%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT207^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 08:45:08 AM UTC 2026
% Result : Theorem 2.90s 1.61s
% Output : Refutation 2.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT207^1 : TPTP v9.2.1. Released v7.0.0.
% 0.09/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n008.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 06:10:54 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : DAT207^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.44 % Domain : Data Structures
% 0.16/0.44 % Problem : Sorted list operations 243
% 0.16/0.44 % Version : [Bla16] axioms : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [Lam09] Lammich (2009), Collections Framework
% 0.16/0.44 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.44 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Bla16]
% 0.16/0.44 % Names : sorted_list_operations__243.p [Bla16]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.33 v9.1.0, 0.00 v7.3.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.16/0.44 % Syntax : Number of formulae : 348 ( 123 unt; 56 typ; 0 def)
% 0.16/0.44 % Number of atoms : 844 ( 453 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 16 ( 2 avg)
% 0.16/0.44 % Number of connectives : 4897 ( 170 ~; 14 |; 82 &;4153 @)
% 0.16/0.44 % ( 0 <=>; 478 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 24 ( 8 avg)
% 0.16/0.44 % Number of types : 2 ( 1 usr)
% 0.16/0.44 % Number of type conns : 277 ( 277 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 56 ( 55 usr; 3 con; 0-5 aty)
% 0.16/0.44 % Number of variables : 1273 ( 34 ^;1134 !; 49 ?;1273 :)
% 0.16/0.44 % ( 56 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.44 % SPC : TH1_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.44 % 2016-07-13 14:41:25.989
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 %----Could-be-implicit typings (4)
% 0.16/0.44 thf(ty_t_List_Olist,type,
% 0.16/0.44 list: $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_Set_Oset,type,
% 0.16/0.44 set: $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_t_itself,type,
% 0.16/0.44 itself: $tType > $tType ).
% 0.16/0.44
% 0.16/0.44 thf(ty_tf_a,type,
% 0.16/0.44 a: $tType ).
% 0.16/0.44
% 0.16/0.44 %----Explicit typings (52)
% 0.16/0.44 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.16/0.44 bounded_lattice:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_HOL_Otype,type,
% 0.16/0.44 type:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Obot,type,
% 0.16/0.44 bot:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Oord,type,
% 0.16/0.44 ord:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Oorder,type,
% 0.16/0.44 order:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Lattices_Olattice,type,
% 0.16/0.44 lattice:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Ono__bot,type,
% 0.16/0.44 no_bot:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Ono__top,type,
% 0.16/0.44 no_top:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Olinorder,type,
% 0.16/0.44 linorder:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Opreorder,type,
% 0.16/0.44 preorder:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.16/0.44 order_bot:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Owellorder,type,
% 0.16/0.44 wellorder:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Orderings_Odense__order,type,
% 0.16/0.44 dense_order:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.16/0.44 semilattice_sup:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 0.16/0.44 bounded_lattice_bot:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.16/0.44 bounde1808546759up_bot:
% 0.16/0.44 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 0.16/0.44 bNF_Greatest_shift:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.16/0.44 sup_sup:
% 0.16/0.44 !>[A: $tType] : ( A > A > A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Oappend,type,
% 0.16/0.44 append:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Obind,type,
% 0.16/0.44 bind:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Oinsert,type,
% 0.16/0.44 insert:
% 0.16/0.44 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Olinorder__class_Osorted__list__of__set,type,
% 0.16/0.44 linord467138063of_set:
% 0.16/0.44 !>[A: $tType] : ( ( set @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Olist_OCons,type,
% 0.16/0.44 cons:
% 0.16/0.44 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Olist_ONil,type,
% 0.16/0.44 nil:
% 0.16/0.44 !>[A: $tType] : ( list @ A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Olist_Omap,type,
% 0.16/0.44 map:
% 0.16/0.44 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Olist__ex1,type,
% 0.16/0.44 list_ex1:
% 0.16/0.44 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Olistrelp,type,
% 0.16/0.44 listrelp:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Omap__tailrec,type,
% 0.16/0.44 map_tailrec:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Omap__tailrec__rev,type,
% 0.16/0.44 map_tailrec_rev:
% 0.16/0.44 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.16/0.44 lexordp_eq:
% 0.16/0.44 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 0.16/0.44 ord_lexordp_eq:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Oproduct__lists,type,
% 0.16/0.44 product_lists:
% 0.16/0.44 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Orev,type,
% 0.16/0.44 rev:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Osplice,type,
% 0.16/0.44 splice:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List_Osublists,type,
% 0.16/0.44 sublists:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_List__More_Ocombinatorial__product,type,
% 0.16/0.44 list_c659805718roduct:
% 0.16/0.44 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Misc_Olist__collect__set,type,
% 0.16/0.44 list_collect_set:
% 0.16/0.44 !>[B: $tType,A: $tType] : ( ( B > ( set @ A ) ) > ( list @ B ) > ( set @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Misc_Omerge,type,
% 0.16/0.44 merge:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Misc_Omerge__list,type,
% 0.16/0.44 merge_list:
% 0.16/0.44 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Misc_Orevg,type,
% 0.16/0.44 revg:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.16/0.44 bot_bot:
% 0.16/0.44 !>[A: $tType] : A ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.16/0.44 ord_less:
% 0.16/0.44 !>[A: $tType] : ( A > A > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Pure_Otype,type,
% 0.16/0.44 type2:
% 0.16/0.44 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_OCollect,type,
% 0.16/0.44 collect:
% 0.16/0.44 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Set_Ois__empty,type,
% 0.16/0.44 is_empty:
% 0.16/0.44 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Odiff__sorted,type,
% 0.16/0.44 sorted1267110213sorted:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Ointer__sorted,type,
% 0.16/0.44 sorted2037043510sorted:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Osubset__sorted,type,
% 0.16/0.44 sorted1061247458sorted:
% 0.16/0.44 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_c_member,type,
% 0.16/0.44 member:
% 0.16/0.44 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_l1_H____,type,
% 0.16/0.44 l1: list @ a ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_l2a____,type,
% 0.16/0.44 l2a: list @ a ).
% 0.16/0.44
% 0.16/0.44 thf(sy_v_x1____,type,
% 0.16/0.44 x1: a ).
% 0.16/0.44
% 0.16/0.44 %----Relevant facts (255)
% 0.16/0.44 thf(fact_0_local_ONil,axiom,
% 0.16/0.44 ( l2a
% 0.16/0.44 = ( nil @ a ) ) ).
% 0.16/0.44
% 0.16/0.44 % local.Nil
% 0.16/0.44 thf(fact_1_ind__hyp,axiom,
% 0.16/0.44 ! [L2: list @ a] :
% 0.16/0.44 ( ( l1 = L2 )
% 0.16/0.44 = ( ( sorted1061247458sorted @ a @ l1 @ L2 )
% 0.16/0.44 & ( sorted1061247458sorted @ a @ L2 @ l1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ind_hyp
% 0.16/0.44 thf(fact_2_subset__sorted_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X1: A,L1: list @ A] :
% 0.16/0.44 ~ ( sorted1061247458sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.simps(2)
% 0.16/0.44 thf(fact_3_list_Oinject,axiom,
% 0.16/0.44 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.16/0.44 ( ( ( cons @ A @ X21 @ X22 )
% 0.16/0.44 = ( cons @ A @ Y21 @ Y22 ) )
% 0.16/0.44 = ( ( X21 = Y21 )
% 0.16/0.44 & ( X22 = Y22 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.inject
% 0.16/0.44 thf(fact_4_subset__sorted_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [L2: list @ A] : ( sorted1061247458sorted @ A @ ( nil @ A ) @ L2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.simps(1)
% 0.16/0.44 thf(fact_5_not__Cons__self2,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.44 ( ( cons @ A @ X @ Xs )
% 0.16/0.44 != Xs ) ).
