ D))))) => ((! [Va2:((rBT_Im246033960le_rbt @ A) @ B),Vb2:A,Vc2:B,Vd2:((rBT_Im246033960le_rbt @ A) @ B),B3:((rBT_Im246033960le_rbt @ A) @ B),K3:A,X3:B,C3:((rBT_Im246033960le_rbt @ A) @ B)]: ((((P @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va2) @ Vb2) @ Vc2) @ Vd2)) @ B3) => ((P @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va2) @ Vb2) @ Vc2) @ Vd2)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B3) @ K3) @ X3) @ C3))))) => ((! [A4:((rBT_Im246033960le_rbt @ A) @ B),K3:A,X3:B,B3:((rBT_Im246033960le_rbt @ A) @ B),Va2:((rBT_Im246033960le_rbt @ A) @ B),Vb2:A,Vc2:B,Vd2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((P @ B3) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va2) @ Vb2) @ Vc2) @ Vd2)) => ((P @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A4) @ K3) @ X3) @ B3)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va2) @ Vb2) @ Vc2) @ Vd2))))) => ((P @ A0) @ A1)))))))))).
% 2.85/1.53 thf(fact_173_ord_Orbt__ins_Oinduct, axiom, (! [B:$tType,A:$tType,P:((A > (B > (B > B))) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))),Less:(A > (A > $o)),A0:(A > (B > (B > B))),A1:A,A22:B,A32:((rBT_Im246033960le_rbt @ A) @ B)]: (((! [F3:(A > (B > (B > B))),K3:A,V3:B]: (((((P @ F3) @ K3) @ V3) @ ((rBT_Im418718756_Empty @ A) @ B)))) => ((! [F3:(A > (B > (B > B))),K3:A,V3:B,L2:((rBT_Im246033960le_rbt @ A) @ B),X3:A,Y2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((Less @ K3) @ X3) => ((((P @ F3) @ K3) @ V3) @ L2)) => (((~ (((Less @ K3) @ X3))) => (((Less @ X3) @ K3) => ((((P @ F3) @ K3) @ V3) @ R2))) => ((((P @ F3) @ K3) @ V3) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L2) @ X3) @ Y2) @ R2)))))) => ((! [F3:(A > (B > (B > B))),K3:A,V3:B,L2:((rBT_Im246033960le_rbt @ A) @ B),X3:A,Y2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: (((((Less @ K3) @ X3) => ((((P @ F3) @ K3) @ V3) @ L2)) => (((~ (((Less @ K3) @ X3))) => (((Less @ X3) @ K3) => ((((P @ F3) @ K3) @ V3) @ R2))) => ((((P @ F3) @ K3) @ V3) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L2) @ X3) @ Y2) @ R2)))))) => ((((P @ A0) @ A1) @ A22) @ A32))))))).
% 2.85/1.53 thf(fact_174_balance_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,D2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ C) @ Y) @ Z) @ D2)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ D2)))))).
% 2.85/1.53 thf(fact_175_balance_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ W) @ X) @ B2)) @ S) @ T) @ C)) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))))))).
% 2.85/1.53 thf(fact_176_balance_Osimps_I7_J, axiom, (! [B:$tType,A:$tType,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C))) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))))))).
% 2.85/1.53 thf(fact_177_balance_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,D2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ C) @ Y) @ Z) @ D2))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ D2)))))).
% 2.85/1.53 thf(fact_178_balance_Osimps_I13_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C)) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Ve) @ Vf) @ Vg) @ Vh))))))).
% 2.85/1.53 thf(fact_179_balance__left_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,C:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ B2)) @ S) @ Y) @ C) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ K) @ X) @ B2)) @ S) @ Y) @ C))))).
% 2.85/1.53 thf(fact_180_ord_Orbt__ins_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o)),F:(A > (B > (B > B))),K:A,V:B]: (((((((((rBT_Im1756508336bt_ins @ A) @ B) @ Less) @ F) @ K) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ V) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_181_balance__left_Osimps_I7_J, axiom, (! [B:$tType,A:$tType,K:A,X:B,Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vb) @ Vc) @ Vd)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_182_balance__left_Osimps_I8_J, axiom, (! [B:$tType,A:$tType,K:A,X:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Ve) @ Vf) @ Vg) @ Vh)) @ Vb) @ Vc) @ Vd)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_183_balance__right_Osimps_I1_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,C:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1053358987_right @ A) @ B) @ A2) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ Y) @ C)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ B2) @ S) @ Y) @ C)))))).
% 2.85/1.53 thf(fact_184_combine_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),B2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,C:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im1591839508ombine @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ K) @ X) @ C)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((((rBT_Im1591839508ombine @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ B2)) @ K) @ X) @ C))))).
% 2.85/1.53 thf(fact_185_combine_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((rBT_Im1591839508ombine @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ B2)) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ ((((rBT_Im1591839508ombine @ A) @ B) @ B2) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))))))).
% 2.85/1.53 thf(fact_186_balance__right_Osimps_I7_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,K:A,X:B]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Va) @ Vb) @ Vc) @ ((rBT_Im418718756_Empty @ A) @ B))) @ K) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_187_balance__right_Osimps_I8_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Va) @ Vb) @ Vc) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Ve) @ Vf) @ Vg) @ Vh))) @ K) @ X) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_188_ord__class_Orbt__ins_Oinduct, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [P:((A > (B > (B > B))) > (A > (B > (((rBT_Im246033960le_rbt @ A) @ B) > $o)))),A0:(A > (B > (B > B))),A1:A,A22:B,A32:((rBT_Im246033960le_rbt @ A) @ B)]: (((! [F3:(A > (B > (B > B))),K3:A,V3:B]: (((((P @ F3) @ K3) @ V3) @ ((rBT_Im418718756_Empty @ A) @ B)))) => ((! [F3:(A > (B > (B > B))),K3:A,V3:B,L2:((rBT_Im246033960le_rbt @ A) @ B),X3:A,Y2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((ord_less @ A) @ K3) @ X3) => ((((P @ F3) @ K3) @ V3) @ L2)) => (((~ ((((ord_less @ A) @ K3) @ X3))) => ((((ord_less @ A) @ X3) @ K3) => ((((P @ F3) @ K3) @ V3) @ R2))) => ((((P @ F3) @ K3) @ V3) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ L2) @ X3) @ Y2) @ R2)))))) => ((! [F3:(A > (B > (B > B))),K3:A,V3:B,L2:((rBT_Im246033960le_rbt @ A) @ B),X3:A,Y2:B,R2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((ord_less @ A) @ K3) @ X3) => ((((P @ F3) @ K3) @ V3) @ L2)) => (((~ ((((ord_less @ A) @ K3) @ X3))) => ((((ord_less @ A) @ X3) @ K3) => ((((P @ F3) @ K3) @ V3) @ R2))) => ((((P @ F3) @ K3) @ V3) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ L2) @ X3) @ Y2) @ R2)))))) => ((((P @ A0) @ A1) @ A22) @ A32)))))))))).
% 2.85/1.53 thf(fact_189_balance_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ W) @ X) @ B2)) @ S) @ T) @ C)) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_190_balance_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C))) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_191_balance_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C))) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_192_balance_Osimps_I6_J, axiom, (! [B:$tType,A:$tType,W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C))) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))))))).
% 2.85/1.53 thf(fact_193_balance_Osimps_I8_J, axiom, (! [B:$tType,A:$tType,W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,D2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ C) @ Y) @ Z) @ D2))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ D2)))))).
% 2.85/1.53 thf(fact_194_balance_Osimps_I10_J, axiom, (! [B:$tType,A:$tType,W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C)) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_195_balance_Osimps_I11_J, axiom, (! [B:$tType,A:$tType,W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C)) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))))))).
% 2.85/1.53 thf(fact_196_balance_Osimps_I12_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),W:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,T:B,C:((rBT_Im246033960le_rbt @ A) @ B),Y:A,Z:B]: ((((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ B2) @ S) @ T) @ C)) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ W) @ X) @ B2)) @ S) @ T) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ Y) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_197_balance__left_Osimps_I11_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vj:A,Vk:B,Vl:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Vi) @ Vj) @ Vk) @ Vl)) @ Vf) @ Vg) @ Vh)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_198_balance__left_Osimps_I10_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,Vf:A,Vg:B,Vh:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((rBT_Im418718756_Empty @ A) @ B)) @ Vf) @ Vg) @ Vh)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_199_balance__right_Osimps_I11_J, axiom, (! [B:$tType,A:$tType,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,Vi:((rBT_Im246033960le_rbt @ A) @ B),Vj:A,Vk:B,Vl:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Ve) @ Vf) @ Vg) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Vi) @ Vj) @ Vk) @ Vl))) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_200_balance__right_Osimps_I10_J, axiom, (! [B:$tType,A:$tType,Ve:((rBT_Im246033960le_rbt @ A) @ B),Vf:A,Vg:B,K:A,X:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ Ve) @ Vf) @ Vg) @ ((rBT_Im418718756_Empty @ A) @ B))) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = ((rBT_Im418718756_Empty @ A) @ B))))).
% 2.85/1.53 thf(fact_201_balance__left_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,A2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,B2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ S) @ Y) @ B2)) = ((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ S) @ Y) @ B2)))))).
% 2.85/1.53 thf(fact_202_balance__right_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ K) @ X) @ B2)) @ S) @ Y) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = ((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ B2)) @ S) @ Y) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)))))).
% 2.85/1.53 thf(fact_203_balance__left_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,K:A,X:B,A2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,B2:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ S) @ Y) @ B2)) = ((((((rBT_Im1648453169alance @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ S) @ Y) @ B2)))))).
% 2.85/1.53 thf(fact_204_balance__right_Osimps_I2_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ K) @ X) @ B2)) @ S) @ Y) @ ((rBT_Im418718756_Empty @ A) @ B)) = ((((((rBT_Im1648453169alance @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ B2)) @ S) @ Y) @ ((rBT_Im418718756_Empty @ A) @ B)))))).
% 2.85/1.53 thf(fact_205_balance__left_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,A2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,B2:((rBT_Im246033960le_rbt @ A) @ B),T:A,Z:B,C:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ S) @ Y) @ B2)) @ T) @ Z) @ C)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) @ K) @ X) @ A2)) @ S) @ Y) @ ((((((rBT_Im1648453169alance @ A) @ B) @ B2) @ T) @ Z) @ ((((rBT_Im945281971_paint @ A) @ B) @ rBT_Impl_Mirabelle_R) @ C))))))).
% 2.85/1.53 thf(fact_206_balance__right_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,C:((rBT_Im246033960le_rbt @ A) @ B),T:A,Z:B,Va:((rBT_Im246033960le_rbt @ A) @ B),Vb:A,Vc:B,Vd:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ B2) @ S) @ Y) @ C))) @ T) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((((((rBT_Im1648453169alance @ A) @ B) @ ((((rBT_Im945281971_paint @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2)) @ K) @ X) @ B2)) @ S) @ Y) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ T) @ Z) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ Va) @ Vb) @ Vc) @ Vd))))))).
% 2.85/1.53 thf(fact_207_balance__left_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,K:A,X:B,A2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,B2:((rBT_Im246033960le_rbt @ A) @ B),T:A,Z:B,C:((rBT_Im246033960le_rbt @ A) @ B)]: ((((((((rBT_Im1278323832e_left @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ A2) @ S) @ Y) @ B2)) @ T) @ Z) @ C)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) @ X) @ A2)) @ S) @ Y) @ ((((((rBT_Im1648453169alance @ A) @ B) @ B2) @ T) @ Z) @ ((((rBT_Im945281971_paint @ A) @ B) @ rBT_Impl_Mirabelle_R) @ C))))))).
% 2.85/1.53 thf(fact_208_balance__right_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,A2:((rBT_Im246033960le_rbt @ A) @ B),K:A,X:B,B2:((rBT_Im246033960le_rbt @ A) @ B),S:A,Y:B,C:((rBT_Im246033960le_rbt @ A) @ B),T:A,Z:B]: ((((((((rBT_Im1053358987_right @ A) @ B) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2) @ K) @ X) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ B2) @ S) @ Y) @ C))) @ T) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B)) = (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_R) @ ((((((rBT_Im1648453169alance @ A) @ B) @ ((((rBT_Im945281971_paint @ A) @ B) @ rBT_Impl_Mirabelle_R) @ A2)) @ K) @ X) @ B2)) @ S) @ Y) @ (((((((rBT_Im480247531Branch @ A) @ B) @ rBT_Impl_Mirabelle_B) @ C) @ T) @ Z) @ ((rBT_Im418718756_Empty @ A) @ B))))))).
% 2.85/1.53 thf(fact_209_local_Oentries__rbt__lookup, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => (((((rBT_Im954575269ntries @ a) @ B) @ T1) = (((rBT_Im954575269ntries @ a) @ B) @ T22)) = (((((rBT_Im35466040lookup @ a) @ B) @ less) @ T1) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T22)))))))).
% 2.85/1.53 thf(fact_210_local_Oentries__eqI, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T1) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T22)) => ((((rBT_Im954575269ntries @ a) @ B) @ T1) = (((rBT_Im954575269ntries @ a) @ B) @ T22)))))))).
% 2.85/1.53 thf(fact_211_local_Orbt__lookup_Osimps_I1_J, axiom, (! [B:$tType,K:a]: (((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B)) @ K) = (none @ B))))).
% 2.85/1.53 thf(fact_212_local_Orbt__lookup__Empty, axiom, (! [B:$tType]: ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ ((rBT_Im418718756_Empty @ a) @ B)) = (^ [X2:a]: ((none @ B))))))).
% 2.85/1.53 thf(fact_213_local_Orbt__lookup__rbt__greater, axiom, (! [B:$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)))))).
% 2.85/1.53 thf(fact_214_local_Orbt__lookup__rbt__less, axiom, (! [B:$tType,K:a,T:((rBT_Im246033960le_rbt @ a) @ B)]: (((((((rBT_Im2075124343t_less @ a) @ B) @ less) @ K) @ T) => ((((((rBT_Im35466040lookup @ a) @ B) @ less) @ T) @ K) = (none @ B)))))).
% 2.85/1.53 thf(fact_215_entries_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: (((((rBT_Im954575269ntries @ A) @ B) @ ((rBT_Im418718756_Empty @ A) @ B)) = (nil @ ((product_prod @ A) @ B)))))).
% 2.85/1.53 thf(fact_216_ord_Orbt__lookup__Empty, axiom, (! [B:$tType,A:$tType,Less:(A > (A > $o))]: ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B)) = (^ [X2:A]: ((none @ B))))))).
% 2.85/1.53 thf(fact_217_ord_Orbt__lookup_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A]: (((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ ((rBT_Im418718756_Empty @ A) @ B)) @ K) = (none @ B))))).
% 2.85/1.53 thf(fact_218_ord_Orbt__lookup__rbt__greater, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im1259024060reater @ A) @ B) @ Less) @ K) @ T) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ T) @ K) = (none @ B)))))).
% 2.85/1.53 thf(fact_219_ord_Orbt__lookup__rbt__less, axiom, (! [A:$tType,B:$tType,Less:(A > (A > $o)),K:A,T:((rBT_Im246033960le_rbt @ A) @ B)]: (((((((rBT_Im2075124343t_less @ A) @ B) @ Less) @ K) @ T) => ((((((rBT_Im35466040lookup @ A) @ B) @ Less) @ T) @ K) = (none @ B)))))).