% 0.16/0.44
% 0.16/0.44 % not_Cons_self2
% 0.16/0.44 thf(fact_6_list__tail__coinc,axiom,
% 0.16/0.44 ! [A: $tType,N1: A,R1: list @ A,N2: A,R2: list @ A] :
% 0.16/0.44 ( ( ( cons @ A @ N1 @ R1 )
% 0.16/0.44 = ( cons @ A @ N2 @ R2 ) )
% 0.16/0.44 => ( ( N1 = N2 )
% 0.16/0.44 & ( R1 = R2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_tail_coinc
% 0.16/0.44 thf(fact_7_subset__sorted_Osimps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X1: A,L1: list @ A,X2: A,L2: list @ A] :
% 0.16/0.44 ( ( sorted1061247458sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( ~ ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( ( X1 = X2 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ L1 @ L2 ) )
% 0.16/0.44 & ( ( X1 != X2 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.simps(3)
% 0.16/0.44 thf(fact_8_shift__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( bNF_Greatest_shift @ A @ B )
% 0.16/0.44 = ( ^ [Lab: ( list @ A ) > B,K: A,Kl: list @ A] : ( Lab @ ( cons @ A @ K @ Kl ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % shift_def
% 0.16/0.44 thf(fact_9_subset__sorted_Oelims_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A,Xa: list @ A] :
% 0.16/0.44 ( ~ ( sorted1061247458sorted @ A @ X @ Xa )
% 0.16/0.44 => ( ( ? [X12: A,L12: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ( Xa
% 0.16/0.44 != ( nil @ A ) ) )
% 0.16/0.44 => ~ ! [X12: A,L12: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ! [X23: A,L22: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ X23 @ L22 ) )
% 0.16/0.44 => ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( ( X12 = X23 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ L12 @ L22 ) )
% 0.16/0.44 & ( ( X12 != X23 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.elims(3)
% 0.16/0.44 thf(fact_10_subset__sorted_Oelims_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A,Xa: list @ A] :
% 0.16/0.44 ( ( sorted1061247458sorted @ A @ X @ Xa )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ! [L22: list @ A] : ( Xa != L22 ) )
% 0.16/0.44 => ~ ! [X12: A,L12: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ! [X23: A,L22: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ X23 @ L22 ) )
% 0.16/0.44 => ~ ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( ( X12 = X23 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ L12 @ L22 ) )
% 0.16/0.44 & ( ( X12 != X23 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.elims(2)
% 0.16/0.44 thf(fact_11_subset__sorted_Oelims_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A,Xa: list @ A,Y: $o] :
% 0.16/0.44 ( ( ( sorted1061247458sorted @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ~ Y )
% 0.16/0.44 => ( ( ? [X12: A,L12: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => Y ) )
% 0.16/0.44 => ~ ! [X12: A,L12: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ! [X23: A,L22: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ X23 @ L22 ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( ~ ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( ( X12 = X23 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ L12 @ L22 ) )
% 0.16/0.44 & ( ( X12 != X23 )
% 0.16/0.44 => ( sorted1061247458sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.elims(1)
% 0.16/0.44 thf(fact_12_list_Odistinct_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,X21: A,X22: list @ A] :
% 0.16/0.44 ( ( nil @ A )
% 0.16/0.44 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.distinct(1)
% 0.16/0.44 thf(fact_13_list_OdiscI,axiom,
% 0.16/0.44 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.16/0.44 ( ( List
% 0.16/0.44 = ( cons @ A @ X21 @ X22 ) )
% 0.16/0.44 => ( List
% 0.16/0.44 != ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.discI
% 0.16/0.44 thf(fact_14_transpose_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,X: list @ ( list @ A )] :
% 0.16/0.44 ( ( X
% 0.16/0.44 != ( nil @ ( list @ A ) ) )
% 0.16/0.44 => ( ! [Xss: list @ ( list @ A )] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.16/0.44 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % transpose.cases
% 0.16/0.44 thf(fact_15_subset__sorted_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.44 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [X12: A,L12: list @ A] : ( P @ ( cons @ A @ X12 @ L12 ) @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X12: A,L12: list @ A,X23: A,L22: list @ A] :
% 0.16/0.44 ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( X12 = X23 )
% 0.16/0.44 => ( P @ L12 @ L22 ) ) )
% 0.16/0.44 => ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( X12 != X23 )
% 0.16/0.44 => ( P @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) )
% 0.16/0.44 => ( P @ ( cons @ A @ X12 @ L12 ) @ ( cons @ A @ X23 @ L22 ) ) ) )
% 0.16/0.44 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % subset_sorted.induct
% 0.16/0.44 thf(fact_16_inter__sorted_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.44 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X12: A,L12: list @ A,X23: A,L22: list @ A] :
% 0.16/0.44 ( ( ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( P @ L12 @ ( cons @ A @ X23 @ L22 ) ) )
% 0.16/0.44 => ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( X12 = X23 )
% 0.16/0.44 => ( P @ L12 @ L22 ) ) )
% 0.16/0.44 => ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( X12 != X23 )
% 0.16/0.44 => ( P @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) )
% 0.16/0.44 => ( P @ ( cons @ A @ X12 @ L12 ) @ ( cons @ A @ X23 @ L22 ) ) ) ) )
% 0.16/0.44 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inter_sorted.induct
% 0.16/0.44 thf(fact_17_mergesort__by__rel__merge__induct,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,R: A > B > $o,Xs: list @ A,Ys: list @ B] :
% 0.16/0.44 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B ) )
% 0.16/0.44 => ( ! [X12: list @ B] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.16/0.44 ( ( R @ X3 @ Y2 )
% 0.16/0.44 => ( ( P @ Xs2 @ ( cons @ B @ Y2 @ Ys2 ) )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.16/0.44 ( ~ ( R @ X3 @ Y2 )
% 0.16/0.44 => ( ( P @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) )
% 0.16/0.44 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % mergesort_by_rel_merge_induct
% 0.16/0.44 thf(fact_18_mergesort__by__rel__merge_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A2: list @ A] :
% 0.16/0.44 ( ! [R3: A > A > $o,X3: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.16/0.44 ( ( ( R3 @ X3 @ Y2 )
% 0.16/0.44 => ( P @ R3 @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.16/0.44 => ( ( ~ ( R3 @ X3 @ Y2 )
% 0.16/0.44 => ( P @ R3 @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 ) )
% 0.16/0.44 => ( P @ R3 @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 0.16/0.44 => ( ! [R3: A > A > $o,Xs2: list @ A] : ( P @ R3 @ Xs2 @ ( nil @ A ) )
% 0.16/0.44 => ( ! [R3: A > A > $o,V: A,Va: list @ A] : ( P @ R3 @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 0.16/0.44 => ( P @ A0 @ A1 @ A2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % mergesort_by_rel_merge.induct
% 0.16/0.44 thf(fact_19_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A2: list @ B] :
% 0.16/0.44 ( ! [F: A > B,X12: list @ B] : ( P @ F @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [F: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.16/0.44 ( ( P @ F @ As @ ( cons @ B @ ( F @ A3 ) @ Bs ) )
% 0.16/0.44 => ( P @ F @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 0.16/0.44 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_tailrec_rev.induct
% 0.16/0.44 thf(fact_20_list__nonempty__induct,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A] :
% 0.16/0.44 ( ( Xs2
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ( ( P @ Xs2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 0.16/0.44 => ( P @ Xs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_nonempty_induct
% 0.16/0.44 thf(fact_21_list__all__zip_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P: ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > $o,A1: list @ A,A2: list @ B] :
% 0.16/0.44 ( ! [P2: A > B > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [P2: A > B > $o,A3: A,As: list @ A,B2: B,Bs: list @ B] :
% 0.16/0.44 ( ( P @ P2 @ As @ Bs )
% 0.16/0.44 => ( P @ P2 @ ( cons @ A @ A3 @ As ) @ ( cons @ B @ B2 @ Bs ) ) )
% 0.16/0.44 => ( ! [P2: A > B > $o,V: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [P2: A > B > $o,V: B,Va: list @ B] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 0.16/0.44 => ( P @ A0 @ A1 @ A2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_all_zip.induct
% 0.16/0.44 thf(fact_22_list__induct__first2,axiom,
% 0.16/0.44 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.16/0.44 ( ( P @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.44 => ( ! [X12: A,X23: A,Xs2: list @ A] :
% 0.16/0.44 ( ( P @ Xs2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X12 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 0.16/0.44 => ( P @ Xs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_induct_first2
% 0.16/0.44 thf(fact_23_remdups__adj_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.16/0.44 ( ( P @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.44 => ( ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.16/0.44 ( ( ( X3 = Y2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 0.16/0.44 => ( ( ( X3 != Y2 )
% 0.16/0.44 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.16/0.44 => ( P @ A0 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % remdups_adj.induct
% 0.16/0.44 thf(fact_24_remdups__adj_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,X: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.16/0.44 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % remdups_adj.cases
% 0.16/0.44 thf(fact_25_list__2pre__induct,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,W1: list @ A,W2: list @ B] :
% 0.16/0.44 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [E: A,W12: list @ A,W22: list @ B] :
% 0.16/0.44 ( ( P @ W12 @ W22 )
% 0.16/0.44 => ( P @ ( cons @ A @ E @ W12 ) @ W22 ) )
% 0.16/0.44 => ( ! [E: B,W13: list @ A,W23: list @ B] :
% 0.16/0.44 ( ( P @ W13 @ W23 )