% 2.85/1.53 thf(fact_220_local_Omap__of__entries, axiom, (! [B:$tType,T:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T) => ((((map_of @ a) @ B) @ (((rBT_Im954575269ntries @ a) @ B) @ T)) = ((((rBT_Im35466040lookup @ a) @ B) @ less) @ T)))))).
% 2.85/1.53 thf(fact_221_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)))) => (! [Y2:a]: (((? [Ys2:(list @ a)]: ((A22 = (((cons @ a) @ Y2) @ Ys2)))) => (~ (((less @ X3) @ Y2))))))))) => (~ ((! [X3:a,Y2:a,Xs2:(list @ a)]: (((A1 = (((cons @ a) @ X3) @ Xs2)) => (! [Ys2:(list @ a)]: (((A22 = (((cons @ a) @ Y2) @ Ys2)) => ((~ (((less @ X3) @ Y2))) => ((~ (((less @ Y2) @ X3))) => (~ (((((lexordp_eq @ a) @ less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.85/1.53 thf(fact_222_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)))))))).
% 2.85/1.53 thf(fact_223_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)))))).
% 2.85/1.53 thf(fact_224_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)))))).
% 2.85/1.53 thf(fact_225_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,Y3:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y3) @ Ys3)) & ((less @ X2) @ Y3))))) | (? [X2:a,Y3:a,Xs3:(list @ a),Ys3:(list @ a)]: (((A1 = (((cons @ a) @ X2) @ Xs3)) & ((A22 = (((cons @ a) @ Y3) @ Ys3)) & ((~ (((less @ X2) @ Y3))) & ((~ (((less @ Y3) @ X2))) & ((((lexordp_eq @ a) @ less) @ Xs3) @ Ys3))))))))))))).
% 2.85/1.53 thf(fact_226_local_Olexordp__eq_Oinducts, axiom, (! [X12:(list @ a),X27:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp_eq @ a) @ less) @ X12) @ X27) => ((! [X1:(list @ a)]: (((P @ (nil @ a)) @ X1))) => ((! [X3:a,Y2:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((less @ X3) @ Y2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y2) @ Ys2))))) => ((! [X3:a,Y2:a,Xs2:(list @ a),Ys2:(list @ a)]: (((~ (((less @ X3) @ Y2))) => ((~ (((less @ Y2) @ X3))) => (((((lexordp_eq @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y2) @ Ys2)))))))) => ((P @ X12) @ X27)))))))).
% 2.85/1.53 thf(fact_227_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((Less @ X) @ Y) | ((~ (((Less @ Y) @ X))) & ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys))))))).
% 2.85/1.53 thf(fact_228_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A))))))).
% 2.85/1.53 thf(fact_229_local_Olexordp__eq__simps_I4_J, axiom, (! [X:a,Xs:(list @ a),Y:a,Ys:(list @ a)]: ((((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (((cons @ a) @ Y) @ Ys)) = (((less @ X) @ Y) | ((~ (((less @ Y) @ X))) & ((((lexordp_eq @ a) @ less) @ Xs) @ Ys))))))).
% 2.85/1.53 thf(fact_230_local_Olexordp__eq__simps_I3_J, axiom, (! [X:a,Xs:(list @ a)]: ((~ (((((lexordp_eq @ a) @ less) @ (((cons @ a) @ X) @ Xs)) @ (nil @ a))))))).
% 2.85/1.53 thf(fact_231_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Ys2:(list @ A)]: ((A22 != Ys2)))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y2:A]: (((? [Ys2:(list @ A)]: ((A22 = (((cons @ A) @ Y2) @ Ys2)))) => (~ (((Less @ X3) @ Y2))))))))) => (~ ((! [X3:A,Y2:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A22 = (((cons @ A) @ Y2) @ Ys2)) => ((~ (((Less @ X3) @ Y2))) => ((~ (((Less @ Y2) @ X3))) => (~ (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.85/1.53 thf(fact_232_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys3)))) | ((? [X2:A,Y3:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys3)) & ((Less2 @ X2) @ Y3))))) | (? [X2:A,Y3:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X2) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys3)) & ((~ (((Less2 @ X2) @ Y3))) & ((~ (((Less2 @ Y3) @ X2))) & ((((lexordp_eq @ A) @ Less2) @ Xs3) @ Ys3))))))))))))))).
% 2.85/1.53 thf(fact_233_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X12:(list @ A),X27:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less) @ X12) @ X27) => ((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [X3:A,Y2:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((Less @ X3) @ Y2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((! [X3:A,Y2:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X3) @ Y2))) => ((~ (((Less @ Y2) @ X3))) => (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))))) => ((P @ X12) @ X27)))))))).
% 2.85/1.53 thf(fact_234_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.85/1.53 thf(fact_235_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.85/1.53 thf(fact_236_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.85/1.53 thf(fact_237_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X26:(list @ A)]: (((P @ X26) => (P @ (((cons @ A) @ X1) @ X26))))) => (P @ List)))))).
% 2.85/1.53 thf(fact_238_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys3)))))))).
% 2.85/1.53 thf(fact_239_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X3) @ Xs2)) @ (nil @ B)))) => ((! [Y2:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y2) @ Ys2)))) => ((! [X3:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.85/1.53 thf(fact_240_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [V3:A,Va2:(list @ A)]: (((P @ (((cons @ A) @ V3) @ Va2)) @ (nil @ A)))) => ((! [X3:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((P @ A0) @ A1))))))).
% 2.85/1.53 thf(fact_241_transpose_Ocases, axiom, (! [A:$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))))))))))).
% 2.85/1.53 thf(fact_242_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X3:A]: ((X != (((cons @ A) @ X3) @ (nil @ A))))) => (~ ((! [X3:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 2.85/1.53 thf(fact_243_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y2:A,Xs2:(list @ A)]: ((((X3 = Y2) => (P @ (((cons @ A) @ X3) @ Xs2))) => (((X3 != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 2.85/1.53 thf(fact_244_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X3) @ Xs2)))))) => (P @ Xs))))))).
% 2.85/1.53 thf(fact_245_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F3:(A > B),X1:(list @ B)]: ((((P @ F3) @ (nil @ A)) @ X1))) => ((! [F3:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F3) @ As) @ (((cons @ B) @ (F3 @ A4)) @ Bs)) => (((P @ F3) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.85/1.53 thf(fact_246_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.85/1.53 thf(fact_247_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: ((((Less @ X) @ Y) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.85/1.53 thf(fact_248_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ (((Less @ X) @ Y))) => ((~ (((Less @ Y) @ X))) => (((((lexordp_eq @ A) @ Less) @ Xs) @ Ys) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))))).
% 2.85/1.53 thf(fact_249_local_Oset__entries__inject, axiom, (! [B:$tType,T1:((rBT_Im246033960le_rbt @ a) @ B),T22:((rBT_Im246033960le_rbt @ a) @ B)]: ((((((rBT_Im759614907sorted @ a) @ B) @ less) @ T1) => (((((rBT_Im759614907sorted @ a) @ B) @ less) @ T22) => ((((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T1)) = ((set2 @ ((product_prod @ a) @ B)) @ (((rBT_Im954575269ntries @ a) @ B) @ T22))) = ((((rBT_Im954575269ntries @ a) @ B) @ T1) = (((rBT_Im954575269ntries @ a) @ B) @ T22)))))))).
% 2.85/1.53 thf(fact_250_local_Olexordp__induct, axiom, (! [Xs:(list @ a),Ys:(list @ a),P:((list @ a) > ((list @ a) > $o))]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => ((! [Y2:a,Ys2:(list @ a)]: (((P @ (nil @ a)) @ (((cons @ a) @ Y2) @ Ys2)))) => ((! [X3:a,Xs2:(list @ a),Y2:a,Ys2:(list @ a)]: ((((less @ X3) @ Y2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ Y2) @ Ys2))))) => ((! [X3:a,Xs2:(list @ a),Ys2:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ a) @ X3) @ Xs2)) @ (((cons @ a) @ X3) @ Ys2)))))) => ((P @ Xs) @ Ys)))))))).
% 2.85/1.53 thf(fact_251_local_Olexordp__antisym, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) => (~ (((((lexordp @ a) @ less) @ Ys) @ Xs))))))).
% 2.85/1.53 thf(fact_252_local_Olexordp__irreflexive, axiom, (! [Xs:(list @ a)]: (((! [X3:a]: ((~ (((less @ X3) @ X3))))) => (~ (((((lexordp @ a) @ less) @ Xs) @ Xs))))))).
% 2.85/1.53 thf(fact_253_local_Olexordp__irreflexive_H, axiom, (! [Xs:(list @ a)]: ((~ (((((lexordp @ a) @ less) @ Xs) @ Xs)))))).
% 2.85/1.53 thf(fact_254_local_Olexordp__linear, axiom, (! [Xs:(list @ a),Ys:(list @ a)]: ((((((lexordp @ a) @ less) @ Xs) @ Ys) | ((Xs = Ys) | ((((lexordp @ a) @ less) @ Ys) @ Xs)))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Oorder, axiom, (! [A5:$tType,A6:$tType]: ((((order @ A6) @ (type2 @ A6)) => ((order @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.85/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A5:$tType,A6:$tType]: ((((ord @ A6) @ (type2 @ A6)) => ((ord @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Oorder_1, axiom, (! [A5:$tType]: (((order @ (set @ A5)) @ (type2 @ (set @ A5)))))).
% 2.85/1.53 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A5:$tType]: (((ord @ (set @ A5)) @ (type2 @ (set @ A5)))))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_3, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.85/1.53 thf(conj_0, conjecture, (((((rBT_Im1259024060reater @ a) @ b) @ less) @ x) @ d)).
% 2.85/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.F0zMB7Y9hR/DTF2DTF19201.p
% 2.85/1.53 ------------------------
% 2.85/1.57 ---- Cleaned THF ---
% 2.85/1.57 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor,type,
% 2.85/1.57 rBT_Im1923302023_color: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_RBT__Impl__Mirabelle__msmaddcmtr_Orbt,type,
% 2.85/1.57 rBT_Im246033960le_rbt: $tType > $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_Product__Type_Oprod,type,
% 2.85/1.57 product_prod: $tType > $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_Option_Ooption,type,
% 2.85/1.57 option: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_List_Olist,type,
% 2.85/1.57 list: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_Set_Oset,type,
% 2.85/1.57 set: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_t_itself,type,
% 2.85/1.57 itself: $tType > $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_tf_b,type,
% 2.85/1.57 b: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(ty_tf_a,type,
% 2.85/1.57 a: $tType ).
% 2.85/1.57
% 2.85/1.57 thf(sy_cl_HOL_Otype,type,
% 2.85/1.57 type:
% 2.85/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_cl_Orderings_Oord,type,
% 2.85/1.57 ord:
% 2.85/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_cl_Orderings_Oorder,type,
% 2.85/1.57 order:
% 2.85/1.57 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_OCons,type,
% 2.85/1.57 cons:
% 2.85/1.57 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_ONil,type,
% 2.85/1.57 nil:
% 2.85/1.57 !>[A: $tType] : ( list @ A ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Olist_Oset,type,
% 2.85/1.57 set2:
% 2.85/1.57 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Oord_Olexordp,type,
% 2.85/1.57 lexordp:
% 2.85/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_List_Oord_Olexordp__eq,type,
% 2.85/1.57 lexordp_eq:
% 2.85/1.57 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Map_Omap__of,type,
% 2.85/1.57 map_of:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( list @ ( product_prod @ A @ B ) ) > A > ( option @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Option_Ooption_ONone,type,
% 2.85/1.57 none:
% 2.85/1.57 !>[A: $tType] : ( option @ A ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.85/1.57 ord_less:
% 2.85/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Orderings_Oorder_Ostrict__mono,type,
% 2.85/1.57 strict_mono:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Pure_Otype,type,
% 2.85/1.57 type2:
% 2.85/1.57 !>[A: $tType] : ( itself @ A ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance,type,
% 2.85/1.57 rBT_Im1648453169alance:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance__left,type,
% 2.85/1.57 rBT_Im1278323832e_left:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Obalance__right,type,
% 2.85/1.57 rBT_Im1053358987_right:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OB,type,
% 2.85/1.57 rBT_Impl_Mirabelle_B: rBT_Im1923302023_color ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocolor_OR,type,
% 2.85/1.57 rBT_Impl_Mirabelle_R: rBT_Im1923302023_color ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Ocombine,type,
% 2.85/1.57 rBT_Im1591839508ombine:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oentries,type,
% 2.85/1.57 rBT_Im954575269ntries:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( rBT_Im246033960le_rbt @ A @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Ois__rbt,type,
% 2.85/1.57 rBT_Im862805236is_rbt:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__greater,type,
% 2.85/1.57 rBT_Im1259024060reater:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__ins,type,
% 2.85/1.57 rBT_Im1756508336bt_ins:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert,type,
% 2.85/1.57 rBT_Im852463031insert:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert__with,type,
% 2.85/1.57 rBT_Im241132701t_with:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__insert__with__key,type,
% 2.85/1.57 rBT_Im627674146th_key:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__less,type,
% 2.85/1.57 rBT_Im2075124343t_less:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > A > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__lookup,type,
% 2.85/1.57 rBT_Im35466040lookup:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > A > ( option @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Oord_Orbt__sorted,type,
% 2.85/1.57 rBT_Im759614907sorted:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Opaint,type,
% 2.85/1.57 rBT_Im945281971_paint:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OBranch,type,
% 2.85/1.57 rBT_Im480247531Branch:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( rBT_Im1923302023_color > ( rBT_Im246033960le_rbt @ A @ B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_RBT__Impl__Mirabelle__msmaddcmtr_Orbt_OEmpty,type,
% 2.85/1.57 rBT_Im418718756_Empty:
% 2.85/1.57 !>[A: $tType,B: $tType] : ( rBT_Im246033960le_rbt @ A @ B ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Set_OCollect,type,
% 2.85/1.57 collect:
% 2.85/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Set__Interval_Oord_OgreaterThan,type,
% 2.85/1.57 set_greaterThan:
% 2.85/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_Set__Interval_Oord_OlessThan,type,
% 2.85/1.57 set_lessThan:
% 2.85/1.57 !>[A: $tType] : ( ( A > A > $o ) > A > ( set @ A ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_c_member,type,
% 2.85/1.57 member:
% 2.85/1.57 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_a____,type,
% 2.85/1.57 a2: rBT_Im246033960le_rbt @ a @ b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_b____,type,
% 2.85/1.57 b2: rBT_Im246033960le_rbt @ a @ b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_c____,type,
% 2.85/1.57 c: rBT_Im246033960le_rbt @ a @ b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_d____,type,
% 2.85/1.57 d: rBT_Im246033960le_rbt @ a @ b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_k,type,
% 2.85/1.57 k: a ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_l,type,
% 2.85/1.57 l: rBT_Im246033960le_rbt @ a @ b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_less,type,
% 2.85/1.57 less: a > a > $o ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_r,type,
% 2.85/1.57 r: rBT_Im246033960le_rbt @ a @ b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_v____,type,
% 2.85/1.57 v: b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_w____,type,
% 2.85/1.57 w: b ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_x____,type,
% 2.85/1.57 x: a ).