% 0.16/0.44 => ( P @ W13 @ ( cons @ B @ E @ W23 ) ) )
% 0.16/0.44 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_2pre_induct
% 0.16/0.44 thf(fact_26_splice_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.44 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.16/0.44 ( ( P @ Xs2 @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.16/0.44 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % splice.induct
% 0.16/0.44 thf(fact_27_list__induct2_H,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.16/0.44 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 0.16/0.44 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.16/0.44 ( ( P @ Xs2 @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 0.16/0.44 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_induct2'
% 0.16/0.44 thf(fact_28_neq__Nil__conv,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 = ( ? [Y3: A,Ys3: list @ A] :
% 0.16/0.44 ( Xs
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % neq_Nil_conv
% 0.16/0.44 thf(fact_29_list_Oinducts,axiom,
% 0.16/0.44 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.16/0.44 ( ( P @ ( nil @ A ) )
% 0.16/0.44 => ( ! [X12: A,X23: list @ A] :
% 0.16/0.44 ( ( P @ X23 )
% 0.16/0.44 => ( P @ ( cons @ A @ X12 @ X23 ) ) )
% 0.16/0.44 => ( P @ List ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.inducts
% 0.16/0.44 thf(fact_30_list_Oexhaust,axiom,
% 0.16/0.44 ! [A: $tType,Y: list @ A] :
% 0.16/0.44 ( ( Y
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ~ ! [X212: A,X222: list @ A] :
% 0.16/0.44 ( Y
% 0.16/0.44 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.exhaust
% 0.16/0.44 thf(fact_31_zipf_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,C: $tType,B: $tType,P: ( A > B > C ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > C,A1: list @ A,A2: list @ B] :
% 0.16/0.44 ( ! [F: A > B > C] : ( P @ F @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [F: A > B > C,A3: A,As: list @ A,B2: B,Bs: list @ B] :
% 0.16/0.44 ( ( P @ F @ As @ Bs )
% 0.16/0.44 => ( P @ F @ ( cons @ A @ A3 @ As ) @ ( cons @ B @ B2 @ Bs ) ) )
% 0.16/0.44 => ( ! [A3: A > B > C,V: A,Va: list @ A] : ( P @ A3 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [A3: A > B > C,V: B,Va: list @ B] : ( P @ A3 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 0.16/0.44 => ( P @ A0 @ A1 @ A2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % zipf.induct
% 0.16/0.44 thf(fact_32_revg_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.16/0.44 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [A3: A,As: list @ A,B2: list @ A] :
% 0.16/0.44 ( ( P @ As @ ( cons @ A @ A3 @ B2 ) )
% 0.16/0.44 => ( P @ ( cons @ A @ A3 @ As ) @ B2 ) )
% 0.16/0.44 => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % revg.induct
% 0.16/0.44 thf(fact_33_quicksort_Ocases,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 != ( nil @ A ) )
% 0.16/0.44 => ~ ! [X3: A,Xs2: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 != ( cons @ A @ X3 @ Xs2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % quicksort.cases
% 0.16/0.44 thf(fact_34_insert__Nil,axiom,
% 0.16/0.44 ! [A: $tType,X: A] :
% 0.16/0.44 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.16/0.44 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % insert_Nil
% 0.16/0.44 thf(fact_35_list__ex1__simps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o] :
% 0.16/0.44 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_ex1_simps(1)
% 0.16/0.44 thf(fact_36_inter__sorted_Oelims,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.16/0.44 ( ( ( sorted2037043510sorted @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( nil @ A ) ) )
% 0.16/0.44 => ( ( ? [V: A,Va: list @ A] :
% 0.16/0.44 ( X
% 0.16/0.44 = ( cons @ A @ V @ Va ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( nil @ A ) ) ) )
% 0.16/0.44 => ~ ! [X12: A,L12: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ! [X23: A,L22: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ X23 @ L22 ) )
% 0.16/0.44 => ~ ( ( ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( sorted2037043510sorted @ A @ L12 @ ( cons @ A @ X23 @ L22 ) ) ) )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( ( X12 = X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( cons @ A @ X12 @ ( sorted2037043510sorted @ A @ L12 @ L22 ) ) ) )
% 0.16/0.44 & ( ( X12 != X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( sorted2037043510sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inter_sorted.elims
% 0.16/0.44 thf(fact_37_diff__sorted_Oelims,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.16/0.44 ( ( ( sorted1267110213sorted @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( nil @ A ) ) )
% 0.16/0.44 => ( ! [V: A,Va: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ V @ Va ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( cons @ A @ V @ Va ) ) ) )
% 0.16/0.44 => ~ ! [X12: A,L12: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ! [X23: A,L22: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ X23 @ L22 ) )
% 0.16/0.44 => ~ ( ( ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( cons @ A @ X12 @ ( sorted1267110213sorted @ A @ L12 @ ( cons @ A @ X23 @ L22 ) ) ) ) )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( ( X12 = X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( sorted1267110213sorted @ A @ L12 @ L22 ) ) )
% 0.16/0.44 & ( ( X12 != X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( sorted1267110213sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % diff_sorted.elims
% 0.16/0.44 thf(fact_38_merge_Oelims,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.16/0.44 ( ( ( merge @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y != Xa ) )
% 0.16/0.44 => ( ! [V: A,Va: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ V @ Va ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( cons @ A @ V @ Va ) ) ) )
% 0.16/0.44 => ~ ! [X12: A,L12: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X12 @ L12 ) )
% 0.16/0.44 => ! [X23: A,L22: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ X23 @ L22 ) )
% 0.16/0.44 => ~ ( ( ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( cons @ A @ X12 @ ( merge @ A @ L12 @ ( cons @ A @ X23 @ L22 ) ) ) ) )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 0.16/0.44 => ( ( ( X12 = X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( cons @ A @ X12 @ ( merge @ A @ L12 @ L22 ) ) ) )
% 0.16/0.44 & ( ( X12 != X23 )
% 0.16/0.44 => ( Y
% 0.16/0.44 = ( cons @ A @ X23 @ ( merge @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge.elims
% 0.16/0.44 thf(fact_39_revg_Oelims,axiom,
% 0.16/0.44 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.16/0.44 ( ( ( revg @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y != Xa ) )
% 0.16/0.44 => ~ ! [A3: A,As: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ A3 @ As ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( revg @ A @ As @ ( cons @ A @ A3 @ Xa ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % revg.elims
% 0.16/0.44 thf(fact_40_list__collect__set__simps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: B > ( set @ A ),A4: B] :
% 0.16/0.44 ( ( list_collect_set @ B @ A @ F2 @ ( cons @ B @ A4 @ ( nil @ B ) ) )
% 0.16/0.44 = ( F2 @ A4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_collect_set_simps(2)
% 0.16/0.44 thf(fact_41_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 0.16/0.44 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq_simps(3)
% 0.16/0.44 thf(fact_42_lexordp__eq_Ocases,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A1: list @ A,A2: list @ A] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ A1 @ A2 )
% 0.16/0.44 => ( ( ( A1
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ! [Ys2: list @ A] : ( A2 != Ys2 ) )
% 0.16/0.44 => ( ! [X3: A] :
% 0.16/0.44 ( ? [Xs2: list @ A] :
% 0.16/0.44 ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Y2: A] :
% 0.16/0.44 ( ? [Ys2: list @ A] :
% 0.16/0.44 ( A2
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.16/0.44 => ~ ( ord_less @ A @ X3 @ Y2 ) ) )
% 0.16/0.44 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.16/0.44 ( ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Ys2: list @ A] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.16/0.44 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.16/0.44 => ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.16/0.44 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq.cases
% 0.16/0.44 thf(fact_43_lexordp__eq_Osimps,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( ord_lexordp_eq @ A )
% 0.16/0.44 = ( ^ [A12: list @ A,A22: list @ A] :
% 0.16/0.44 ( ? [Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( A22 = Ys3 ) )
% 0.16/0.44 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X4 @ Xs3 ) )
% 0.16/0.44 & ( A22
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.16/0.44 & ( ord_less @ A @ X4 @ Y3 ) )
% 0.16/0.44 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X4 @ Xs3 ) )
% 0.16/0.44 & ( A22
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.16/0.44 & ~ ( ord_less @ A @ X4 @ Y3 )
% 0.16/0.44 & ~ ( ord_less @ A @ Y3 @ X4 )
% 0.16/0.44 & ( ord_lexordp_eq @ A @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq.simps
% 0.16/0.44 thf(fact_44_mem__Collect__eq,axiom,
% 0.16/0.44 ! [A: $tType,A4: A,P: A > $o] :
% 0.16/0.44 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.16/0.44 = ( P @ A4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % mem_Collect_eq
% 0.16/0.44 thf(fact_45_Collect__mem__eq,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ( ( collect @ A
% 0.16/0.44 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 0.16/0.44 = A5 ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_mem_eq
% 0.16/0.44 thf(fact_46_Collect__cong,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.44 ( ! [X3: A] :
% 0.16/0.44 ( ( P @ X3 )
% 0.16/0.44 = ( Q @ X3 ) )
% 0.16/0.44 => ( ( collect @ A @ P )
% 0.16/0.44 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_cong
% 0.16/0.44 thf(fact_47_ext,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.16/0.44 ( ! [X3: A] :
% 0.16/0.44 ( ( F2 @ X3 )
% 0.16/0.44 = ( G @ X3 ) )
% 0.16/0.44 => ( F2 = G ) ) ).