% 2.85/1.57
% 2.85/1.57 thf(sy_v_y____,type,
% 2.85/1.57 y: a ).
% 2.85/1.57
% 2.85/1.57 thf(fact_0_local_Oantisym__conv3,axiom,
% 2.85/1.57 ! [Y: a,X: a] :
% 2.85/1.57 ( ~ ( less @ Y @ X )
% 2.85/1.57 => ( ( ~ ( less @ X @ Y ) )
% 2.85/1.57 = ( X = Y ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_1_local_Odual__order_Oasym,axiom,
% 2.85/1.57 ! [B2: a,A2: a] :
% 2.85/1.57 ( ( less @ B2 @ A2 )
% 2.85/1.57 => ~ ( less @ A2 @ B2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_2_local_Odual__order_Ostrict__implies__not__eq,axiom,
% 2.85/1.57 ! [B2: a,A2: a] :
% 2.85/1.57 ( ( less @ B2 @ A2 )
% 2.85/1.57 => ( A2 != B2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_3_local_Odual__order_Ostrict__trans,axiom,
% 2.85/1.57 ! [B2: a,A2: a,C: a] :
% 2.85/1.57 ( ( less @ B2 @ A2 )
% 2.85/1.57 => ( ( less @ C @ B2 )
% 2.85/1.57 => ( less @ C @ A2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_4_local_Oless__asym,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ~ ( less @ Y @ X ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_5_local_Oless__asym_H,axiom,
% 2.85/1.57 ! [A2: a,B2: a] :
% 2.85/1.57 ( ( less @ A2 @ B2 )
% 2.85/1.57 => ~ ( less @ B2 @ A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_6_local_Oless__imp__neq,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ( X != Y ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_7_local_Oless__imp__not__eq,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ( X != Y ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_8_local_Oless__imp__not__eq2,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ( Y != X ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_9_local_Oless__imp__not__less,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ~ ( less @ Y @ X ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_10_local_Oless__imp__triv,axiom,
% 2.85/1.57 ! [X: a,Y: a,P: $o] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ( ( less @ Y @ X )
% 2.85/1.57 => P ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_11_local_Oless__irrefl,axiom,
% 2.85/1.57 ! [X: a] :
% 2.85/1.57 ~ ( less @ X @ X ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_12_local_Oless__linear,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 | ( X = Y )
% 2.85/1.57 | ( less @ Y @ X ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_13_local_Oless__not__sym,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ~ ( less @ Y @ X ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_14_local_Oless__trans,axiom,
% 2.85/1.57 ! [X: a,Y: a,Z: a] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ( ( less @ Y @ Z )
% 2.85/1.57 => ( less @ X @ Z ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_15_local_Olinorder__cases,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ~ ( less @ X @ Y )
% 2.85/1.57 => ( ( X != Y )
% 2.85/1.57 => ( less @ Y @ X ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_16_local_OneqE,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( X != Y )
% 2.85/1.57 => ( ~ ( less @ X @ Y )
% 2.85/1.57 => ( less @ Y @ X ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_17_local_Oneq__iff,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( X != Y )
% 2.85/1.57 = ( ( less @ X @ Y )
% 2.85/1.57 | ( less @ Y @ X ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_18_local_Onot__less__iff__gr__or__eq,axiom,
% 2.85/1.57 ! [X: a,Y: a] :
% 2.85/1.57 ( ( ~ ( less @ X @ Y ) )
% 2.85/1.57 = ( ( less @ Y @ X )
% 2.85/1.57 | ( X = Y ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_19_local_Oord__eq__less__trans,axiom,
% 2.85/1.57 ! [A2: a,B2: a,C: a] :
% 2.85/1.57 ( ( A2 = B2 )
% 2.85/1.57 => ( ( less @ B2 @ C )
% 2.85/1.57 => ( less @ A2 @ C ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_20_local_Oord__less__eq__trans,axiom,
% 2.85/1.57 ! [A2: a,B2: a,C: a] :
% 2.85/1.57 ( ( less @ A2 @ B2 )
% 2.85/1.57 => ( ( B2 = C )
% 2.85/1.57 => ( less @ A2 @ C ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_21_local_Oorder_Oasym,axiom,
% 2.85/1.57 ! [A2: a,B2: a] :
% 2.85/1.57 ( ( less @ A2 @ B2 )
% 2.85/1.57 => ~ ( less @ B2 @ A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_22_local_Oorder_Oirrefl,axiom,
% 2.85/1.57 ! [A2: a] :
% 2.85/1.57 ~ ( less @ A2 @ A2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_23_local_Oorder_Ostrict__implies__not__eq,axiom,
% 2.85/1.57 ! [A2: a,B2: a] :
% 2.85/1.57 ( ( less @ A2 @ B2 )
% 2.85/1.57 => ( A2 != B2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_24_local_Oorder_Ostrict__trans,axiom,
% 2.85/1.57 ! [A2: a,B2: a,C: a] :
% 2.85/1.57 ( ( less @ A2 @ B2 )
% 2.85/1.57 => ( ( less @ B2 @ C )
% 2.85/1.57 => ( less @ A2 @ C ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_25_local_Orbt__greater__trans,axiom,
% 2.85/1.57 ! [C2: $tType,X: a,Y: a,T: rBT_Im246033960le_rbt @ a @ C2] :
% 2.85/1.57 ( ( less @ X @ Y )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ C2 @ less @ Y @ T )
% 2.85/1.57 => ( rBT_Im1259024060reater @ a @ C2 @ less @ X @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_26__092_060open_062x_A_060_Ay_A_092_060and_062_Ay_A_092_060guillemotleft_062_124_Ad_092_060close_062,axiom,
% 2.85/1.57 ( ( less @ x @ y )
% 2.85/1.57 & ( rBT_Im1259024060reater @ a @ b @ less @ y @ d ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_27_local_Ostrict__mono__eq,axiom,
% 2.85/1.57 ! [B: $tType] :
% 2.85/1.57 ( ( order @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.85/1.57 ( ( strict_mono @ a @ B @ less @ F )
% 2.85/1.57 => ( ( ( F @ X )
% 2.85/1.57 = ( F @ Y ) )
% 2.85/1.57 = ( X = Y ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_28_assms_I4_J,axiom,
% 2.85/1.57 rBT_Im1259024060reater @ a @ b @ less @ k @ r ).
% 2.85/1.57
% 2.85/1.57 thf(fact_29_combine__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,K: a,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ L )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.85/1.57 => ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im1591839508ombine @ a @ B @ L @ R ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_30__092_060open_062x_A_092_060guillemotleft_062_124_Ac_092_060close_062,axiom,
% 2.85/1.57 rBT_Im1259024060reater @ a @ b @ less @ x @ c ).
% 2.85/1.57
% 2.85/1.57 thf(fact_31_local_Obalance__right__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ A2 )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ B2 )
% 2.85/1.57 => ( ( less @ K @ X )
% 2.85/1.57 => ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im1053358987_right @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_32_local_Obalance__left__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ A2 )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ B2 )
% 2.85/1.57 => ( ( less @ K @ X )
% 2.85/1.57 => ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im1278323832e_left @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_33_assms_I2_J,axiom,
% 2.85/1.57 rBT_Im759614907sorted @ a @ b @ less @ r ).
% 2.85/1.57
% 2.85/1.57 thf(fact_34_assms_I1_J,axiom,
% 2.85/1.57 rBT_Im759614907sorted @ a @ b @ less @ l ).
% 2.85/1.57
% 2.85/1.57 thf(fact_35__092_060open_062x_A_060_Ak_A_092_060and_062_Ak_A_092_060guillemotleft_062_124_Ac_092_060close_062,axiom,
% 2.85/1.57 ( ( less @ x @ k )
% 2.85/1.57 & ( rBT_Im1259024060reater @ a @ b @ less @ k @ c ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_36_local_Orbt__less__trans,axiom,
% 2.85/1.57 ! [C2: $tType,X: a,T: rBT_Im246033960le_rbt @ a @ C2,Y: a] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ X @ T )
% 2.85/1.57 => ( ( less @ X @ Y )
% 2.85/1.57 => ( rBT_Im2075124343t_less @ a @ C2 @ less @ Y @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_37_local_Olexordp__eq__antisym,axiom,
% 2.85/1.57 ! [Xs: list @ a,Ys: list @ a] :
% 2.85/1.57 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.85/1.57 => ( ( lexordp_eq @ a @ less @ Ys @ Xs )
% 2.85/1.57 => ( Xs = Ys ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_38_local_Olexordp__eq__linear,axiom,
% 2.85/1.57 ! [Xs: list @ a,Ys: list @ a] :
% 2.85/1.57 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.85/1.57 | ( lexordp_eq @ a @ less @ Ys @ Xs ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_39_local_Olexordp__eq__refl,axiom,
% 2.85/1.57 ! [Xs: list @ a] : ( lexordp_eq @ a @ less @ Xs @ Xs ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_40_local_Olexordp__eq__trans,axiom,
% 2.85/1.57 ! [Xs: list @ a,Ys: list @ a,Zs: list @ a] :
% 2.85/1.57 ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.85/1.57 => ( ( lexordp_eq @ a @ less @ Ys @ Zs )
% 2.85/1.57 => ( lexordp_eq @ a @ less @ Xs @ Zs ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_41_assms_I3_J,axiom,
% 2.85/1.57 rBT_Im2075124343t_less @ a @ b @ less @ k @ l ).
% 2.85/1.57
% 2.85/1.57 thf(fact_42_combine__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,K: a,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ R )
% 2.85/1.57 => ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im1591839508ombine @ a @ B @ L @ R ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_43_local_Obalance__left__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ A2 )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ B2 )
% 2.85/1.57 => ( ( less @ X @ K )
% 2.85/1.57 => ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im1278323832e_left @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_44_local_Obalance__right__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,K: a,A2: rBT_Im246033960le_rbt @ a @ B,B2: rBT_Im246033960le_rbt @ a @ B,X: a,T: B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ A2 )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ B2 )
% 2.85/1.57 => ( ( less @ X @ K )
% 2.85/1.57 => ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im1053358987_right @ a @ B @ A2 @ X @ T @ B2 ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_45_mem__Collect__eq,axiom,
% 2.85/1.57 ! [A: $tType,A2: A,P: A > $o] :
% 2.85/1.57 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.85/1.57 = ( P @ A2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_46_Collect__mem__eq,axiom,
% 2.85/1.57 ! [A: $tType,A3: set @ A] :
% 2.85/1.57 ( ( collect @ A
% 2.85/1.57 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 2.85/1.57 = A3 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_47_Collect__cong,axiom,
% 2.85/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.85/1.57 ( ! [X3: A] :
% 2.85/1.57 ( ( P @ X3 )
% 2.85/1.57 = ( Q @ X3 ) )
% 2.85/1.57 => ( ( collect @ A @ P )
% 2.85/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_48_ext,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.85/1.57 ( ! [X3: A] :
% 2.85/1.57 ( ( F @ X3 )
% 2.85/1.57 = ( G @ X3 ) )
% 2.85/1.57 => ( F = G ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_49_local_Obalance__left__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.85/1.57 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1278323832e_left @ a @ B @ L @ K @ V @ R ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_50_local_Obalance__right__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.85/1.57 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1053358987_right @ a @ B @ L @ K @ V @ R ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_51_local_Orbt__insertw__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: B > B > B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im241132701t_with @ a @ B @ less @ F @ K @ V @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_52_local_Orbt__insert__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im852463031insert @ a @ B @ less @ K @ V @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_53_local_Orbt__insertwk__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: a > B > B > B,K: a,X: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im627674146th_key @ a @ B @ less @ F @ K @ X @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_54_local_Ois__rbt__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ T ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_55__C2_C,axiom,
% 2.85/1.57 rBT_Im1259024060reater @ a @ b @ less @ x @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_56__C3_C,axiom,
% 2.85/1.57 rBT_Im2075124343t_less @ a @ b @ less @ y @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_57__092_060open_062k_A_060_Ay_A_092_060and_062_Ab_A_124_092_060guillemotleft_062_Ak_092_060close_062,axiom,
% 2.85/1.57 ( ( less @ k @ y )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_58__092_060open_062b_A_124_092_060guillemotleft_062_Ay_092_060close_062,axiom,
% 2.85/1.57 rBT_Im2075124343t_less @ a @ b @ less @ y @ b2 ).