% 0.16/0.44
% 0.16/0.44 % ext
% 0.16/0.44 thf(fact_48_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.16/0.44 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.16/0.44 = ( ( Less @ X @ Y )
% 0.16/0.44 | ( ~ ( Less @ Y @ X )
% 0.16/0.44 & ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq_simps(4)
% 0.16/0.44 thf(fact_49_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq_simps(1)
% 0.16/0.44 thf(fact_50_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.16/0.44 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 0.16/0.44 = ( Xs
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq_simps(2)
% 0.16/0.44 thf(fact_51_lexordp__eq__simps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_simps(1)
% 0.16/0.44 thf(fact_52_lexordp__eq__simps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Xs: list @ A] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 0.16/0.44 = ( Xs
% 0.16/0.44 = ( nil @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_simps(2)
% 0.16/0.44 thf(fact_53_lexordp__eq__simps_I4_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.16/0.44 = ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 | ( ~ ( ord_less @ A @ Y @ X )
% 0.16/0.44 & ( ord_lexordp_eq @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_simps(4)
% 0.16/0.44 thf(fact_54_lexordp__eq__simps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Xs: list @ A] :
% 0.16/0.44 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_simps(3)
% 0.16/0.44 thf(fact_55_merge__list_Oinduct,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [P: ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) > $o,A0: list @ ( list @ A ),A1: list @ ( list @ A )] :
% 0.16/0.44 ( ( P @ ( nil @ ( list @ A ) ) @ ( nil @ ( list @ A ) ) )
% 0.16/0.44 => ( ! [L: list @ A] : ( P @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.44 => ( ! [La: list @ A,Acc2: list @ ( list @ A )] :
% 0.16/0.44 ( ( P @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ La @ Acc2 ) )
% 0.16/0.44 => ( P @ ( cons @ ( list @ A ) @ La @ Acc2 ) @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.44 => ( ! [La: list @ A,Acc2: list @ ( list @ A ),L: list @ A] :
% 0.16/0.44 ( ( P @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L @ ( cons @ ( list @ A ) @ La @ Acc2 ) ) )
% 0.16/0.44 => ( P @ ( cons @ ( list @ A ) @ La @ Acc2 ) @ ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) ) )
% 0.16/0.44 => ( ! [Acc2: list @ ( list @ A ),L12: list @ A,L22: list @ A,Ls: list @ ( list @ A )] :
% 0.16/0.44 ( ( P @ ( cons @ ( list @ A ) @ ( merge @ A @ L12 @ L22 ) @ Acc2 ) @ Ls )
% 0.16/0.44 => ( P @ Acc2 @ ( cons @ ( list @ A ) @ L12 @ ( cons @ ( list @ A ) @ L22 @ Ls ) ) ) )
% 0.16/0.44 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.induct
% 0.16/0.44 thf(fact_56_ord_Olexordp__eq__refl,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq_refl
% 0.16/0.44 thf(fact_57_lexordp__eq__refl,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_refl
% 0.16/0.44 thf(fact_58_lexordp__eq__trans,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.16/0.44 => ( ( ord_lexordp_eq @ A @ Ys @ Zs )
% 0.16/0.44 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_trans
% 0.16/0.44 thf(fact_59_lexordp__eq__linear,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.16/0.44 | ( ord_lexordp_eq @ A @ Ys @ Xs ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_linear
% 0.16/0.44 thf(fact_60_lexordp__eq__antisym,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.16/0.44 => ( ( ord_lexordp_eq @ A @ Ys @ Xs )
% 0.16/0.44 => ( Xs = Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq_antisym
% 0.16/0.44 thf(fact_61_lexordp__eq_ONil,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq.Nil
% 0.16/0.44 thf(fact_62_ord_Olexordp__eq_OCons,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( Less @ X @ Y )
% 0.16/0.44 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq.Cons
% 0.16/0.44 thf(fact_63_ord_Olexordp__eq_OCons__eq,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ~ ( Less @ X @ Y )
% 0.16/0.44 => ( ~ ( Less @ Y @ X )
% 0.16/0.44 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys )
% 0.16/0.44 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq.Cons_eq
% 0.16/0.44 thf(fact_64_ord_Olexordp__eq_ONil,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq.Nil
% 0.16/0.44 thf(fact_65_merge_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [L2: list @ A] :
% 0.16/0.44 ( ( merge @ A @ ( nil @ A ) @ L2 )
% 0.16/0.44 = L2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge.simps(1)
% 0.16/0.44 thf(fact_66_inter__sorted_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [L2: list @ A] :
% 0.16/0.44 ( ( sorted2037043510sorted @ A @ ( nil @ A ) @ L2 )
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inter_sorted.simps(1)
% 0.16/0.44 thf(fact_67_diff__sorted_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [L2: list @ A] :
% 0.16/0.44 ( ( sorted1267110213sorted @ A @ ( nil @ A ) @ L2 )
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % diff_sorted.simps(1)
% 0.16/0.44 thf(fact_68_revg_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,A4: A,As2: list @ A,B3: list @ A] :
% 0.16/0.44 ( ( revg @ A @ ( cons @ A @ A4 @ As2 ) @ B3 )
% 0.16/0.44 = ( revg @ A @ As2 @ ( cons @ A @ A4 @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % revg.simps(2)
% 0.16/0.44 thf(fact_69_revg_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,B3: list @ A] :
% 0.16/0.44 ( ( revg @ A @ ( nil @ A ) @ B3 )
% 0.16/0.44 = B3 ) ).
% 0.16/0.44
% 0.16/0.44 % revg.simps(1)
% 0.16/0.44 thf(fact_70_lexordp__eq_OCons__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ~ ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ( ~ ( ord_less @ A @ Y @ X )
% 0.16/0.44 => ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.16/0.44 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq.Cons_eq
% 0.16/0.44 thf(fact_71_lexordp__eq_OCons,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq.Cons
% 0.16/0.44 thf(fact_72_ord_Olexordp__eq_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,A1: list @ A,A2: list @ A] :
% 0.16/0.44 ( ( lexordp_eq @ A @ Less @ A1 @ A2 )
% 0.16/0.44 => ( ( ( A1
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ! [Ys2: list @ A] : ( A2 != Ys2 ) )
% 0.16/0.44 => ( ! [X3: A] :
% 0.16/0.44 ( ? [Xs2: list @ A] :
% 0.16/0.44 ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Y2: A] :
% 0.16/0.44 ( ? [Ys2: list @ A] :
% 0.16/0.44 ( A2
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.16/0.44 => ~ ( Less @ X3 @ Y2 ) ) )
% 0.16/0.44 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 0.16/0.44 ( ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Ys2: list @ A] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.16/0.44 => ( ~ ( Less @ X3 @ Y2 )
% 0.16/0.44 => ( ~ ( Less @ Y2 @ X3 )
% 0.16/0.44 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq.cases
% 0.16/0.44 thf(fact_73_ord_Olexordp__eq_Osimps,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( lexordp_eq @ A )
% 0.16/0.44 = ( ^ [Less2: A > A > $o,A12: list @ A,A22: list @ A] :
% 0.16/0.44 ( ? [Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( A22 = Ys3 ) )
% 0.16/0.44 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X4 @ Xs3 ) )
% 0.16/0.44 & ( A22
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.16/0.44 & ( Less2 @ X4 @ Y3 ) )
% 0.16/0.44 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X4 @ Xs3 ) )
% 0.16/0.44 & ( A22
% 0.16/0.44 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.16/0.44 & ~ ( Less2 @ X4 @ Y3 )
% 0.16/0.44 & ~ ( Less2 @ Y3 @ X4 )
% 0.16/0.44 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq.simps
% 0.16/0.44 thf(fact_74_ord_Olexordp__eq_Oinducts,axiom,
% 0.16/0.44 ! [A: $tType,Less: A > A > $o,X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.16/0.44 ( ( lexordp_eq @ A @ Less @ X1 @ X2 )
% 0.16/0.44 => ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.44 ( ( Less @ X3 @ Y2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.16/0.44 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.44 ( ~ ( Less @ X3 @ Y2 )
% 0.16/0.44 => ( ~ ( Less @ Y2 @ X3 )
% 0.16/0.44 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 )
% 0.16/0.44 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) )
% 0.16/0.44 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ord.lexordp_eq.inducts
% 0.16/0.44 thf(fact_75_merge_Osimps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X1: A,X2: A,L1: list @ A,L2: list @ A] :
% 0.16/0.44 ( ( ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( cons @ A @ X1 @ ( merge @ A @ L1 @ ( cons @ A @ X2 @ L2 ) ) ) ) )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( ( X1 = X2 )
% 0.16/0.44 => ( ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( cons @ A @ X1 @ ( merge @ A @ L1 @ L2 ) ) ) )
% 0.16/0.44 & ( ( X1 != X2 )
% 0.16/0.44 => ( ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( cons @ A @ X2 @ ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge.simps(3)
% 0.16/0.44 thf(fact_76_merge_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [V2: A,Va2: list @ A] :
% 0.16/0.44 ( ( merge @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 0.16/0.44 = ( cons @ A @ V2 @ Va2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge.simps(2)
% 0.16/0.44 thf(fact_77_diff__sorted_Osimps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X1: A,X2: A,L1: list @ A,L2: list @ A] :
% 0.16/0.44 ( ( ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( cons @ A @ X1 @ ( sorted1267110213sorted @ A @ L1 @ ( cons @ A @ X2 @ L2 ) ) ) ) )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( ( X1 = X2 )
% 0.16/0.44 => ( ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( sorted1267110213sorted @ A @ L1 @ L2 ) ) )
% 0.16/0.44 & ( ( X1 != X2 )
% 0.16/0.44 => ( ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % diff_sorted.simps(3)
% 0.16/0.44 thf(fact_78_inter__sorted_Osimps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X1: A,X2: A,L1: list @ A,L2: list @ A] :