% 2.85/1.57
% 2.85/1.57 thf(fact_59_local_Opaint__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,C: rBT_Im1923302023_color] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_60_local_Orbt__sorted_Osimps_I2_J,axiom,
% 2.85/1.57 ! [B: $tType,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ a @ B,K: a,V: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ C @ L @ K @ V @ R ) )
% 2.85/1.57 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.85/1.57 & ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.85/1.57 & ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.85/1.57 & ( rBT_Im759614907sorted @ a @ B @ less @ R ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_61_local_Obalance__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.85/1.57 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1648453169alance @ a @ B @ L @ K @ V @ R ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_62_local_Orbt__insertwk__is__rbt,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: a > B > B > B,K: a,X: B] :
% 2.85/1.57 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im627674146th_key @ a @ B @ less @ F @ K @ X @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_63_local_Orbt__insert__is__rbt,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im852463031insert @ a @ B @ less @ K @ V @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_64_local_Orbt__insertw__is__rbt,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: B > B > B,K: a,V: B] :
% 2.85/1.57 ( ( rBT_Im862805236is_rbt @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im241132701t_with @ a @ B @ less @ F @ K @ V @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_65_rbt_Oinject,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: 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] :
% 2.85/1.57 ( ( ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ Y21 @ Y22 @ Y23 @ Y24 @ Y25 ) )
% 2.85/1.57 = ( ( X21 = Y21 )
% 2.85/1.57 & ( X22 = Y22 )
% 2.85/1.57 & ( X23 = Y23 )
% 2.85/1.57 & ( X24 = Y24 )
% 2.85/1.57 & ( X25 = Y25 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_66_local_Orbt__greater__simps_I2_J,axiom,
% 2.85/1.57 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.85/1.57 = ( ( less @ K @ Kt )
% 2.85/1.57 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Lt )
% 2.85/1.57 & ( rBT_Im1259024060reater @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_67_local_Orbt__less__simps_I2_J,axiom,
% 2.85/1.57 ! [C2: $tType,K: a,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ a @ C2,Kt: a,V: C2,Rt: rBT_Im246033960le_rbt @ a @ C2] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ ( rBT_Im480247531Branch @ a @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.85/1.57 = ( ( less @ Kt @ K )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Lt )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ a @ C2 @ less @ K @ Rt ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_68_local_Obalance__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,V: a,A2: rBT_Im246033960le_rbt @ a @ B,K: a,X: B,B2: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ ( rBT_Im1648453169alance @ a @ B @ A2 @ K @ X @ B2 ) )
% 2.85/1.57 = ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ A2 )
% 2.85/1.57 & ( rBT_Im1259024060reater @ a @ B @ less @ V @ B2 )
% 2.85/1.57 & ( less @ V @ K ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_69_local_Obalance__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,V: a,A2: rBT_Im246033960le_rbt @ a @ B,K: a,X: B,B2: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ ( rBT_Im1648453169alance @ a @ B @ A2 @ K @ X @ B2 ) )
% 2.85/1.57 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ A2 )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ a @ B @ less @ V @ B2 )
% 2.85/1.57 & ( less @ K @ V ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_70_local_Opaint__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,V: a,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) )
% 2.85/1.57 = ( rBT_Im1259024060reater @ a @ B @ less @ V @ T ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_71_local_Opaint__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,V: a,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) )
% 2.85/1.57 = ( rBT_Im2075124343t_less @ a @ B @ less @ V @ T ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_72_Empty,axiom,
% 2.85/1.57 ( ( rBT_Im1591839508ombine @ a @ b @ b2 @ c )
% 2.85/1.57 = ( rBT_Im418718756_Empty @ a @ b ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_73_paint_Osimps_I2_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,C: rBT_Im1923302023_color,Uu: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im945281971_paint @ A @ B @ C @ ( rBT_Im480247531Branch @ A @ B @ Uu @ L @ K @ V @ R ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V @ R ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_74_ord_Orbt__greater__simps_I2_J,axiom,
% 2.85/1.57 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.85/1.57 = ( ( Less @ K @ Kt )
% 2.85/1.57 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Lt )
% 2.85/1.57 & ( rBT_Im1259024060reater @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_75_ord_Orbt__less__simps_I2_J,axiom,
% 2.85/1.57 ! [C2: $tType,A: $tType,Less: A > A > $o,K: A,C: rBT_Im1923302023_color,Lt: rBT_Im246033960le_rbt @ A @ C2,Kt: A,V: C2,Rt: rBT_Im246033960le_rbt @ A @ C2] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ ( rBT_Im480247531Branch @ A @ C2 @ C @ Lt @ Kt @ V @ Rt ) )
% 2.85/1.57 = ( ( Less @ Kt @ K )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Lt )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ A @ C2 @ Less @ K @ Rt ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_76_ord_Obalance__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ A @ B @ Less @ V @ ( rBT_Im1648453169alance @ A @ B @ A2 @ K @ X @ B2 ) )
% 2.85/1.57 = ( ( rBT_Im1259024060reater @ A @ B @ Less @ V @ A2 )
% 2.85/1.57 & ( rBT_Im1259024060reater @ A @ B @ Less @ V @ B2 )
% 2.85/1.57 & ( Less @ V @ K ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_77_ord_Obalance__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ ( rBT_Im1648453169alance @ A @ B @ A2 @ K @ X @ B2 ) )
% 2.85/1.57 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ A2 )
% 2.85/1.57 & ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ B2 )
% 2.85/1.57 & ( Less @ K @ V ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_78_ord_Opaint__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,T: rBT_Im246033960le_rbt @ A @ B,C: rBT_Im1923302023_color] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ A @ B @ Less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_79_ord_Opaint__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ A @ B @ Less @ V @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) )
% 2.85/1.57 = ( rBT_Im1259024060reater @ A @ B @ Less @ V @ T ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_80_ord_Opaint__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,V: A,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) )
% 2.85/1.57 = ( rBT_Im2075124343t_less @ A @ B @ Less @ V @ T ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_81_ord_Orbt__sorted_Osimps_I2_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,C: rBT_Im1923302023_color,L: rBT_Im246033960le_rbt @ A @ B,K: A,V: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im480247531Branch @ A @ B @ C @ L @ K @ V @ R ) )
% 2.85/1.57 = ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ L )
% 2.85/1.57 & ( rBT_Im1259024060reater @ A @ B @ Less @ K @ R )
% 2.85/1.57 & ( rBT_Im759614907sorted @ A @ B @ Less @ L )
% 2.85/1.57 & ( rBT_Im759614907sorted @ A @ B @ Less @ R ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_82_ord_Ois__rbt__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im862805236is_rbt @ A @ B @ Less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ A @ B @ Less @ T ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_83__C4_Ohyps_C,axiom,
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ b @ less @ b2 )
% 2.85/1.57 => ( ( rBT_Im759614907sorted @ a @ b @ less @ c )
% 2.85/1.57 => ( ( rBT_Im2075124343t_less @ a @ b @ less @ k @ b2 )
% 2.85/1.57 => ( ( rBT_Im1259024060reater @ a @ b @ less @ k @ c )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im1591839508ombine @ a @ b @ b2 @ c ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_84_local_Oins__rbt__sorted,axiom,
% 2.85/1.57 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B,F: a > B > B > B,K: a,X: B] :
% 2.85/1.57 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.85/1.57 => ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ X @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_85_local_Ostrict__monoD,axiom,
% 2.85/1.57 ! [B: $tType] :
% 2.85/1.57 ( ( order @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.85/1.57 ( ( strict_mono @ a @ B @ less @ F )
% 2.85/1.57 => ( ( less @ X @ Y )
% 2.85/1.57 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_86_local_Ostrict__monoI,axiom,
% 2.85/1.57 ! [B: $tType] :
% 2.85/1.57 ( ( order @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: a > B] :
% 2.85/1.57 ( ! [X3: a,Y2: a] :
% 2.85/1.57 ( ( less @ X3 @ Y2 )
% 2.85/1.57 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 2.85/1.57 => ( strict_mono @ a @ B @ less @ F ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_87_local_Ostrict__mono__def,axiom,
% 2.85/1.57 ! [B: $tType] :
% 2.85/1.57 ( ( order @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: a > B] :
% 2.85/1.57 ( ( strict_mono @ a @ B @ less @ F )
% 2.85/1.57 = ( ! [X2: a,Y3: a] :
% 2.85/1.57 ( ( less @ X2 @ Y3 )
% 2.85/1.57 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_88_local_Ostrict__mono__less,axiom,
% 2.85/1.57 ! [B: $tType] :
% 2.85/1.57 ( ( order @ B @ ( type2 @ B ) )
% 2.85/1.57 => ! [F: a > B,X: a,Y: a] :
% 2.85/1.57 ( ( strict_mono @ a @ B @ less @ F )
% 2.85/1.57 => ( ( ord_less @ B @ ( F @ X ) @ ( F @ Y ) )
% 2.85/1.57 = ( less @ X @ Y ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_89_local_Olexordp__eq_ONil,axiom,
% 2.85/1.57 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_90_local_Orbt__sorted_Osimps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType] : ( rBT_Im759614907sorted @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_91_local_OEmpty__is__rbt,axiom,
% 2.85/1.57 ! [B: $tType] : ( rBT_Im862805236is_rbt @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_92_local_Orbt__insert__def,axiom,
% 2.85/1.57 ! [B: $tType] :
% 2.85/1.57 ( ( rBT_Im852463031insert @ a @ B @ less )
% 2.85/1.57 = ( rBT_Im627674146th_key @ a @ B @ less
% 2.85/1.57 @ ^ [Uu2: a,Uv: B,Nv: B] : Nv ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_93_local_Orbt__insertw__def,axiom,
% 2.85/1.57 ! [B: $tType,F: B > B > B] :
% 2.85/1.57 ( ( rBT_Im241132701t_with @ a @ B @ less @ F )
% 2.85/1.57 = ( rBT_Im627674146th_key @ a @ B @ less
% 2.85/1.57 @ ^ [Uu2: a] : F ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_94_local_Olexordp__eq__simps_I1_J,axiom,
% 2.85/1.57 ! [Ys: list @ a] : ( lexordp_eq @ a @ less @ ( nil @ a ) @ Ys ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_95_local_Olexordp__eq__simps_I2_J,axiom,
% 2.85/1.57 ! [Xs: list @ a] :
% 2.85/1.57 ( ( lexordp_eq @ a @ less @ Xs @ ( nil @ a ) )
% 2.85/1.57 = ( Xs
% 2.85/1.57 = ( nil @ a ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_96_local_Oins__rbt__greater,axiom,
% 2.85/1.57 ! [B: $tType,V: a,F: a > B > B > B,K: a,X: B,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ X @ T ) )
% 2.85/1.57 = ( ( rBT_Im1259024060reater @ a @ B @ less @ V @ T )
% 2.85/1.57 & ( less @ V @ K ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_97_local_Oins__rbt__less,axiom,
% 2.85/1.57 ! [B: $tType,V: a,F: a > B > B > B,K: a,X: B,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ X @ T ) )
% 2.85/1.57 = ( ( rBT_Im2075124343t_less @ a @ B @ less @ V @ T )
% 2.85/1.57 & ( less @ K @ V ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_98_local_Orbt__greater__simps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,K: a] : ( rBT_Im1259024060reater @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_99_local_Orbt__less__simps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,K: a] : ( rBT_Im2075124343t_less @ a @ B @ less @ K @ ( rBT_Im418718756_Empty @ a @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_100_rbt_Odistinct_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,X21: rBT_Im1923302023_color,X22: rBT_Im246033960le_rbt @ A @ B,X23: A,X24: B,X25: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im418718756_Empty @ A @ B )
% 2.85/1.57 != ( rBT_Im480247531Branch @ A @ B @ X21 @ X22 @ X23 @ X24 @ X25 ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_101_rbt_Oinduct,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > $o,Rbt: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( P @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 => ( ! [X1: rBT_Im1923302023_color,X26: rBT_Im246033960le_rbt @ A @ B,X32: A,X4: B,X5: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( P @ X26 )
% 2.85/1.57 => ( ( P @ X5 )
% 2.85/1.57 => ( P @ ( rBT_Im480247531Branch @ A @ B @ X1 @ X26 @ X32 @ X4 @ X5 ) ) ) )
% 2.85/1.57 => ( P @ Rbt ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_102_rbt_Oexhaust,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Y: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( Y
% 2.85/1.57 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 => ~ ! [X212: rBT_Im1923302023_color,X222: rBT_Im246033960le_rbt @ A @ B,X232: A,X242: B,X252: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( Y
% 2.85/1.57 != ( rBT_Im480247531Branch @ A @ B @ X212 @ X222 @ X232 @ X242 @ X252 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_103_ord_Orbt__sorted_Osimps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im759614907sorted @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_104_ord_Orbt__greater__simps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im1259024060reater @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_105_ord_Orbt__less__simps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o,K: A] : ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_106_ord_Orbt__insert__def,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( rBT_Im852463031insert @ A @ B )
% 2.85/1.57 = ( ^ [Less2: A > A > $o] :
% 2.85/1.57 ( rBT_Im627674146th_key @ A @ B @ Less2
% 2.85/1.57 @ ^ [Uu2: A,Uv: B,Nv: B] : Nv ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_107_ord_Orbt__insertw__def,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType] :
% 2.85/1.57 ( ( rBT_Im241132701t_with @ A @ B )
% 2.85/1.57 = ( ^ [Less2: A > A > $o,F2: B > B > B] :
% 2.85/1.57 ( rBT_Im627674146th_key @ A @ B @ Less2
% 2.85/1.57 @ ^ [Uu2: A] : F2 ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_108_paint_Osimps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,C: rBT_Im1923302023_color] :
% 2.85/1.57 ( ( rBT_Im945281971_paint @ A @ B @ C @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_109_balance__left_Osimps_I6_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,K: A,X: B] :
% 2.85/1.57 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_110_combine_Osimps_I1_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,X: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ X )
% 2.85/1.57 = X ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_111_balance__right_Osimps_I6_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,K: A,X: B] :
% 2.85/1.57 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_112_ord_OEmpty__is__rbt,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Less: A > A > $o] : ( rBT_Im862805236is_rbt @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_113_combine_Osimps_I2_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ Va @ Vb @ Vc @ Vd ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ V @ Va @ Vb @ Vc @ Vd ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_114__C4_Oprems_C_I4_J,axiom,
% 2.85/1.57 rBT_Im1259024060reater @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_115__C4_Oprems_C_I2_J,axiom,
% 2.85/1.57 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ c @ y @ w @ d ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_116_local_OgreaterThan__def,axiom,
% 2.85/1.57 ! [L: a] :
% 2.85/1.57 ( ( set_greaterThan @ a @ less @ L )
% 2.85/1.57 = ( collect @ a @ ( less @ L ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_117_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.85/1.57 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.85/1.57 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 2.85/1.57 = ( Xs
% 2.85/1.57 = ( nil @ A ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_118_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.85/1.57 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_119__C4_Oprems_C_I3_J,axiom,
% 2.85/1.57 rBT_Im2075124343t_less @ a @ b @ less @ k @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_120_local_Orbt__ins_Osimps_I2_J,axiom,
% 2.85/1.57 ! [B: $tType,K: a,X: a,F: a > B > B > B,V: B,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( ( less @ K @ X )
% 2.85/1.57 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 2.85/1.57 = ( rBT_Im1648453169alance @ a @ B @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 2.85/1.57 & ( ~ ( less @ K @ X )
% 2.85/1.57 => ( ( ( less @ X @ K )
% 2.85/1.57 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 2.85/1.57 = ( rBT_Im1648453169alance @ a @ B @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ R ) ) ) )
% 2.85/1.57 & ( ~ ( less @ X @ K )
% 2.85/1.57 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_121_local_Orbt__insert__with__key__def,axiom,
% 2.85/1.57 ! [B: $tType,F: a > B > B > B,K: a,V: B,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.57 ( ( rBT_Im627674146th_key @ a @ B @ less @ F @ K @ V @ T )
% 2.85/1.57 = ( rBT_Im945281971_paint @ a @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ T ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_122__C4_Oprems_C_I1_J,axiom,
% 2.85/1.57 rBT_Im759614907sorted @ a @ b @ less @ ( rBT_Im480247531Branch @ a @ b @ rBT_Impl_Mirabelle_B @ a2 @ x @ v @ b2 ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_123_local_OgreaterThan__iff,axiom,
% 2.85/1.57 ! [I: a,K: a] :
% 2.85/1.57 ( ( member @ a @ I @ ( set_greaterThan @ a @ less @ K ) )
% 2.85/1.57 = ( less @ K @ I ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_124_balance_Osimps_I23_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_125_balance_Osimps_I27_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_126_balance_Osimps_I29_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vi: rBT_Im246033960le_rbt @ A @ B,Vn: A,Vo: B,Vp: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_127_balance_Osimps_I39_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_128_balance_Osimps_I43_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_129_balance_Osimps_I45_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vn: A,Vo: B,Vp: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vn @ Vo @ Vp ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_130_balance_Osimps_I14_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_131_balance_Osimps_I15_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_132_balance_Osimps_I16_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_133_balance_Osimps_I17_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Vb: A,Vc: B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_134_balance_Osimps_I18_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_135_balance_Osimps_I19_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) ) ) ).
% 2.85/1.57
% 2.85/1.57 thf(fact_136_balance_Osimps_I20_J,axiom,
% 2.85/1.57 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Vb: A,Vc: B,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.57 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) )
% 2.85/1.57 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_137_balance_Osimps_I21_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,S: A,T: B,V: rBT_Im1923302023_color,Ve: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_138_balance_Osimps_I22_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_139_balance_Osimps_I24_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_140_balance_Osimps_I25_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vf: A,Vg: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_141_balance_Osimps_I26_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_142_balance_Osimps_I28_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,V: rBT_Im1923302023_color,Vf: A,Vg: B,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_143_balance_Osimps_I32_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_144_balance_Osimps_I33_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vb: A,Vc: B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_145_balance_Osimps_I34_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vb: A,Vc: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_146_balance_Osimps_I35_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ Vd ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_147_balance_Osimps_I36_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_148_balance_Osimps_I37_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: rBT_Im246033960le_rbt @ A @ B,Vg: A,Vh: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,S: A,T: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vf @ Vg @ Vh @ Vi ) @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_149_balance_Osimps_I40_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ Vh ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_150_balance_Osimps_I41_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: A,Vg: B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_151_balance_Osimps_I42_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vf: A,Vg: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vi @ Vj @ Vk @ Vl ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_152_balance_Osimps_I44_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,V: rBT_Im1923302023_color,Vj: rBT_Im246033960le_rbt @ A @ B,Vk: A,Vl: B,Vm: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,S: A,T: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Vj @ Vk @ Vl @ Vm ) @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_153_balance__left_Osimps_I9_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_154_balance__right_Osimps_I9_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,K: A,X: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_155_ord_Orbt__ins_Osimps_I2_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Less: A > A > $o,K: A,X: A,F: A > B > B > B,V: B,L: rBT_Im246033960le_rbt @ A @ B,Y: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( ( Less @ K @ X )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 2.85/1.58 & ( ~ ( Less @ K @ X )
% 2.85/1.58 => ( ( ( Less @ X @ K )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im1648453169alance @ A @ B @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ R ) ) ) )
% 2.85/1.58 & ( ~ ( Less @ X @ K )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_156_ord_Olexordp__eq__refl,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_157_ord_Orbt__insert__with__key__def,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType] :
% 2.85/1.58 ( ( rBT_Im627674146th_key @ A @ B )
% 2.85/1.58 = ( ^ [Less2: A > A > $o,F2: A > B > B > B,K2: A,V2: B,T2: rBT_Im246033960le_rbt @ A @ B] : ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im1756508336bt_ins @ A @ B @ Less2 @ F2 @ K2 @ V2 @ T2 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_158_ord_Olexordp__eq_ONil,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_159_local_OlessThan__def,axiom,
% 2.85/1.58 ! [U: a] :
% 2.85/1.58 ( ( set_lessThan @ a @ less @ U )
% 2.85/1.58 = ( collect @ a
% 2.85/1.58 @ ^ [X2: a] : ( less @ X2 @ U ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_160_local_Orbt__ins_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,F: a > B > B > B,K: a,V: B] :
% 2.85/1.58 ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im418718756_Empty @ a @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ a @ B ) @ K @ V @ ( rBT_Im418718756_Empty @ a @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_161_local_Orbt__ins_Oinduct,axiom,
% 2.85/1.58 ! [B: $tType,P: ( a > B > B > B ) > a > B > ( rBT_Im246033960le_rbt @ a @ B ) > $o,A0: a > B > B > B,A1: a,A22: B,A32: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ! [F3: a > B > B > B,K3: a,V3: B] : ( P @ F3 @ K3 @ V3 @ ( rBT_Im418718756_Empty @ a @ B ) )
% 2.85/1.58 => ( ! [F3: a > B > B > B,K3: a,V3: B,L2: rBT_Im246033960le_rbt @ a @ B,X3: a,Y2: B,R2: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( ( less @ K3 @ X3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 2.85/1.58 => ( ( ~ ( less @ K3 @ X3 )
% 2.85/1.58 => ( ( less @ X3 @ K3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 2.85/1.58 => ( ! [F3: a > B > B > B,K3: a,V3: B,L2: rBT_Im246033960le_rbt @ a @ B,X3: a,Y2: B,R2: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( ( less @ K3 @ X3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 2.85/1.58 => ( ( ~ ( less @ K3 @ X3 )
% 2.85/1.58 => ( ( less @ X3 @ K3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 2.85/1.58 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_162_local_Orbt__lookup__balance,axiom,
% 2.85/1.58 ! [B: $tType,L: rBT_Im246033960le_rbt @ a @ B,R: rBT_Im246033960le_rbt @ a @ B,K: a,V: B,X: a] :
% 2.85/1.58 ( ( rBT_Im759614907sorted @ a @ B @ less @ L )
% 2.85/1.58 => ( ( rBT_Im759614907sorted @ a @ B @ less @ R )
% 2.85/1.58 => ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ L )
% 2.85/1.58 => ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ R )
% 2.85/1.58 => ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im1648453169alance @ a @ B @ L @ K @ V @ R ) @ X )
% 2.85/1.58 = ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_B @ L @ K @ V @ R ) @ X ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_163_local_Orbt__ins_Osimps_I3_J,axiom,
% 2.85/1.58 ! [B: $tType,K: a,X: a,F: a > B > B > B,V: B,L: rBT_Im246033960le_rbt @ a @ B,Y: B,R: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( ( less @ K @ X )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 2.85/1.58 & ( ~ ( less @ K @ X )
% 2.85/1.58 => ( ( ( less @ X @ K )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ R ) ) ) )
% 2.85/1.58 & ( ~ ( less @ X @ K )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ a @ B @ less @ F @ K @ V @ ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ a @ B @ rBT_Impl_Mirabelle_R @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_164_local_OlessThan__iff,axiom,
% 2.85/1.58 ! [I: a,K: a] :
% 2.85/1.58 ( ( member @ a @ I @ ( set_lessThan @ a @ less @ K ) )
% 2.85/1.58 = ( less @ I @ K ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_165_local_Opaint__rbt__lookup,axiom,
% 2.85/1.58 ! [B: $tType,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im945281971_paint @ a @ B @ C @ T ) )
% 2.85/1.58 = ( rBT_Im35466040lookup @ a @ B @ less @ T ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_166_color_Oexhaust,axiom,
% 2.85/1.58 ! [Y: rBT_Im1923302023_color] :
% 2.85/1.58 ( ( Y != rBT_Impl_Mirabelle_R )
% 2.85/1.58 => ( Y = rBT_Impl_Mirabelle_B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_167_color_Oinduct,axiom,
% 2.85/1.58 ! [P: rBT_Im1923302023_color > $o,Color: rBT_Im1923302023_color] :
% 2.85/1.58 ( ( P @ rBT_Impl_Mirabelle_R )
% 2.85/1.58 => ( ( P @ rBT_Impl_Mirabelle_B )
% 2.85/1.58 => ( P @ Color ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_168_color_Odistinct_I1_J,axiom,
% 2.85/1.58 rBT_Impl_Mirabelle_R != rBT_Impl_Mirabelle_B ).
% 2.85/1.58
% 2.85/1.58 thf(fact_169_ord_Orbt__ins_Osimps_I3_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Less: A > A > $o,K: A,X: A,F: A > B > B > B,V: B,L: rBT_Im246033960le_rbt @ A @ B,Y: B,R: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( ( Less @ K @ X )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ L ) @ X @ Y @ R ) ) )
% 2.85/1.58 & ( ~ ( Less @ K @ X )
% 2.85/1.58 => ( ( ( Less @ X @ K )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ R ) ) ) )
% 2.85/1.58 & ( ~ ( Less @ X @ K )
% 2.85/1.58 => ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ Y @ R ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L @ X @ ( F @ K @ Y @ V ) @ R ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_170_ord_Opaint__rbt__lookup,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Less: A > A > $o,C: rBT_Im1923302023_color,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im945281971_paint @ A @ B @ C @ T ) )
% 2.85/1.58 = ( rBT_Im35466040lookup @ A @ B @ Less @ T ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_171_rbt__cases,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( T
% 2.85/1.58 != ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 => ( ! [L2: rBT_Im246033960le_rbt @ A @ B,K3: A,V3: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( T
% 2.85/1.58 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ K3 @ V3 @ R2 ) )
% 2.85/1.58 => ~ ! [L2: rBT_Im246033960le_rbt @ A @ B,K3: A,V3: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( T
% 2.85/1.58 != ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ K3 @ V3 @ R2 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_172_combine_Oinduct,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,P: ( rBT_Im246033960le_rbt @ A @ B ) > ( rBT_Im246033960le_rbt @ A @ B ) > $o,A0: rBT_Im246033960le_rbt @ A @ B,A1: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ! [X1: rBT_Im246033960le_rbt @ A @ B] : ( P @ ( rBT_Im418718756_Empty @ A @ B ) @ X1 )
% 2.85/1.58 => ( ! [V3: rBT_Im1923302023_color,Va2: rBT_Im246033960le_rbt @ A @ B,Vb2: A,Vc2: B,Vd2: rBT_Im246033960le_rbt @ A @ B] : ( P @ ( rBT_Im480247531Branch @ A @ B @ V3 @ Va2 @ Vb2 @ Vc2 @ Vd2 ) @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 => ( ! [A4: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,B3: rBT_Im246033960le_rbt @ A @ B,C3: rBT_Im246033960le_rbt @ A @ B,S2: A,Y2: B,D: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( P @ B3 @ C3 )
% 2.85/1.58 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A4 @ K3 @ X3 @ B3 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C3 @ S2 @ Y2 @ D ) ) )
% 2.85/1.58 => ( ! [A4: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,B3: rBT_Im246033960le_rbt @ A @ B,C3: rBT_Im246033960le_rbt @ A @ B,S2: A,Y2: B,D: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( P @ B3 @ C3 )
% 2.85/1.58 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A4 @ K3 @ X3 @ B3 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C3 @ S2 @ Y2 @ D ) ) )
% 2.85/1.58 => ( ! [Va2: rBT_Im246033960le_rbt @ A @ B,Vb2: A,Vc2: B,Vd2: rBT_Im246033960le_rbt @ A @ B,B3: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,C3: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) @ B3 )
% 2.85/1.58 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B3 @ K3 @ X3 @ C3 ) ) )
% 2.85/1.58 => ( ! [A4: rBT_Im246033960le_rbt @ A @ B,K3: A,X3: B,B3: rBT_Im246033960le_rbt @ A @ B,Va2: rBT_Im246033960le_rbt @ A @ B,Vb2: A,Vc2: B,Vd2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( P @ B3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) )
% 2.85/1.58 => ( P @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A4 @ K3 @ X3 @ B3 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va2 @ Vb2 @ Vc2 @ Vd2 ) ) )
% 2.85/1.58 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_173_ord_Orbt__ins_Oinduct,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,P: ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > $o,Less: A > A > $o,A0: A > B > B > B,A1: A,A22: B,A32: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ! [F3: A > B > B > B,K3: A,V3: B] : ( P @ F3 @ K3 @ V3 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( ( Less @ K3 @ X3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 2.85/1.58 => ( ( ~ ( Less @ K3 @ X3 )
% 2.85/1.58 => ( ( Less @ X3 @ K3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 2.85/1.58 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( ( Less @ K3 @ X3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 2.85/1.58 => ( ( ~ ( Less @ K3 @ X3 )
% 2.85/1.58 => ( ( Less @ X3 @ K3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 2.85/1.58 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_174_balance_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,D2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C @ Y @ Z @ D2 ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ D2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_175_balance_Osimps_I3_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ W @ X @ B2 ) @ S @ T @ C ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_176_balance_Osimps_I7_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_177_balance_Osimps_I9_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,D2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C @ Y @ Z @ D2 ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ D2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_178_balance_Osimps_I13_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Ve @ Vf @ Vg @ Vh ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_179_balance__left_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ S @ Y @ C )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ K @ X @ B2 ) @ S @ Y @ C ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_180_ord_Orbt__ins_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Less: A > A > $o,F: A > B > B > B,K: A,V: B] :
% 2.85/1.58 ( ( rBT_Im1756508336bt_ins @ A @ B @ Less @ F @ K @ V @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ V @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_181_balance__left_Osimps_I7_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,K: A,X: B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_182_balance__left_Osimps_I8_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,K: A,X: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ Vh ) @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_183_balance__right_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ Y @ C ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ B2 @ S @ Y @ C ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_184_combine_Osimps_I5_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,B2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ K @ X @ C ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ B2 ) @ K @ X @ C ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_185_combine_Osimps_I6_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1591839508ombine @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im1591839508ombine @ A @ B @ B2 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_186_balance__right_Osimps_I7_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,K: A,X: B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Va @ Vb @ Vc @ ( rBT_Im418718756_Empty @ A @ B ) ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_187_balance__right_Osimps_I8_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B,K: A,X: B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Va @ Vb @ Vc @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ Vh ) ) @ K @ X @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_188_ord__class_Orbt__ins_Oinduct,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType] :
% 2.85/1.58 ( ( ord @ A @ ( type2 @ A ) )