% 0.16/0.44 ( ( ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( sorted2037043510sorted @ A @ L1 @ ( cons @ A @ X2 @ L2 ) ) ) )
% 0.16/0.44 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 0.16/0.44 => ( ( ( X1 = X2 )
% 0.16/0.44 => ( ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( cons @ A @ X1 @ ( sorted2037043510sorted @ A @ L1 @ L2 ) ) ) )
% 0.16/0.44 & ( ( X1 != X2 )
% 0.16/0.44 => ( ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 0.16/0.44 = ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inter_sorted.simps(3)
% 0.16/0.44 thf(fact_79_diff__sorted_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [V2: A,Va2: list @ A] :
% 0.16/0.44 ( ( sorted1267110213sorted @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 0.16/0.44 = ( cons @ A @ V2 @ Va2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % diff_sorted.simps(2)
% 0.16/0.44 thf(fact_80_inter__sorted_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [V2: A,Va2: list @ A] :
% 0.16/0.44 ( ( sorted2037043510sorted @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inter_sorted.simps(2)
% 0.16/0.44 thf(fact_81_lexordp__eq_Oinducts,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.16/0.44 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 0.16/0.44 => ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 0.16/0.44 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.44 ( ( ord_less @ A @ X3 @ Y2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.16/0.44 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.16/0.44 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.16/0.44 => ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.16/0.44 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys2 )
% 0.16/0.44 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) )
% 0.16/0.44 => ( P @ X1 @ X2 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % lexordp_eq.inducts
% 0.16/0.44 thf(fact_82_sublists_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( sublists @ A @ ( nil @ A ) )
% 0.16/0.44 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sublists.simps(1)
% 0.16/0.44 thf(fact_83_product__lists_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.16/0.44 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % product_lists.simps(1)
% 0.16/0.44 thf(fact_84_merge__list_Oelims,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: list @ ( list @ A ),Xa: list @ ( list @ A ),Y: list @ A] :
% 0.16/0.44 ( ( ( merge_list @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ ( list @ A ) ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ ( list @ A ) ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( nil @ A ) ) ) )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ ( list @ A ) ) )
% 0.16/0.44 => ! [L: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.44 => ( Y != L ) ) )
% 0.16/0.44 => ( ! [La: list @ A,Acc2: list @ ( list @ A )] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ ( list @ A ) @ La @ Acc2 ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ ( list @ A ) ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ La @ Acc2 ) ) ) ) )
% 0.16/0.44 => ( ! [La: list @ A,Acc2: list @ ( list @ A )] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ ( list @ A ) @ La @ Acc2 ) )
% 0.16/0.44 => ! [L: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L @ ( cons @ ( list @ A ) @ La @ Acc2 ) ) ) ) ) )
% 0.16/0.44 => ~ ! [L12: list @ A,L22: list @ A,Ls: list @ ( list @ A )] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ ( list @ A ) @ L12 @ ( cons @ ( list @ A ) @ L22 @ Ls ) ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( merge_list @ A @ ( cons @ ( list @ A ) @ ( merge @ A @ L12 @ L22 ) @ X ) @ Ls ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.elims
% 0.16/0.44 thf(fact_85_combinatorial__product_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( list_c659805718roduct @ A @ ( nil @ ( list @ A ) ) )
% 0.16/0.44 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % combinatorial_product.simps(1)
% 0.16/0.44 thf(fact_86_map__tailrec__rev_Oelims,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 0.16/0.44 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa @ Xb )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( Xa
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y != Xb ) )
% 0.16/0.44 => ~ ! [A3: A,As: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ A3 @ As ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_tailrec_rev.elims
% 0.16/0.44 thf(fact_87_list__collect__set__map__simps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F2: B > ( set @ A ),X: C > B,A4: C] :
% 0.16/0.44 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( cons @ C @ A4 @ ( nil @ C ) ) ) )
% 0.16/0.44 = ( F2 @ ( X @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_collect_set_map_simps(2)
% 0.16/0.44 thf(fact_88_bind__simps_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: B > ( list @ A )] :
% 0.16/0.44 ( ( bind @ B @ A @ ( nil @ B ) @ F2 )
% 0.16/0.44 = ( nil @ A ) ) ).
% 0.16/0.44
% 0.16/0.44 % bind_simps(1)
% 0.16/0.44 thf(fact_89_splice_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,V2: A,Va2: list @ A] :
% 0.16/0.44 ( ( splice @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 0.16/0.44 = ( cons @ A @ V2 @ Va2 ) ) ).
% 0.16/0.44
% 0.16/0.44 % splice.simps(2)
% 0.16/0.44 thf(fact_90_Nil__is__map__conv,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.16/0.44 ( ( ( nil @ A )
% 0.16/0.44 = ( map @ B @ A @ F2 @ Xs ) )
% 0.16/0.44 = ( Xs
% 0.16/0.44 = ( nil @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Nil_is_map_conv
% 0.16/0.44 thf(fact_91_map__is__Nil__conv,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.16/0.44 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 = ( Xs
% 0.16/0.44 = ( nil @ B ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_is_Nil_conv
% 0.16/0.44 thf(fact_92_list_Omap__disc__iff,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: A > B,A4: list @ A] :
% 0.16/0.44 ( ( ( map @ A @ B @ F2 @ A4 )
% 0.16/0.44 = ( nil @ B ) )
% 0.16/0.44 = ( A4
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.map_disc_iff
% 0.16/0.44 thf(fact_93_splice__Nil2,axiom,
% 0.16/0.44 ! [A: $tType,Xs: list @ A] :
% 0.16/0.44 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 0.16/0.44 = Xs ) ).
% 0.16/0.44
% 0.16/0.44 % splice_Nil2
% 0.16/0.44 thf(fact_94_map__eq__Cons__conv,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 0.16/0.44 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.16/0.44 = ( cons @ A @ Y @ Ys ) )
% 0.16/0.44 = ( ? [Z: B,Zs2: list @ B] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( cons @ B @ Z @ Zs2 ) )
% 0.16/0.44 & ( ( F2 @ Z )
% 0.16/0.44 = Y )
% 0.16/0.44 & ( ( map @ B @ A @ F2 @ Zs2 )
% 0.16/0.44 = Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_eq_Cons_conv
% 0.16/0.44 thf(fact_95_Cons__eq__map__conv,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys: list @ B] :
% 0.16/0.44 ( ( ( cons @ A @ X @ Xs )
% 0.16/0.44 = ( map @ B @ A @ F2 @ Ys ) )
% 0.16/0.44 = ( ? [Z: B,Zs2: list @ B] :
% 0.16/0.44 ( ( Ys
% 0.16/0.44 = ( cons @ B @ Z @ Zs2 ) )
% 0.16/0.44 & ( X
% 0.16/0.44 = ( F2 @ Z ) )
% 0.16/0.44 & ( Xs
% 0.16/0.44 = ( map @ B @ A @ F2 @ Zs2 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Cons_eq_map_conv
% 0.16/0.44 thf(fact_96_map__eq__Cons__D,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 0.16/0.44 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.16/0.44 = ( cons @ A @ Y @ Ys ) )
% 0.16/0.44 => ? [Z2: B,Zs3: list @ B] :
% 0.16/0.44 ( ( Xs
% 0.16/0.44 = ( cons @ B @ Z2 @ Zs3 ) )
% 0.16/0.44 & ( ( F2 @ Z2 )
% 0.16/0.44 = Y )
% 0.16/0.44 & ( ( map @ B @ A @ F2 @ Zs3 )
% 0.16/0.44 = Ys ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_eq_Cons_D
% 0.16/0.44 thf(fact_97_Cons__eq__map__D,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys: list @ B] :
% 0.16/0.44 ( ( ( cons @ A @ X @ Xs )
% 0.16/0.44 = ( map @ B @ A @ F2 @ Ys ) )
% 0.16/0.44 => ? [Z2: B,Zs3: list @ B] :
% 0.16/0.44 ( ( Ys
% 0.16/0.44 = ( cons @ B @ Z2 @ Zs3 ) )
% 0.16/0.44 & ( X
% 0.16/0.44 = ( F2 @ Z2 ) )
% 0.16/0.44 & ( Xs
% 0.16/0.44 = ( map @ B @ A @ F2 @ Zs3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Cons_eq_map_D
% 0.16/0.44 thf(fact_98_map__eq__consE,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: B > A,Ls2: list @ B,Fa: A,Fl: list @ A] :
% 0.16/0.44 ( ( ( map @ B @ A @ F2 @ Ls2 )
% 0.16/0.44 = ( cons @ A @ Fa @ Fl ) )
% 0.16/0.44 => ~ ! [A3: B,L: list @ B] :
% 0.16/0.44 ( ( Ls2
% 0.16/0.44 = ( cons @ B @ A3 @ L ) )
% 0.16/0.44 => ( ( ( F2 @ A3 )
% 0.16/0.44 = Fa )
% 0.16/0.44 => ( ( map @ B @ A @ F2 @ L )
% 0.16/0.44 != Fl ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_eq_consE
% 0.16/0.44 thf(fact_99_list_Osimps_I9_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: A > B,X21: A,X22: list @ A] :
% 0.16/0.44 ( ( map @ A @ B @ F2 @ ( cons @ A @ X21 @ X22 ) )
% 0.16/0.44 = ( cons @ B @ ( F2 @ X21 ) @ ( map @ A @ B @ F2 @ X22 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.simps(9)
% 0.16/0.44 thf(fact_100_map__consI_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,W: list @ A,F2: B > A,Ww: list @ B,A4: B] :
% 0.16/0.44 ( ( W
% 0.16/0.44 = ( map @ B @ A @ F2 @ Ww ) )
% 0.16/0.44 => ( ( cons @ A @ ( F2 @ A4 ) @ W )
% 0.16/0.44 = ( map @ B @ A @ F2 @ ( cons @ B @ A4 @ Ww ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_consI(1)
% 0.16/0.44 thf(fact_101_list_Osimps_I8_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: A > B] :
% 0.16/0.44 ( ( map @ A @ B @ F2 @ ( nil @ A ) )
% 0.16/0.44 = ( nil @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 % list.simps(8)
% 0.16/0.44 thf(fact_102_splice_Osimps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.16/0.44 ( ( splice @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.16/0.44 = ( cons @ A @ X @ ( cons @ A @ Y @ ( splice @ A @ Xs @ Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % splice.simps(3)
% 0.16/0.44 thf(fact_103_splice_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,Ys: list @ A] :
% 0.16/0.44 ( ( splice @ A @ ( nil @ A ) @ Ys )
% 0.16/0.44 = Ys ) ).