% 2.85/1.58 => ! [P: ( A > B > B > B ) > A > B > ( rBT_Im246033960le_rbt @ A @ B ) > $o,A0: A > B > B > B,A1: A,A22: B,A32: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ! [F3: A > B > B > B,K3: A,V3: B] : ( P @ F3 @ K3 @ V3 @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( ( ord_less @ A @ K3 @ X3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 2.85/1.58 => ( ( ~ ( ord_less @ A @ K3 @ X3 )
% 2.85/1.58 => ( ( ord_less @ A @ X3 @ K3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 2.85/1.58 => ( ! [F3: A > B > B > B,K3: A,V3: B,L2: rBT_Im246033960le_rbt @ A @ B,X3: A,Y2: B,R2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( ( ord_less @ A @ K3 @ X3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ L2 ) )
% 2.85/1.58 => ( ( ~ ( ord_less @ A @ K3 @ X3 )
% 2.85/1.58 => ( ( ord_less @ A @ X3 @ K3 )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ R2 ) ) )
% 2.85/1.58 => ( P @ F3 @ K3 @ V3 @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ L2 @ X3 @ Y2 @ R2 ) ) ) )
% 2.85/1.58 => ( P @ A0 @ A1 @ A22 @ A32 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_189_balance_Osimps_I2_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ W @ X @ B2 ) @ S @ T @ C ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_190_balance_Osimps_I4_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_191_balance_Osimps_I5_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_192_balance_Osimps_I6_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_193_balance_Osimps_I8_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,D2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ C @ Y @ Z @ D2 ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ D2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_194_balance_Osimps_I10_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_195_balance_Osimps_I11_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_196_balance_Osimps_I12_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,W: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,T: B,C: rBT_Im246033960le_rbt @ A @ B,Y: A,Z: B] :
% 2.85/1.58 ( ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ B2 @ S @ T @ C ) @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ W @ X @ B2 ) @ S @ T @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ Y @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_197_balance__left_Osimps_I11_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Vi @ Vj @ Vk @ Vl ) @ Vf @ Vg @ Vh ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_198_balance__left_Osimps_I10_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,Vf: A,Vg: B,Vh: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im418718756_Empty @ A @ B ) @ Vf @ Vg @ Vh ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_199_balance__right_Osimps_I11_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,Vi: rBT_Im246033960le_rbt @ A @ B,Vj: A,Vk: B,Vl: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Vi @ Vj @ Vk @ Vl ) ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_200_balance__right_Osimps_I10_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Ve: rBT_Im246033960le_rbt @ A @ B,Vf: A,Vg: B,K: A,X: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ Ve @ Vf @ Vg @ ( rBT_Im418718756_Empty @ A @ B ) ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im418718756_Empty @ A @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_201_balance__left_Osimps_I3_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) )
% 2.85/1.58 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ S @ Y @ B2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_202_balance__right_Osimps_I3_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_203_balance__left_Osimps_I2_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) )
% 2.85/1.58 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ S @ Y @ B2 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_204_balance__right_Osimps_I2_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_205_balance__left_Osimps_I5_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) @ T @ Z @ C ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) @ K @ X @ A2 ) @ S @ Y @ ( rBT_Im1648453169alance @ A @ B @ B2 @ T @ Z @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ C ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_206_balance__right_Osimps_I5_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B,Va: rBT_Im246033960le_rbt @ A @ B,Vb: A,Vc: B,Vd: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ B2 @ S @ Y @ C ) ) @ T @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ A2 ) @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ T @ Z @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ Va @ Vb @ Vc @ Vd ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_207_balance__left_Osimps_I4_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,K: A,X: B,A2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,B2: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B,C: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1278323832e_left @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ A2 @ S @ Y @ B2 ) @ T @ Z @ C ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ ( rBT_Im418718756_Empty @ A @ B ) @ K @ X @ A2 ) @ S @ Y @ ( rBT_Im1648453169alance @ A @ B @ B2 @ T @ Z @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ C ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_208_balance__right_Osimps_I4_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,A2: rBT_Im246033960le_rbt @ A @ B,K: A,X: B,B2: rBT_Im246033960le_rbt @ A @ B,S: A,Y: B,C: rBT_Im246033960le_rbt @ A @ B,T: A,Z: B] :
% 2.85/1.58 ( ( rBT_Im1053358987_right @ A @ B @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ A2 @ K @ X @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ B2 @ S @ Y @ C ) ) @ T @ Z @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_R @ ( rBT_Im1648453169alance @ A @ B @ ( rBT_Im945281971_paint @ A @ B @ rBT_Impl_Mirabelle_R @ A2 ) @ K @ X @ B2 ) @ S @ Y @ ( rBT_Im480247531Branch @ A @ B @ rBT_Impl_Mirabelle_B @ C @ T @ Z @ ( rBT_Im418718756_Empty @ A @ B ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_209_local_Oentries__rbt__lookup,axiom,
% 2.85/1.58 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.85/1.58 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.85/1.58 => ( ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 2.85/1.58 = ( rBT_Im954575269ntries @ a @ B @ T22 ) )
% 2.85/1.58 = ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 2.85/1.58 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_210_local_Oentries__eqI,axiom,
% 2.85/1.58 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.85/1.58 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.85/1.58 => ( ( ( rBT_Im35466040lookup @ a @ B @ less @ T1 )
% 2.85/1.58 = ( rBT_Im35466040lookup @ a @ B @ less @ T22 ) )
% 2.85/1.58 => ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 2.85/1.58 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_211_local_Orbt__lookup_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,K: a] :
% 2.85/1.58 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) @ K )
% 2.85/1.58 = ( none @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_212_local_Orbt__lookup__Empty,axiom,
% 2.85/1.58 ! [B: $tType] :
% 2.85/1.58 ( ( rBT_Im35466040lookup @ a @ B @ less @ ( rBT_Im418718756_Empty @ a @ B ) )
% 2.85/1.58 = ( ^ [X2: a] : ( none @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_213_local_Orbt__lookup__rbt__greater,axiom,
% 2.85/1.58 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im1259024060reater @ a @ B @ less @ K @ T )
% 2.85/1.58 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.85/1.58 = ( none @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_214_local_Orbt__lookup__rbt__less,axiom,
% 2.85/1.58 ! [B: $tType,K: a,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im2075124343t_less @ a @ B @ less @ K @ T )
% 2.85/1.58 => ( ( rBT_Im35466040lookup @ a @ B @ less @ T @ K )
% 2.85/1.58 = ( none @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_215_entries_Osimps_I1_J,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType] :
% 2.85/1.58 ( ( rBT_Im954575269ntries @ A @ B @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( nil @ ( product_prod @ A @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_216_ord_Orbt__lookup__Empty,axiom,
% 2.85/1.58 ! [B: $tType,A: $tType,Less: A > A > $o] :
% 2.85/1.58 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) )
% 2.85/1.58 = ( ^ [X2: A] : ( none @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_217_ord_Orbt__lookup_Osimps_I1_J,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,Less: A > A > $o,K: A] :
% 2.85/1.58 ( ( rBT_Im35466040lookup @ A @ B @ Less @ ( rBT_Im418718756_Empty @ A @ B ) @ K )
% 2.85/1.58 = ( none @ B ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_218_ord_Orbt__lookup__rbt__greater,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im1259024060reater @ A @ B @ Less @ K @ T )
% 2.85/1.58 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 2.85/1.58 = ( none @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_219_ord_Orbt__lookup__rbt__less,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,Less: A > A > $o,K: A,T: rBT_Im246033960le_rbt @ A @ B] :
% 2.85/1.58 ( ( rBT_Im2075124343t_less @ A @ B @ Less @ K @ T )
% 2.85/1.58 => ( ( rBT_Im35466040lookup @ A @ B @ Less @ T @ K )
% 2.85/1.58 = ( none @ B ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_220_local_Omap__of__entries,axiom,
% 2.85/1.58 ! [B: $tType,T: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im759614907sorted @ a @ B @ less @ T )
% 2.85/1.58 => ( ( map_of @ a @ B @ ( rBT_Im954575269ntries @ a @ B @ T ) )
% 2.85/1.58 = ( rBT_Im35466040lookup @ a @ B @ less @ T ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_221_local_Olexordp__eq_Ocases,axiom,
% 2.85/1.58 ! [A1: list @ a,A22: list @ a] :
% 2.85/1.58 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 2.85/1.58 => ( ( ( A1
% 2.85/1.58 = ( nil @ a ) )
% 2.85/1.58 => ! [Ys2: list @ a] : ( A22 != Ys2 ) )
% 2.85/1.58 => ( ! [X3: a] :
% 2.85/1.58 ( ? [Xs2: list @ a] :
% 2.85/1.58 ( A1
% 2.85/1.58 = ( cons @ a @ X3 @ Xs2 ) )
% 2.85/1.58 => ! [Y2: a] :
% 2.85/1.58 ( ? [Ys2: list @ a] :
% 2.85/1.58 ( A22
% 2.85/1.58 = ( cons @ a @ Y2 @ Ys2 ) )
% 2.85/1.58 => ~ ( less @ X3 @ Y2 ) ) )
% 2.85/1.58 => ~ ! [X3: a,Y2: a,Xs2: list @ a] :
% 2.85/1.58 ( ( A1
% 2.85/1.58 = ( cons @ a @ X3 @ Xs2 ) )
% 2.85/1.58 => ! [Ys2: list @ a] :
% 2.85/1.58 ( ( A22
% 2.85/1.58 = ( cons @ a @ Y2 @ Ys2 ) )
% 2.85/1.58 => ( ~ ( less @ X3 @ Y2 )
% 2.85/1.58 => ( ~ ( less @ Y2 @ X3 )
% 2.85/1.58 => ~ ( lexordp_eq @ a @ less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_222_local_Olexordp__eq_OCons__eq,axiom,
% 2.85/1.58 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.85/1.58 ( ~ ( less @ X @ Y )
% 2.85/1.58 => ( ~ ( less @ Y @ X )
% 2.85/1.58 => ( ( lexordp_eq @ a @ less @ Xs @ Ys )
% 2.85/1.58 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_223_local_Olexordp__eq_OCons,axiom,
% 2.85/1.58 ! [X: a,Y: a,Xs: list @ a,Ys: list @ a] :
% 2.85/1.58 ( ( less @ X @ Y )
% 2.85/1.58 => ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_224_list_Oinject,axiom,
% 2.85/1.58 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.85/1.58 ( ( ( cons @ A @ X21 @ X22 )
% 2.85/1.58 = ( cons @ A @ Y21 @ Y22 ) )
% 2.85/1.58 = ( ( X21 = Y21 )
% 2.85/1.58 & ( X22 = Y22 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_225_local_Olexordp__eq_Osimps,axiom,
% 2.85/1.58 ! [A1: list @ a,A22: list @ a] :
% 2.85/1.58 ( ( lexordp_eq @ a @ less @ A1 @ A22 )
% 2.85/1.58 = ( ? [Ys3: list @ a] :
% 2.85/1.58 ( ( A1
% 2.85/1.58 = ( nil @ a ) )
% 2.85/1.58 & ( A22 = Ys3 ) )
% 2.85/1.58 | ? [X2: a,Y3: a,Xs3: list @ a,Ys3: list @ a] :
% 2.85/1.58 ( ( A1
% 2.85/1.58 = ( cons @ a @ X2 @ Xs3 ) )
% 2.85/1.58 & ( A22
% 2.85/1.58 = ( cons @ a @ Y3 @ Ys3 ) )
% 2.85/1.58 & ( less @ X2 @ Y3 ) )
% 2.85/1.58 | ? [X2: a,Y3: a,Xs3: list @ a,Ys3: list @ a] :
% 2.85/1.58 ( ( A1
% 2.85/1.58 = ( cons @ a @ X2 @ Xs3 ) )
% 2.85/1.58 & ( A22
% 2.85/1.58 = ( cons @ a @ Y3 @ Ys3 ) )
% 2.85/1.58 & ~ ( less @ X2 @ Y3 )
% 2.85/1.58 & ~ ( less @ Y3 @ X2 )
% 2.85/1.58 & ( lexordp_eq @ a @ less @ Xs3 @ Ys3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_226_local_Olexordp__eq_Oinducts,axiom,
% 2.85/1.58 ! [X12: list @ a,X27: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.85/1.58 ( ( lexordp_eq @ a @ less @ X12 @ X27 )
% 2.85/1.58 => ( ! [X1: list @ a] : ( P @ ( nil @ a ) @ X1 )
% 2.85/1.58 => ( ! [X3: a,Y2: a,Xs2: list @ a,Ys2: list @ a] :
% 2.85/1.58 ( ( less @ X3 @ Y2 )
% 2.85/1.58 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y2 @ Ys2 ) ) )
% 2.85/1.58 => ( ! [X3: a,Y2: a,Xs2: list @ a,Ys2: list @ a] :
% 2.85/1.58 ( ~ ( less @ X3 @ Y2 )
% 2.85/1.58 => ( ~ ( less @ Y2 @ X3 )
% 2.85/1.58 => ( ( lexordp_eq @ a @ less @ Xs2 @ Ys2 )
% 2.85/1.58 => ( ( P @ Xs2 @ Ys2 )
% 2.85/1.58 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y2 @ Ys2 ) ) ) ) ) )
% 2.85/1.58 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_227_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.85/1.58 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.85/1.58 = ( ( Less @ X @ Y )
% 2.85/1.58 | ( ~ ( Less @ Y @ X )
% 2.85/1.58 & ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_228_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 2.85/1.58 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_229_local_Olexordp__eq__simps_I4_J,axiom,
% 2.85/1.58 ! [X: a,Xs: list @ a,Y: a,Ys: list @ a] :
% 2.85/1.58 ( ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( cons @ a @ Y @ Ys ) )
% 2.85/1.58 = ( ( less @ X @ Y )
% 2.85/1.58 | ( ~ ( less @ Y @ X )
% 2.85/1.58 & ( lexordp_eq @ a @ less @ Xs @ Ys ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_230_local_Olexordp__eq__simps_I3_J,axiom,
% 2.85/1.58 ! [X: a,Xs: list @ a] :
% 2.85/1.58 ~ ( lexordp_eq @ a @ less @ ( cons @ a @ X @ Xs ) @ ( nil @ a ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_231_ord_Olexordp__eq_Ocases,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.85/1.58 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 2.85/1.58 => ( ( ( A1
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 => ! [Ys2: list @ A] : ( A22 != Ys2 ) )
% 2.85/1.58 => ( ! [X3: A] :
% 2.85/1.58 ( ? [Xs2: list @ A] :
% 2.85/1.58 ( A1
% 2.85/1.58 = ( cons @ A @ X3 @ Xs2 ) )
% 2.85/1.58 => ! [Y2: A] :
% 2.85/1.58 ( ? [Ys2: list @ A] :
% 2.85/1.58 ( A22
% 2.85/1.58 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.85/1.58 => ~ ( Less @ X3 @ Y2 ) ) )
% 2.85/1.58 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.85/1.58 ( ( A1
% 2.85/1.58 = ( cons @ A @ X3 @ Xs2 ) )
% 2.85/1.58 => ! [Ys2: list @ A] :
% 2.85/1.58 ( ( A22
% 2.85/1.58 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.85/1.58 => ( ~ ( Less @ X3 @ Y2 )
% 2.85/1.58 => ( ~ ( Less @ Y2 @ X3 )
% 2.85/1.58 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_232_ord_Olexordp__eq_Osimps,axiom,
% 2.85/1.58 ! [A: $tType] :
% 2.85/1.58 ( ( lexordp_eq @ A )
% 2.85/1.58 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.85/1.58 ( ? [Ys3: list @ A] :
% 2.85/1.58 ( ( A12
% 2.85/1.58 = ( nil @ A ) )
% 2.85/1.58 & ( A23 = Ys3 ) )
% 2.85/1.58 | ? [X2: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 2.85/1.58 ( ( A12
% 2.85/1.58 = ( cons @ A @ X2 @ Xs3 ) )
% 2.85/1.58 & ( A23
% 2.85/1.58 = ( cons @ A @ Y3 @ Ys3 ) )
% 2.85/1.58 & ( Less2 @ X2 @ Y3 ) )
% 2.85/1.58 | ? [X2: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 2.85/1.58 ( ( A12
% 2.85/1.58 = ( cons @ A @ X2 @ Xs3 ) )
% 2.85/1.58 & ( A23
% 2.85/1.58 = ( cons @ A @ Y3 @ Ys3 ) )
% 2.85/1.58 & ~ ( Less2 @ X2 @ Y3 )
% 2.85/1.58 & ~ ( Less2 @ Y3 @ X2 )
% 2.85/1.58 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_233_ord_Olexordp__eq_Oinducts,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,X12: list @ A,X27: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.85/1.58 ( ( lexordp_eq @ A @ Less @ X12 @ X27 )
% 2.85/1.58 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.85/1.58 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.85/1.58 ( ( Less @ X3 @ Y2 )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.85/1.58 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.85/1.58 ( ~ ( Less @ X3 @ Y2 )
% 2.85/1.58 => ( ~ ( Less @ Y2 @ X3 )
% 2.85/1.58 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 )
% 2.85/1.58 => ( ( P @ Xs2 @ Ys2 )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) )
% 2.85/1.58 => ( P @ X12 @ X27 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_234_list_Odistinct_I1_J,axiom,
% 2.85/1.58 ! [A: $tType,X21: A,X22: list @ A] :
% 2.85/1.58 ( ( nil @ A )
% 2.85/1.58 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_235_list_OdiscI,axiom,
% 2.85/1.58 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.85/1.58 ( ( List
% 2.85/1.58 = ( cons @ A @ X21 @ X22 ) )
% 2.85/1.58 => ( List
% 2.85/1.58 != ( nil @ A ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_236_list_Oexhaust,axiom,
% 2.85/1.58 ! [A: $tType,Y: list @ A] :
% 2.85/1.58 ( ( Y
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ~ ! [X212: A,X222: list @ A] :
% 2.85/1.58 ( Y
% 2.85/1.58 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_237_list_Oinducts,axiom,
% 2.85/1.58 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.85/1.58 ( ( P @ ( nil @ A ) )
% 2.85/1.58 => ( ! [X1: A,X26: list @ A] :
% 2.85/1.58 ( ( P @ X26 )
% 2.85/1.58 => ( P @ ( cons @ A @ X1 @ X26 ) ) )
% 2.85/1.58 => ( P @ List ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_238_neq__Nil__conv,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 = ( ? [Y3: A,Ys3: list @ A] :
% 2.85/1.58 ( Xs
% 2.85/1.58 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_239_list__induct2_H,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.85/1.58 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.85/1.58 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 2.85/1.58 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 2.85/1.58 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 2.85/1.58 ( ( P @ Xs2 @ Ys2 )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 2.85/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_240_splice_Oinduct,axiom,
% 2.85/1.58 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.85/1.58 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.85/1.58 => ( ! [V3: A,Va2: list @ A] : ( P @ ( cons @ A @ V3 @ Va2 ) @ ( nil @ A ) )
% 2.85/1.58 => ( ! [X3: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.85/1.58 ( ( P @ Xs2 @ Ys2 )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.85/1.58 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_241_transpose_Ocases,axiom,
% 2.85/1.58 ! [A: $tType,X: list @ ( list @ A )] :
% 2.85/1.58 ( ( X
% 2.85/1.58 != ( nil @ ( list @ A ) ) )
% 2.85/1.58 => ( ! [Xss: list @ ( list @ A )] :
% 2.85/1.58 ( X
% 2.85/1.58 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.85/1.58 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.85/1.58 ( X
% 2.85/1.58 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_242_remdups__adj_Ocases,axiom,
% 2.85/1.58 ! [A: $tType,X: list @ A] :
% 2.85/1.58 ( ( X
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ! [X3: A] :
% 2.85/1.58 ( X
% 2.85/1.58 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.85/1.58 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.85/1.58 ( X
% 2.85/1.58 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_243_remdups__adj_Oinduct,axiom,
% 2.85/1.58 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.85/1.58 ( ( P @ ( nil @ A ) )
% 2.85/1.58 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.85/1.58 => ( ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.85/1.58 ( ( ( X3 = Y2 )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 2.85/1.58 => ( ( ( X3 != Y2 )
% 2.85/1.58 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.85/1.58 => ( P @ A0 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_244_list__nonempty__induct,axiom,
% 2.85/1.58 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.85/1.58 ( ( Xs
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.85/1.58 => ( ! [X3: A,Xs2: list @ A] :
% 2.85/1.58 ( ( Xs2
% 2.85/1.58 != ( nil @ A ) )
% 2.85/1.58 => ( ( P @ Xs2 )
% 2.85/1.58 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 2.85/1.58 => ( P @ Xs ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_245_map__tailrec__rev_Oinduct,axiom,
% 2.85/1.58 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.85/1.58 ( ! [F3: A > B,X1: list @ B] : ( P @ F3 @ ( nil @ A ) @ X1 )
% 2.85/1.58 => ( ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.85/1.58 ( ( P @ F3 @ As @ ( cons @ B @ ( F3 @ A4 ) @ Bs ) )
% 2.85/1.58 => ( P @ F3 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.85/1.58 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_246_not__Cons__self2,axiom,
% 2.85/1.58 ! [A: $tType,X: A,Xs: list @ A] :
% 2.85/1.58 ( ( cons @ A @ X @ Xs )
% 2.85/1.58 != Xs ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_247_ord_Olexordp__eq_OCons,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ( ( Less @ X @ Y )
% 2.85/1.58 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_248_ord_Olexordp__eq_OCons__eq,axiom,
% 2.85/1.58 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.85/1.58 ( ~ ( Less @ X @ Y )
% 2.85/1.58 => ( ~ ( Less @ Y @ X )
% 2.85/1.58 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys )
% 2.85/1.58 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_249_local_Oset__entries__inject,axiom,
% 2.85/1.58 ! [B: $tType,T1: rBT_Im246033960le_rbt @ a @ B,T22: rBT_Im246033960le_rbt @ a @ B] :
% 2.85/1.58 ( ( rBT_Im759614907sorted @ a @ B @ less @ T1 )
% 2.85/1.58 => ( ( rBT_Im759614907sorted @ a @ B @ less @ T22 )
% 2.85/1.58 => ( ( ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T1 ) )
% 2.85/1.58 = ( set2 @ ( product_prod @ a @ B ) @ ( rBT_Im954575269ntries @ a @ B @ T22 ) ) )
% 2.85/1.58 = ( ( rBT_Im954575269ntries @ a @ B @ T1 )
% 2.85/1.58 = ( rBT_Im954575269ntries @ a @ B @ T22 ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_250_local_Olexordp__induct,axiom,
% 2.85/1.58 ! [Xs: list @ a,Ys: list @ a,P: ( list @ a ) > ( list @ a ) > $o] :
% 2.85/1.58 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.85/1.58 => ( ! [Y2: a,Ys2: list @ a] : ( P @ ( nil @ a ) @ ( cons @ a @ Y2 @ Ys2 ) )
% 2.85/1.58 => ( ! [X3: a,Xs2: list @ a,Y2: a,Ys2: list @ a] :
% 2.85/1.58 ( ( less @ X3 @ Y2 )
% 2.85/1.58 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ Y2 @ Ys2 ) ) )
% 2.85/1.58 => ( ! [X3: a,Xs2: list @ a,Ys2: list @ a] :
% 2.85/1.58 ( ( lexordp @ a @ less @ Xs2 @ Ys2 )
% 2.85/1.58 => ( ( P @ Xs2 @ Ys2 )
% 2.85/1.58 => ( P @ ( cons @ a @ X3 @ Xs2 ) @ ( cons @ a @ X3 @ Ys2 ) ) ) )
% 2.85/1.58 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_251_local_Olexordp__antisym,axiom,
% 2.85/1.58 ! [Xs: list @ a,Ys: list @ a] :
% 2.85/1.58 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.85/1.58 => ~ ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_252_local_Olexordp__irreflexive,axiom,
% 2.85/1.58 ! [Xs: list @ a] :
% 2.85/1.58 ( ! [X3: a] :
% 2.85/1.58 ~ ( less @ X3 @ X3 )
% 2.85/1.58 => ~ ( lexordp @ a @ less @ Xs @ Xs ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_253_local_Olexordp__irreflexive_H,axiom,
% 2.85/1.58 ! [Xs: list @ a] :
% 2.85/1.58 ~ ( lexordp @ a @ less @ Xs @ Xs ) ).
% 2.85/1.58
% 2.85/1.58 thf(fact_254_local_Olexordp__linear,axiom,
% 2.85/1.58 ! [Xs: list @ a,Ys: list @ a] :
% 2.85/1.58 ( ( lexordp @ a @ less @ Xs @ Ys )
% 2.85/1.58 | ( Xs = Ys )
% 2.85/1.58 | ( lexordp @ a @ less @ Ys @ Xs ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.85/1.58 ! [A5: $tType,A6: $tType] :
% 2.85/1.58 ( ( order @ A6 @ ( type2 @ A6 ) )
% 2.85/1.58 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_fun___Orderings_Oord,axiom,
% 2.85/1.58 ! [A5: $tType,A6: $tType] :
% 2.85/1.58 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 2.85/1.58 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 2.85/1.58 ! [A5: $tType] : ( order @ ( set @ A5 ) @ ( type2 @ ( set @ A5 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 2.85/1.58 ! [A5: $tType] : ( ord @ ( set @ A5 ) @ ( type2 @ ( set @ A5 ) ) ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 2.85/1.58 order @ $o @ ( type2 @ $o ) ).
% 2.85/1.58
% 2.85/1.58 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 2.85/1.58 ord @ $o @ ( type2 @ $o ) ).
% 2.85/1.58
% 2.85/1.58 thf(conj_0,conjecture,
% 2.85/1.58 rBT_Im1259024060reater @ a @ b @ less @ x @ d ).
% 2.85/1.58 ------------------------
% 2.97/1.61 % (19531)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_19201 for (2999ds/4Mi)
% 2.97/1.61 % (19531)Instruction limit reached!
% 2.97/1.61 % (19531)------------------------------
% 2.97/1.61 % (19531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (19531)Termination reason: Unknown
% 2.97/1.61 % (19531)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (19531)Memory used [KB]: 1663
% 2.97/1.61 % (19531)Time elapsed: 0.003 s
% 2.97/1.61 % (19531)Instructions burned: 6 (million)
% 2.97/1.61 % (19531)------------------------------
% 2.97/1.61 % (19531)------------------------------
% 2.97/1.61 % (19534)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_19201 for (2999ds/2Mi)
% 2.97/1.61 % (19534)Instruction limit reached!
% 2.97/1.61 % (19534)------------------------------
% 2.97/1.61 % (19534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (19534)Termination reason: Unknown
% 2.97/1.61 % (19534)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (19534)Memory used [KB]: 1407
% 2.97/1.61 % (19534)Time elapsed: 0.003 s
% 2.97/1.61 % (19534)Instructions burned: 2 (million)
% 2.97/1.61 % (19534)------------------------------
% 2.97/1.61 % (19534)------------------------------
% 2.97/1.61 % (19530)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/183Mi)
% 2.97/1.61 % (19532)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_19201 for (2999ds/27Mi)
% 2.97/1.61 % (19533)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/2Mi)
% 2.97/1.61 % (19535)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_19201 for (2999ds/275Mi)
% 2.97/1.61 % (19536)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/18Mi)
% 2.97/1.61 % (19533)Instruction limit reached!
% 2.97/1.61 % (19533)------------------------------
% 2.97/1.61 % (19533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (19533)Termination reason: Unknown
% 2.97/1.61 % (19533)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (19533)Memory used [KB]: 1407
% 2.97/1.61 % (19533)Time elapsed: 0.003 s
% 2.97/1.61 % (19533)Instructions burned: 2 (million)
% 2.97/1.61 % (19533)------------------------------
% 2.97/1.61 % (19533)------------------------------
% 2.97/1.62 % (19537)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/3Mi)
% 2.97/1.62 % (19537)Instruction limit reached!
% 2.97/1.62 % (19537)------------------------------
% 2.97/1.62 % (19537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (19537)Termination reason: Unknown
% 2.97/1.62 % (19537)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (19537)Memory used [KB]: 1407
% 2.97/1.62 % (19537)Time elapsed: 0.003 s
% 2.97/1.62 % (19537)Instructions burned: 4 (million)
% 2.97/1.62 % (19537)------------------------------
% 2.97/1.62 % (19537)------------------------------
% 2.97/1.63 % (19536)Instruction limit reached!
% 2.97/1.63 % (19536)------------------------------
% 2.97/1.63 % (19536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.63 % (19536)Termination reason: Unknown
% 2.97/1.63 % (19536)Termination phase: shuffling
% 2.97/1.63 % (19538)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_19201 for (2999ds/37Mi)
% 2.97/1.63
% 2.97/1.63 % (19536)Memory used [KB]: 1791
% 2.97/1.63 % (19536)Time elapsed: 0.014 s
% 2.97/1.63 % (19536)Instructions burned: 19 (million)
% 2.97/1.63 % (19536)------------------------------
% 2.97/1.63 % (19536)------------------------------
% 2.97/1.63 % (19540)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_19201 for (2999ds/3Mi)
% 2.97/1.63 % (19532)Instruction limit reached!
% 2.97/1.63 % (19532)------------------------------
% 2.97/1.63 % (19532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.63 % (19532)Termination reason: Unknown
% 2.97/1.63 % (19532)Termination phase: shuffling
% 2.97/1.63
% 2.97/1.63 % (19532)Memory used [KB]: 1791
% 2.97/1.63 % (19532)Time elapsed: 0.019 s
% 2.97/1.63 % (19532)Instructions burned: 27 (million)
% 2.97/1.63 % (19532)------------------------------
% 2.97/1.63 % (19532)------------------------------
% 2.97/1.63 % (19540)Instruction limit reached!
% 2.97/1.63 % (19540)------------------------------
% 2.97/1.63 % (19540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.63 % (19540)Termination reason: Unknown
% 2.97/1.63 % (19540)Termination phase: shuffling
% 2.97/1.63
% 2.97/1.63 % (19540)Memory used [KB]: 1407
% 2.97/1.63 % (19540)Time elapsed: 0.003 s
% 2.97/1.63 % (19540)Instructions burned: 4 (million)
% 2.97/1.63 % (19540)------------------------------
% 2.97/1.63 % (19540)------------------------------
% 2.97/1.63 % (19539)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_19201 for (2999ds/15Mi)
% 2.97/1.64 % (19539)Instruction limit reached!
% 2.97/1.64 % (19539)------------------------------
% 2.97/1.64 % (19539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (19539)Termination reason: Unknown
% 2.97/1.64 % (19539)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (19539)Memory used [KB]: 1663
% 2.97/1.64 % (19539)Time elapsed: 0.011 s
% 2.97/1.64 % (19539)Instructions burned: 15 (million)
% 2.97/1.64 % (19539)------------------------------
% 2.97/1.64 % (19539)------------------------------
% 2.97/1.64 % (19543)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/16Mi)
% 2.97/1.64 % (19538)Instruction limit reached!
% 2.97/1.64 % (19538)------------------------------
% 2.97/1.64 % (19538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (19538)Termination reason: Unknown
% 2.97/1.64 % (19538)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (19538)Memory used [KB]: 2046
% 2.97/1.64 % (19538)Time elapsed: 0.019 s
% 2.97/1.64 % (19538)Instructions burned: 38 (million)
% 2.97/1.64 % (19538)------------------------------
% 2.97/1.64 % (19538)------------------------------
% 2.97/1.64 % (19541)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_19201 for (2999ds/1041Mi)
% 2.97/1.65 % (19543)Instruction limit reached!
% 2.97/1.65 % (19543)------------------------------
% 2.97/1.65 % (19543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.65 % (19543)Termination reason: Unknown
% 2.97/1.65 % (19543)Termination phase: shuffling
% 2.97/1.65
% 2.97/1.65 % (19543)Memory used [KB]: 1663
% 2.97/1.65 % (19543)Time elapsed: 0.008 s
% 2.97/1.65 % (19543)Instructions burned: 18 (million)
% 2.97/1.65 % (19543)------------------------------
% 2.97/1.65 % (19543)------------------------------
% 2.97/1.65 % (19542)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/7Mi)
% 2.97/1.65 % (19542)Instruction limit reached!
% 2.97/1.65 % (19542)------------------------------
% 2.97/1.65 % (19542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.65 % (19542)Termination reason: Unknown
% 2.97/1.65 % (19542)Termination phase: shuffling
% 2.97/1.65
% 2.97/1.65 % (19542)Memory used [KB]: 1535
% 2.97/1.65 % (19542)Time elapsed: 0.006 s
% 2.97/1.65 % (19542)Instructions burned: 7 (million)
% 2.97/1.65 % (19542)------------------------------
% 2.97/1.65 % (19542)------------------------------
% 2.97/1.66 % (19545)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_19201 for (2999ds/3Mi)
% 2.97/1.66 % (19545)Instruction limit reached!
% 2.97/1.66 % (19545)------------------------------
% 2.97/1.66 % (19545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (19545)Termination reason: Unknown
% 2.97/1.66 % (19545)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (19545)Memory used [KB]: 1407
% 2.97/1.66 % (19545)Time elapsed: 0.003 s
% 2.97/1.66 % (19545)Instructions burned: 6 (million)
% 2.97/1.66 % (19545)------------------------------
% 2.97/1.66 % (19545)------------------------------
% 2.97/1.66 % (19546)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/7Mi)
% 2.97/1.66 % (19544)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_19201 for (2999ds/3Mi)
% 2.97/1.66 % (19546)Instruction limit reached!