% 0.16/0.44
% 0.16/0.44 % splice.simps(1)
% 0.16/0.44 thf(fact_104_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: A > B,A4: A,As2: list @ A,Bs2: list @ B] :
% 0.16/0.44 ( ( map_tailrec_rev @ A @ B @ F2 @ ( cons @ A @ A4 @ As2 ) @ Bs2 )
% 0.16/0.44 = ( map_tailrec_rev @ A @ B @ F2 @ As2 @ ( cons @ B @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_tailrec_rev.simps(2)
% 0.16/0.44 thf(fact_105_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: A > B,Bs2: list @ B] :
% 0.16/0.44 ( ( map_tailrec_rev @ A @ B @ F2 @ ( nil @ A ) @ Bs2 )
% 0.16/0.44 = Bs2 ) ).
% 0.16/0.44
% 0.16/0.44 % map_tailrec_rev.simps(1)
% 0.16/0.44 thf(fact_106_merge__list_Osimps_I1_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( nil @ ( list @ A ) ) )
% 0.16/0.44 = ( nil @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.simps(1)
% 0.16/0.44 thf(fact_107_merge__list_Osimps_I2_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [L3: list @ A] :
% 0.16/0.44 ( ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L3 @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.44 = L3 ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.simps(2)
% 0.16/0.44 thf(fact_108_merge__list_Osimps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [La2: list @ A,Acc22: list @ ( list @ A )] :
% 0.16/0.44 ( ( merge_list @ A @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) @ ( nil @ ( list @ A ) ) )
% 0.16/0.44 = ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.simps(3)
% 0.16/0.44 thf(fact_109_merge__list_Osimps_I4_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [La2: list @ A,Acc22: list @ ( list @ A ),L3: list @ A] :
% 0.16/0.44 ( ( merge_list @ A @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) @ ( cons @ ( list @ A ) @ L3 @ ( nil @ ( list @ A ) ) ) )
% 0.16/0.44 = ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L3 @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.simps(4)
% 0.16/0.44 thf(fact_110_merge__list_Osimps_I5_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Acc22: list @ ( list @ A ),L1: list @ A,L2: list @ A,Ls2: list @ ( list @ A )] :
% 0.16/0.44 ( ( merge_list @ A @ Acc22 @ ( cons @ ( list @ A ) @ L1 @ ( cons @ ( list @ A ) @ L2 @ Ls2 ) ) )
% 0.16/0.44 = ( merge_list @ A @ ( cons @ ( list @ A ) @ ( merge @ A @ L1 @ L2 ) @ Acc22 ) @ Ls2 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % merge_list.simps(5)
% 0.16/0.44 thf(fact_111_splice_Oelims,axiom,
% 0.16/0.44 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.16/0.44 ( ( ( splice @ A @ X @ Xa )
% 0.16/0.44 = Y )
% 0.16/0.44 => ( ( ( X
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y != Xa ) )
% 0.16/0.44 => ( ! [V: A,Va: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ V @ Va ) )
% 0.16/0.44 => ( ( Xa
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( cons @ A @ V @ Va ) ) ) )
% 0.16/0.44 => ~ ! [X3: A,Xs2: list @ A] :
% 0.16/0.44 ( ( X
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Y2: A,Ys2: list @ A] :
% 0.16/0.44 ( ( Xa
% 0.16/0.44 = ( cons @ A @ Y2 @ Ys2 ) )
% 0.16/0.44 => ( Y
% 0.16/0.44 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ ( splice @ A @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % splice.elims
% 0.16/0.44 thf(fact_112_map__eq__map__tailrec,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( map @ A @ B )
% 0.16/0.44 = ( map_tailrec @ A @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 % map_eq_map_tailrec
% 0.16/0.44 thf(fact_113_list__collect__set__map__simps_I1_J,axiom,
% 0.16/0.44 ! [C: $tType,B: $tType,A: $tType,F2: B > ( set @ A ),X: C > B] :
% 0.16/0.44 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( nil @ C ) ) )
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_collect_set_map_simps(1)
% 0.16/0.44 thf(fact_114_list__collect__set__map__simps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,C: $tType,F2: B > ( set @ A ),X: C > B,A4: C,L3: list @ C] :
% 0.16/0.44 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( cons @ C @ A4 @ L3 ) ) )
% 0.16/0.44 = ( sup_sup @ ( set @ A ) @ ( F2 @ ( X @ A4 ) ) @ ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ L3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_collect_set_map_simps(3)
% 0.16/0.44 thf(fact_115_listrelp_Oinducts,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,R4: A > B > $o,X1: list @ A,X2: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.16/0.44 ( ( listrelp @ A @ B @ R4 @ X1 @ X2 )
% 0.16/0.44 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.16/0.44 => ( ! [X3: A,Y2: B,Xs2: list @ A,Ys2: list @ B] :
% 0.16/0.44 ( ( R4 @ X3 @ Y2 )
% 0.16/0.44 => ( ( listrelp @ A @ B @ R4 @ Xs2 @ Ys2 )
% 0.16/0.44 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.44 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) ) )
% 0.16/0.44 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % listrelp.inducts
% 0.16/0.44 thf(fact_116_listrelp_Osimps,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( listrelp @ A @ B )
% 0.16/0.44 = ( ^ [R5: A > B > $o,A12: list @ A,A22: list @ B] :
% 0.16/0.44 ( ( ( A12
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 & ( A22
% 0.16/0.44 = ( nil @ B ) ) )
% 0.16/0.44 | ? [X4: A,Y3: B,Xs3: list @ A,Ys3: list @ B] :
% 0.16/0.44 ( ( A12
% 0.16/0.44 = ( cons @ A @ X4 @ Xs3 ) )
% 0.16/0.44 & ( A22
% 0.16/0.44 = ( cons @ B @ Y3 @ Ys3 ) )
% 0.16/0.44 & ( R5 @ X4 @ Y3 )
% 0.16/0.44 & ( listrelp @ A @ B @ R5 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % listrelp.simps
% 0.16/0.44 thf(fact_117_listrelp_Ocases,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,R4: A > B > $o,A1: list @ A,A2: list @ B] :
% 0.16/0.44 ( ( listrelp @ A @ B @ R4 @ A1 @ A2 )
% 0.16/0.44 => ( ( ( A1
% 0.16/0.44 = ( nil @ A ) )
% 0.16/0.44 => ( A2
% 0.16/0.44 != ( nil @ B ) ) )
% 0.16/0.44 => ~ ! [X3: A,Y2: B,Xs2: list @ A] :
% 0.16/0.44 ( ( A1
% 0.16/0.44 = ( cons @ A @ X3 @ Xs2 ) )
% 0.16/0.44 => ! [Ys2: list @ B] :
% 0.16/0.44 ( ( A2
% 0.16/0.44 = ( cons @ B @ Y2 @ Ys2 ) )
% 0.16/0.44 => ( ( R4 @ X3 @ Y2 )
% 0.16/0.44 => ~ ( listrelp @ A @ B @ R4 @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % listrelp.cases
% 0.16/0.44 thf(fact_118_list__collect__set__simps_I1_J,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType,F2: B > ( set @ A )] :
% 0.16/0.44 ( ( list_collect_set @ B @ A @ F2 @ ( nil @ B ) )
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_collect_set_simps(1)
% 0.16/0.44 thf(fact_119_list__collect__set__simps_I3_J,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,F2: B > ( set @ A ),A4: B,L3: list @ B] :
% 0.16/0.44 ( ( list_collect_set @ B @ A @ F2 @ ( cons @ B @ A4 @ L3 ) )
% 0.16/0.44 = ( sup_sup @ ( set @ A ) @ ( F2 @ A4 ) @ ( list_collect_set @ B @ A @ F2 @ L3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % list_collect_set_simps(3)
% 0.16/0.44 thf(fact_120_set__notEmptyE,axiom,
% 0.16/0.44 ! [A: $tType,S: set @ A] :
% 0.16/0.44 ( ( S
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ~ ! [X3: A] :
% 0.16/0.44 ~ ( member @ A @ X3 @ S ) ) ).
% 0.16/0.44
% 0.16/0.44 % set_notEmptyE
% 0.16/0.44 thf(fact_121_memb__imp__not__empty,axiom,
% 0.16/0.44 ! [A: $tType,X: A,S: set @ A] :
% 0.16/0.44 ( ( member @ A @ X @ S )
% 0.16/0.44 => ( S
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % memb_imp_not_empty
% 0.16/0.44 thf(fact_122_listrelp_OCons,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,R4: A > B > $o,X: A,Y: B,Xs: list @ A,Ys: list @ B] :
% 0.16/0.44 ( ( R4 @ X @ Y )
% 0.16/0.44 => ( ( listrelp @ A @ B @ R4 @ Xs @ Ys )
% 0.16/0.44 => ( listrelp @ A @ B @ R4 @ ( cons @ A @ X @ Xs ) @ ( cons @ B @ Y @ Ys ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % listrelp.Cons
% 0.16/0.44 thf(fact_123_listrelp_ONil,axiom,
% 0.16/0.44 ! [A: $tType,B: $tType,R4: A > B > $o] : ( listrelp @ A @ B @ R4 @ ( nil @ A ) @ ( nil @ B ) ) ).