% 2.97/1.66 % (19546)------------------------------
% 2.97/1.66 % (19546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (19546)Termination reason: Unknown
% 2.97/1.66 % (19546)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (19546)Memory used [KB]: 1535
% 2.97/1.66 % (19546)Time elapsed: 0.004 s
% 2.97/1.66 % (19546)Instructions burned: 7 (million)
% 2.97/1.66 % (19546)------------------------------
% 2.97/1.66 % (19546)------------------------------
% 2.97/1.66 % (19544)Instruction limit reached!
% 2.97/1.66 % (19544)------------------------------
% 2.97/1.66 % (19544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (19544)Termination reason: Unknown
% 2.97/1.66 % (19544)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (19544)Memory used [KB]: 1407
% 2.97/1.66 % (19544)Time elapsed: 0.004 s
% 2.97/1.66 % (19544)Instructions burned: 4 (million)
% 2.97/1.66 % (19544)------------------------------
% 2.97/1.66 % (19544)------------------------------
% 2.97/1.67 % (19535)First to succeed.
% 2.97/1.67 % (19548)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19201 for (2999ds/4Mi)
% 2.97/1.67 % (19535)Refutation found. Thanks to Tanya!
% 2.97/1.67 % SZS status Theorem for DTF2THF_19201
% 2.97/1.67 % SZS output start Proof for DTF2THF_19201
% 2.97/1.67 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.97/1.67 thf(type_def_7, type, list: ($tType) > $tType).
% 2.97/1.67 thf(type_def_8, type, set: ($tType) > $tType).
% 2.97/1.67 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 2.97/1.67 thf(type_def_10, type, option: ($tType) > $tType).
% 2.97/1.67 thf(type_def_11, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 2.97/1.67 thf(type_def_12, type, rBT_Im1923302023_color: $tType).
% 2.97/1.67 thf(type_def_13, type, a: $tType).
% 2.97/1.67 thf(type_def_14, type, b: $tType).
% 2.97/1.67 thf(func_def_0, type, rBT_Im1923302023_color: $tType).
% 2.97/1.67 thf(func_def_1, type, rBT_Im246033960le_rbt: ($tType * $tType) > $tType).
% 2.97/1.67 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 2.97/1.67 thf(func_def_3, type, option: ($tType) > $tType).
% 2.97/1.67 thf(func_def_4, type, list: ($tType) > $tType).
% 2.97/1.67 thf(func_def_5, type, set: ($tType) > $tType).
% 2.97/1.67 thf(func_def_6, type, itself: ($tType) > $tType).
% 2.97/1.67 thf(func_def_7, type, b: $tType).
% 2.97/1.67 thf(func_def_8, type, a: $tType).
% 2.97/1.67 thf(func_def_9, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.67 thf(func_def_10, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.67 thf(func_def_11, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.97/1.67 thf(func_def_12, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.97/1.67 thf(func_def_13, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.97/1.67 thf(func_def_14, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 2.97/1.67 thf(func_def_15, type, lexordp: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 2.97/1.67 thf(func_def_16, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 2.97/1.67 thf(func_def_17, type, map_of: !>[X0: $tType, X1: $tType]:(list @ product_prod @ X0 @ X1 > X0 > option @ X1)).
% 2.97/1.67 thf(func_def_18, type, none: !>[X0: $tType]:(option @ X0)).
% 2.97/1.67 thf(func_def_19, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.97/1.67 thf(func_def_20, type, strict_mono: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > $o)).
% 2.97/1.67 thf(func_def_21, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.97/1.67 thf(func_def_22, type, rBT_Im1648453169alance: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_23, type, rBT_Im1278323832e_left: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_24, type, rBT_Im1053358987_right: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_25, type, rBT_Impl_Mirabelle_B: rBT_Im1923302023_color).
% 2.97/1.67 thf(func_def_26, type, rBT_Impl_Mirabelle_R: rBT_Im1923302023_color).
% 2.97/1.67 thf(func_def_27, type, rBT_Im1591839508ombine: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_28, type, rBT_Im954575269ntries: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1 > list @ product_prod @ X0 @ X1)).
% 2.97/1.67 thf(func_def_29, type, rBT_Im862805236is_rbt: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.97/1.67 thf(func_def_30, type, rBT_Im1259024060reater: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.97/1.67 thf(func_def_31, type, rBT_Im1756508336bt_ins: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1 > X1 > X1) > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_32, type, rBT_Im852463031insert: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_33, type, rBT_Im241132701t_with: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X1 > X1) > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_34, type, rBT_Im627674146th_key: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1 > X1 > X1) > X0 > X1 > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_35, type, rBT_Im2075124343t_less: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > X0 > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.97/1.67 thf(func_def_36, type, rBT_Im35466040lookup: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > X0 > option @ X1)).
% 2.97/1.67 thf(func_def_37, type, rBT_Im759614907sorted: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > rBT_Im246033960le_rbt @ X0 @ X1 > $o)).
% 2.97/1.67 thf(func_def_38, type, rBT_Im945281971_paint: !>[X0: $tType, X1: $tType]:(rBT_Im1923302023_color > rBT_Im246033960le_rbt @ X0 @ X1 > rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_39, 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)).
% 2.97/1.67 thf(func_def_40, type, rBT_Im418718756_Empty: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X0 @ X1)).
% 2.97/1.67 thf(func_def_41, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.97/1.67 thf(func_def_42, type, set_greaterThan: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.97/1.67 thf(func_def_43, type, set_lessThan: !>[X0: $tType]:((X0 > X0 > $o) > X0 > set @ X0)).
% 2.97/1.67 thf(func_def_44, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.97/1.67 thf(func_def_45, type, a2: rBT_Im246033960le_rbt @ a @ b).
% 2.97/1.67 thf(func_def_46, type, b2: rBT_Im246033960le_rbt @ a @ b).
% 2.97/1.67 thf(func_def_47, type, c: rBT_Im246033960le_rbt @ a @ b).
% 2.97/1.67 thf(func_def_48, type, d: rBT_Im246033960le_rbt @ a @ b).
% 2.97/1.67 thf(func_def_49, type, k: a).
% 2.97/1.67 thf(func_def_50, type, l: rBT_Im246033960le_rbt @ a @ b).
% 2.97/1.67 thf(func_def_51, type, less: a > a > $o).
% 2.97/1.67 thf(func_def_52, type, r: rBT_Im246033960le_rbt @ a @ b).
% 2.97/1.67 thf(func_def_53, type, v: b).
% 2.97/1.67 thf(func_def_54, type, w: b).
% 2.97/1.67 thf(func_def_55, type, x: a).
% 2.97/1.67 thf(func_def_56, type, y: a).
% 2.97/1.67 thf(func_def_73, type, sK0: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im1923302023_color)).
% 2.97/1.67 thf(func_def_74, type, sK1: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.97/1.67 thf(func_def_75, type, sK2: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X1)).
% 2.97/1.67 thf(func_def_76, type, sK3: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > X0)).
% 2.97/1.67 thf(func_def_77, type, sK4: !>[X0: $tType, X1: $tType]:(rBT_Im246033960le_rbt @ X1 @ X0 > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.97/1.67 thf(func_def_78, type, sK5: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im1923302023_color)).
% 2.97/1.67 thf(func_def_79, type, sK6: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.97/1.67 thf(func_def_80, type, sK7: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X1)).
% 2.97/1.67 thf(func_def_81, type, sK8: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > X0)).
% 2.97/1.67 thf(func_def_82, type, sK9: !>[X0: $tType, X1: $tType]:((rBT_Im246033960le_rbt @ X1 @ X0 > $o) > rBT_Im246033960le_rbt @ X1 @ X0)).
% 2.97/1.67 thf(func_def_83, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.97/1.67 thf(func_def_85, type, ph12: !>[X0: $tType]:(X0)).
% 2.97/1.67 thf(f830,plain,(
% 2.97/1.67 $false),
% 2.97/1.67 inference(subsumption_resolution,[status(thm)],[f829,f709])).
% 2.97/1.67 thf(f709,plain,(
% 2.97/1.67 ((less @ x @ y) = $true)),
% 2.97/1.67 inference(cnf_transformation,[status(thm)],[f474])).
% 2.97/1.67 thf(f474,plain,(
% 2.97/1.67 ((rBT_Im1259024060reater @ a @ b @ less @ y @ d) = $true) & ((less @ x @ y) = $true)),
% 2.97/1.67 inference(fool_elimination,[status(thm)],[f473])).
% 2.97/1.67 thf(f473,plain,(
% 2.97/1.67 (less @ x @ y) & (rBT_Im1259024060reater @ a @ b @ less @ y @ d)),
% 2.97/1.67 inference(rectify,[status(thm)],[f27])).
% 2.97/1.67 thf(f27,axiom,(
% 2.97/1.67 (less @ x @ y) & (rBT_Im1259024060reater @ a @ b @ less @ y @ d)),
% 2.97/1.67 file('/export/starexec/sandbox/tmp/tmp.F0zMB7Y9hR/DTF2THF_19201.p',fact_26__092_060open_062x_A_060_Ay_A_092_060and_062_Ay_A_092_060guillemotleft_062_124_Ad_092_060close_062)).
% 2.97/1.67 thf(f829,plain,(
% 2.97/1.67 ((less @ x @ y) != $true)),
% 2.97/1.67 inference(trivial_inequality_removal,[status(thm)],[f827])).
% 2.97/1.67 thf(f827,plain,(
% 2.97/1.67 ((less @ x @ y) != $true) | ($true != $true)),
% 2.97/1.67 inference(superposition,[status(thm)],[f825,f710])).
% 2.97/1.67 thf(f710,plain,(
% 2.97/1.67 ((rBT_Im1259024060reater @ a @ b @ less @ y @ d) = $true)),
% 2.97/1.67 inference(cnf_transformation,[status(thm)],[f474])).
% 2.97/1.67 thf(f825,plain,(
% 2.97/1.67 ( ! [X0 : a] : (($true != (rBT_Im1259024060reater @ a @ b @ less @ X0 @ d)) | ($true != (less @ x @ X0))) )),
% 2.97/1.67 inference(trivial_inequality_removal,[status(thm)],[f824])).
% 2.97/1.67 thf(f824,plain,(
% 2.97/1.67 ( ! [X0 : a] : (($true != (rBT_Im1259024060reater @ a @ b @ less @ X0 @ d)) | ($true != (less @ x @ X0)) | ($true != $true)) )),
% 2.97/1.67 inference(superposition,[status(thm)],[f735,f747])).
% 2.97/1.67 thf(f747,plain,(
% 2.97/1.67 ( ! [X0 : $tType,X2 : a,X3 : rBT_Im246033960le_rbt @ a @ X0,X1 : a] : (($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X1 @ X3)) | ((less @ X1 @ X2) != $true) | ($true != (rBT_Im1259024060reater @ a @ X0 @ less @ X2 @ X3))) )),
% 2.97/1.67 inference(cnf_transformation,[status(thm)],[f664])).
% 2.97/1.67 thf(f664,plain,(
% 2.97/1.67 ! [X0 : $tType,X1 : a,X2 : a,X3 : rBT_Im246033960le_rbt @ a @ X0] : (($true != (rBT_Im1259024060reater @ a @ X0 @ less @ X2 @ X3)) | ($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X1 @ X3)) | ((less @ X1 @ X2) != $true))),
% 2.97/1.67 inference(flattening,[status(thm)],[f663])).
% 2.97/1.67 thf(f663,plain,(
% 2.97/1.67 ! [X0 : $tType,X1 : a,X2 : a,X3 : rBT_Im246033960le_rbt @ a @ X0] : ((($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X1 @ X3)) | ($true != (rBT_Im1259024060reater @ a @ X0 @ less @ X2 @ X3))) | ((less @ X1 @ X2) != $true))),
% 2.97/1.67 inference(ennf_transformation,[status(thm)],[f464])).
% 2.97/1.67 thf(f464,plain,(
% 2.97/1.67 ! [X0 : $tType,X1 : a,X2 : a,X3 : rBT_Im246033960le_rbt @ a @ X0] : (((less @ X1 @ X2) = $true) => (($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X2 @ X3)) => ($true = (rBT_Im1259024060reater @ a @ X0 @ less @ X1 @ X3))))),
% 2.97/1.67 inference(fool_elimination,[status(thm)],[f463])).
% 2.97/1.67 thf(f463,plain,(
% 2.97/1.67 ! [X0 : $tType,X1 : a,X2 : a,X3 : rBT_Im246033960le_rbt @ a @ X0] : ((less @ X1 @ X2) => ((rBT_Im1259024060reater @ a @ X0 @ less @ X2 @ X3) => (rBT_Im1259024060reater @ a @ X0 @ less @ X1 @ X3)))),
% 2.97/1.67 inference(rectify,[status(thm)],[f26])).
% 2.97/1.67 thf(f26,axiom,(
% 2.97/1.67 ! [X9 : $tType,X3 : a,X2 : a,X10 : rBT_Im246033960le_rbt @ a @ X9] : ((less @ X3 @ X2) => ((rBT_Im1259024060reater @ a @ X9 @ less @ X2 @ X10) => (rBT_Im1259024060reater @ a @ X9 @ less @ X3 @ X10)))),
% 2.97/1.67 file('/export/starexec/sandbox/tmp/tmp.F0zMB7Y9hR/DTF2THF_19201.p',fact_25_local_Orbt__greater__trans)).
% 2.97/1.67 thf(f735,plain,(
% 2.97/1.67 ((rBT_Im1259024060reater @ a @ b @ less @ x @ d) != $true)),
% 2.97/1.67 inference(cnf_transformation,[status(thm)],[f589])).
% 2.97/1.67 thf(f589,plain,(
% 2.97/1.67 ((rBT_Im1259024060reater @ a @ b @ less @ x @ d) != $true)),
% 2.97/1.67 inference(flattening,[status(thm)],[f570])).
% 2.97/1.67 thf(f570,plain,(
% 2.97/1.67 ~((rBT_Im1259024060reater @ a @ b @ less @ x @ d) = $true)),
% 2.97/1.67 inference(fool_elimination,[status(thm)],[f569])).
% 2.97/1.67 thf(f569,plain,(
% 2.97/1.67 ~(rBT_Im1259024060reater @ a @ b @ less @ x @ d)),
% 2.97/1.67 inference(rectify,[status(thm)],[f263])).
% 2.97/1.67 thf(f263,negated_conjecture,(
% 2.97/1.67 ~(rBT_Im1259024060reater @ a @ b @ less @ x @ d)),
% 2.97/1.67 inference(negated_conjecture,[status(cth)],[f262])).
% 2.97/1.67 thf(f262,conjecture,(
% 2.97/1.67 (rBT_Im1259024060reater @ a @ b @ less @ x @ d)),
% 2.97/1.67 file('/export/starexec/sandbox/tmp/tmp.F0zMB7Y9hR/DTF2THF_19201.p',conj_0)).
% 2.97/1.67 % SZS output end Proof for DTF2THF_19201
% 2.97/1.67 % (19535)------------------------------
% 2.97/1.67 % (19535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (19535)Termination reason: Refutation
% 2.97/1.67
% 2.97/1.67 % (19535)Memory used [KB]: 6780
% 2.97/1.67 % (19535)Time elapsed: 0.053 s
% 2.97/1.67 % (19535)Instructions burned: 121 (million)
% 2.97/1.67 % (19535)------------------------------
% 2.97/1.67 % (19535)------------------------------
% 2.97/1.67 % (19529)Success in time 0.082 s
%------------------------------------------------------------------------------