% 0.16/0.44
% 0.16/0.44 % listrelp.Nil
% 0.16/0.44 thf(fact_124_Un__empty,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 0.16/0.44 ( ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 = ( ( A5
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 & ( B4
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Un_empty
% 0.16/0.44 thf(fact_125_sup__bot_Oright__neutral,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A] :
% 0.16/0.44 ( ( sup_sup @ A @ A4 @ ( bot_bot @ A ) )
% 0.16/0.44 = A4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_bot.right_neutral
% 0.16/0.44 thf(fact_126_sup__bot_Oleft__neutral,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A] :
% 0.16/0.44 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A4 )
% 0.16/0.44 = A4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_bot.left_neutral
% 0.16/0.44 thf(fact_127_sup__eq__bot__iff,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ( sup_sup @ A @ X @ Y )
% 0.16/0.44 = ( bot_bot @ A ) )
% 0.16/0.44 = ( ( X
% 0.16/0.44 = ( bot_bot @ A ) )
% 0.16/0.44 & ( Y
% 0.16/0.44 = ( bot_bot @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_eq_bot_iff
% 0.16/0.44 thf(fact_128_empty__iff,axiom,
% 0.16/0.44 ! [A: $tType,C2: A] :
% 0.16/0.44 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % empty_iff
% 0.16/0.44 thf(fact_129_all__not__in__conv,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ( ( ! [X4: A] :
% 0.16/0.44 ~ ( member @ A @ X4 @ A5 ) )
% 0.16/0.44 = ( A5
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % all_not_in_conv
% 0.16/0.44 thf(fact_130_Collect__empty__eq,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o] :
% 0.16/0.44 ( ( ( collect @ A @ P )
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 = ( ! [X4: A] :
% 0.16/0.44 ~ ( P @ X4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Collect_empty_eq
% 0.16/0.44 thf(fact_131_empty__Collect__eq,axiom,
% 0.16/0.44 ! [A: $tType,P: A > $o] :
% 0.16/0.44 ( ( ( bot_bot @ ( set @ A ) )
% 0.16/0.44 = ( collect @ A @ P ) )
% 0.16/0.44 = ( ! [X4: A] :
% 0.16/0.44 ~ ( P @ X4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % empty_Collect_eq
% 0.16/0.44 thf(fact_132_sup__apply,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.16/0.44 => ( ( sup_sup @ ( A > B ) )
% 0.16/0.44 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( sup_sup @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_apply
% 0.16/0.44 thf(fact_133_sup_Oidem,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A] :
% 0.16/0.44 ( ( sup_sup @ A @ A4 @ A4 )
% 0.16/0.44 = A4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.idem
% 0.16/0.44 thf(fact_134_sup__idem,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A] :
% 0.16/0.44 ( ( sup_sup @ A @ X @ X )
% 0.16/0.44 = X ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_idem
% 0.16/0.44 thf(fact_135_sup_Oleft__idem,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A,B3: A] :
% 0.16/0.44 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B3 ) )
% 0.16/0.44 = ( sup_sup @ A @ A4 @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.left_idem
% 0.16/0.44 thf(fact_136_sup__left__idem,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.16/0.44 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_left_idem
% 0.16/0.44 thf(fact_137_sup_Oright__idem,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A,B3: A] :
% 0.16/0.44 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B3 ) @ B3 )
% 0.16/0.44 = ( sup_sup @ A @ A4 @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.right_idem
% 0.16/0.44 thf(fact_138_UnCI,axiom,
% 0.16/0.44 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 0.16/0.44 ( ( ~ ( member @ A @ C2 @ B4 )
% 0.16/0.44 => ( member @ A @ C2 @ A5 ) )
% 0.16/0.44 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UnCI
% 0.16/0.44 thf(fact_139_Un__iff,axiom,
% 0.16/0.44 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.16/0.44 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.16/0.44 = ( ( member @ A @ C2 @ A5 )
% 0.16/0.44 | ( member @ A @ C2 @ B4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Un_iff
% 0.16/0.44 thf(fact_140_bot__eq__sup__iff,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ( bot_bot @ A )
% 0.16/0.44 = ( sup_sup @ A @ X @ Y ) )
% 0.16/0.44 = ( ( X
% 0.16/0.44 = ( bot_bot @ A ) )
% 0.16/0.44 & ( Y
% 0.16/0.44 = ( bot_bot @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bot_eq_sup_iff
% 0.16/0.44 thf(fact_141_bot__set__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bot_bot @ ( set @ A ) )
% 0.16/0.44 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bot_set_def
% 0.16/0.44 thf(fact_142_emptyE,axiom,
% 0.16/0.44 ! [A: $tType,A4: A] :
% 0.16/0.44 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % emptyE
% 0.16/0.44 thf(fact_143_equals0D,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,A4: A] :
% 0.16/0.44 ( ( A5
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 => ~ ( member @ A @ A4 @ A5 ) ) ).
% 0.16/0.44
% 0.16/0.44 % equals0D
% 0.16/0.44 thf(fact_144_equals0I,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ( ! [Y2: A] :
% 0.16/0.44 ~ ( member @ A @ Y2 @ A5 )
% 0.16/0.44 => ( A5
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % equals0I
% 0.16/0.44 thf(fact_145_ex__in__conv,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ( ( ? [X4: A] : ( member @ A @ X4 @ A5 ) )
% 0.16/0.44 = ( A5
% 0.16/0.44 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ex_in_conv
% 0.16/0.44 thf(fact_146_not__psubset__empty,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ~ ( ord_less @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % not_psubset_empty
% 0.16/0.44 thf(fact_147_inf__sup__aci_I8_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( lattice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.16/0.44 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inf_sup_aci(8)
% 0.16/0.44 thf(fact_148_inf__sup__aci_I7_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( lattice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,Z3: A] :
% 0.16/0.44 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) )
% 0.16/0.44 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inf_sup_aci(7)
% 0.16/0.44 thf(fact_149_inf__sup__aci_I6_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( lattice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,Z3: A] :
% 0.16/0.44 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z3 )
% 0.16/0.44 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inf_sup_aci(6)
% 0.16/0.44 thf(fact_150_inf__sup__aci_I5_J,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( lattice @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( sup_sup @ A )
% 0.16/0.44 = ( ^ [X4: A,Y3: A] : ( sup_sup @ A @ Y3 @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % inf_sup_aci(5)
% 0.16/0.44 thf(fact_151_sup__fun__def,axiom,
% 0.16/0.44 ! [B: $tType,A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.16/0.44 => ( ( sup_sup @ ( A > B ) )
% 0.16/0.44 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( sup_sup @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_fun_def
% 0.16/0.44 thf(fact_152_sup_Oassoc,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A,B3: A,C2: A] :
% 0.16/0.44 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B3 ) @ C2 )
% 0.16/0.44 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.assoc
% 0.16/0.44 thf(fact_153_sup__assoc,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,Z3: A] :
% 0.16/0.44 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z3 )
% 0.16/0.44 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_assoc
% 0.16/0.44 thf(fact_154_sup_Ocommute,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( sup_sup @ A )
% 0.16/0.44 = ( ^ [A6: A,B5: A] : ( sup_sup @ A @ B5 @ A6 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.commute
% 0.16/0.44 thf(fact_155_sup__commute,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( sup_sup @ A )
% 0.16/0.44 = ( ^ [X4: A,Y3: A] : ( sup_sup @ A @ Y3 @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_commute
% 0.16/0.44 thf(fact_156_sup_Oleft__commute,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [B3: A,A4: A,C2: A] :
% 0.16/0.44 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A4 @ C2 ) )
% 0.16/0.44 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.left_commute
% 0.16/0.44 thf(fact_157_sup__left__commute,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,Z3: A] :
% 0.16/0.44 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) )
% 0.16/0.44 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_left_commute
% 0.16/0.44 thf(fact_158_UnE,axiom,
% 0.16/0.44 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.16/0.44 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.16/0.44 => ( ~ ( member @ A @ C2 @ A5 )
% 0.16/0.44 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UnE
% 0.16/0.44 thf(fact_159_UnI1,axiom,
% 0.16/0.44 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 0.16/0.44 ( ( member @ A @ C2 @ A5 )
% 0.16/0.44 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UnI1
% 0.16/0.44 thf(fact_160_UnI2,axiom,
% 0.16/0.44 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 0.16/0.44 ( ( member @ A @ C2 @ B4 )
% 0.16/0.44 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % UnI2
% 0.16/0.44 thf(fact_161_bex__Un,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 0.16/0.44 ( ( ? [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.16/0.44 & ( P @ X4 ) ) )
% 0.16/0.44 = ( ? [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ A5 )
% 0.16/0.44 & ( P @ X4 ) )
% 0.16/0.44 | ? [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ B4 )
% 0.16/0.44 & ( P @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bex_Un
% 0.16/0.44 thf(fact_162_ball__Un,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 0.16/0.44 ( ( ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.16/0.44 => ( P @ X4 ) ) )
% 0.16/0.44 = ( ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ A5 )
% 0.16/0.44 => ( P @ X4 ) )
% 0.16/0.44 & ! [X4: A] :
% 0.16/0.44 ( ( member @ A @ X4 @ B4 )
% 0.16/0.44 => ( P @ X4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % ball_Un
% 0.16/0.44 thf(fact_163_Un__assoc,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A,C3: set @ A] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) @ C3 )
% 0.16/0.44 = ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Un_assoc
% 0.16/0.44 thf(fact_164_Un__absorb,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) @ A5 @ A5 )
% 0.16/0.44 = A5 ) ).
% 0.16/0.44
% 0.16/0.44 % Un_absorb
% 0.16/0.44 thf(fact_165_Un__commute,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) )
% 0.16/0.44 = ( ^ [A7: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A7 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Un_commute
% 0.16/0.44 thf(fact_166_Un__left__absorb,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 0.16/0.44 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % Un_left_absorb
% 0.16/0.44 thf(fact_167_Un__left__commute,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A,C3: set @ A] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) )
% 0.16/0.44 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Un_left_commute
% 0.16/0.44 thf(fact_168_sup_Ostrict__coboundedI2,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [C2: A,B3: A,A4: A] :
% 0.16/0.44 ( ( ord_less @ A @ C2 @ B3 )
% 0.16/0.44 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.strict_coboundedI2
% 0.16/0.44 thf(fact_169_sup_Ostrict__coboundedI1,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [C2: A,A4: A,B3: A] :
% 0.16/0.44 ( ( ord_less @ A @ C2 @ A4 )
% 0.16/0.44 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.strict_coboundedI1
% 0.16/0.44 thf(fact_170_sup_Ostrict__order__iff,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ( ( ord_less @ A )
% 0.16/0.44 = ( ^ [B5: A,A6: A] :
% 0.16/0.44 ( ( A6
% 0.16/0.44 = ( sup_sup @ A @ A6 @ B5 ) )
% 0.16/0.44 & ( A6 != B5 ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.strict_order_iff
% 0.16/0.44 thf(fact_171_sup_Ostrict__boundedE,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [B3: A,C2: A,A4: A] :
% 0.16/0.44 ( ( ord_less @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A4 )
% 0.16/0.44 => ~ ( ( ord_less @ A @ B3 @ A4 )
% 0.16/0.44 => ~ ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup.strict_boundedE
% 0.16/0.44 thf(fact_172_less__supI2,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,B3: A,A4: A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ B3 )
% 0.16/0.44 => ( ord_less @ A @ X @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_supI2
% 0.16/0.44 thf(fact_173_less__supI1,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,A4: A,B3: A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ A4 )
% 0.16/0.44 => ( ord_less @ A @ X @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_supI1
% 0.16/0.44 thf(fact_174_sup__bot__left,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A] :
% 0.16/0.44 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.16/0.44 = X ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_bot_left
% 0.16/0.44 thf(fact_175_sup__bot__right,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A] :
% 0.16/0.44 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.16/0.44 = X ) ) ).
% 0.16/0.44
% 0.16/0.44 % sup_bot_right
% 0.16/0.44 thf(fact_176_Un__empty__left,axiom,
% 0.16/0.44 ! [A: $tType,B4: set @ A] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 0.16/0.44 = B4 ) ).
% 0.16/0.44
% 0.16/0.44 % Un_empty_left
% 0.16/0.44 thf(fact_177_Un__empty__right,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A] :
% 0.16/0.44 ( ( sup_sup @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.44 = A5 ) ).
% 0.16/0.44
% 0.16/0.44 % Un_empty_right
% 0.16/0.44 thf(fact_178_bot__apply,axiom,
% 0.16/0.44 ! [C: $tType,D: $tType] :
% 0.16/0.44 ( ( bot @ C @ ( type2 @ C ) )
% 0.16/0.44 => ( ( bot_bot @ ( D > C ) )
% 0.16/0.44 = ( ^ [X4: D] : ( bot_bot @ C ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bot_apply
% 0.16/0.44 thf(fact_179_bot_Onot__eq__extremum,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A] :
% 0.16/0.44 ( ( A4
% 0.16/0.44 != ( bot_bot @ A ) )
% 0.16/0.44 = ( ord_less @ A @ ( bot_bot @ A ) @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bot.not_eq_extremum
% 0.16/0.44 thf(fact_180_bot_Oextremum__strict,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order_bot @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A] :
% 0.16/0.44 ~ ( ord_less @ A @ A4 @ ( bot_bot @ A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % bot.extremum_strict
% 0.16/0.44 thf(fact_181_Set_Ois__empty__def,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( is_empty @ A )
% 0.16/0.44 = ( ^ [A7: set @ A] :
% 0.16/0.44 ( A7
% 0.16/0.44 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % Set.is_empty_def
% 0.16/0.44 thf(fact_182_psubset__trans,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A,C3: set @ A] :
% 0.16/0.44 ( ( ord_less @ ( set @ A ) @ A5 @ B4 )
% 0.16/0.44 => ( ( ord_less @ ( set @ A ) @ B4 @ C3 )
% 0.16/0.44 => ( ord_less @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % psubset_trans
% 0.16/0.44 thf(fact_183_psubsetD,axiom,
% 0.16/0.44 ! [A: $tType,A5: set @ A,B4: set @ A,C2: A] :
% 0.16/0.44 ( ( ord_less @ ( set @ A ) @ A5 @ B4 )
% 0.16/0.44 => ( ( member @ A @ C2 @ A5 )
% 0.16/0.44 => ( member @ A @ C2 @ B4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % psubsetD
% 0.16/0.44 thf(fact_184_dual__order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [B3: A,A4: A] :
% 0.16/0.44 ( ( ord_less @ A @ B3 @ A4 )
% 0.16/0.44 => ( A4 != B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % dual_order.strict_implies_not_eq
% 0.16/0.44 thf(fact_185_order_Ostrict__implies__not__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A,B3: A] :
% 0.16/0.44 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.44 => ( A4 != B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % order.strict_implies_not_eq
% 0.16/0.44 thf(fact_186_not__less__iff__gr__or__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.16/0.44 = ( ( ord_less @ A @ Y @ X )
% 0.16/0.44 | ( X = Y ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % not_less_iff_gr_or_eq
% 0.16/0.44 thf(fact_187_dual__order_Ostrict__trans,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [B3: A,A4: A,C2: A] :
% 0.16/0.44 ( ( ord_less @ A @ B3 @ A4 )
% 0.16/0.44 => ( ( ord_less @ A @ C2 @ B3 )
% 0.16/0.44 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % dual_order.strict_trans
% 0.16/0.44 thf(fact_188_less__imp__not__less,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_imp_not_less
% 0.16/0.44 thf(fact_189_order_Ostrict__trans,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A,B3: A,C2: A] :
% 0.16/0.44 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.44 => ( ( ord_less @ A @ B3 @ C2 )
% 0.16/0.44 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % order.strict_trans
% 0.16/0.44 thf(fact_190_dual__order_Oirrefl,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A] :
% 0.16/0.44 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.16/0.44
% 0.16/0.44 % dual_order.irrefl
% 0.16/0.44 thf(fact_191_linorder__cases,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ~ ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ( ( X != Y )
% 0.16/0.44 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % linorder_cases
% 0.16/0.44 thf(fact_192_less__imp__triv,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A,P: $o] :
% 0.16/0.44 ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ( ( ord_less @ A @ Y @ X )
% 0.16/0.44 => P ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_imp_triv
% 0.16/0.44 thf(fact_193_less__imp__not__eq2,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ( Y != X ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_imp_not_eq2
% 0.16/0.44 thf(fact_194_antisym__conv3,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [Y: A,X: A] :
% 0.16/0.44 ( ~ ( ord_less @ A @ Y @ X )
% 0.16/0.44 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.16/0.44 = ( X = Y ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % antisym_conv3
% 0.16/0.44 thf(fact_195_less__induct,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [P: A > $o,A4: A] :
% 0.16/0.44 ( ! [X3: A] :
% 0.16/0.44 ( ! [Y4: A] :
% 0.16/0.44 ( ( ord_less @ A @ Y4 @ X3 )
% 0.16/0.44 => ( P @ Y4 ) )
% 0.16/0.44 => ( P @ X3 ) )
% 0.16/0.44 => ( P @ A4 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_induct
% 0.16/0.44 thf(fact_196_less__not__sym,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_not_sym
% 0.16/0.44 thf(fact_197_less__imp__not__eq,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [X: A,Y: A] :
% 0.16/0.44 ( ( ord_less @ A @ X @ Y )
% 0.16/0.44 => ( X != Y ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % less_imp_not_eq
% 0.16/0.44 thf(fact_198_dual__order_Oasym,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [B3: A,A4: A] :
% 0.16/0.44 ( ( ord_less @ A @ B3 @ A4 )
% 0.16/0.44 => ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% 0.16/0.44
% 0.16/0.44 % dual_order.asym
% 0.16/0.44 thf(fact_199_ord__less__eq__trans,axiom,
% 0.16/0.44 ! [A: $tType] :
% 0.16/0.44 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.44 => ! [A4: A,B3: A,C2: A] :
% 0.16/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.45 => ( ( B3 = C2 )
% 0.16/0.45 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % ord_less_eq_trans
% 0.16/0.45 thf(fact_200_ord__eq__less__trans,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [A4: A,B3: A,C2: A] :
% 0.16/0.45 ( ( A4 = B3 )
% 0.16/0.45 => ( ( ord_less @ A @ B3 @ C2 )
% 0.16/0.45 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % ord_eq_less_trans
% 0.16/0.45 thf(fact_201_less__irrefl,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A] :
% 0.16/0.45 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.16/0.45
% 0.16/0.45 % less_irrefl
% 0.16/0.45 thf(fact_202_less__linear,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A] :
% 0.16/0.45 ( ( ord_less @ A @ X @ Y )
% 0.16/0.45 | ( X = Y )
% 0.16/0.45 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % less_linear
% 0.16/0.45 thf(fact_203_less__trans,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A,Z3: A] :
% 0.16/0.45 ( ( ord_less @ A @ X @ Y )
% 0.16/0.45 => ( ( ord_less @ A @ Y @ Z3 )
% 0.16/0.45 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % less_trans
% 0.16/0.45 thf(fact_204_less__asym_H,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [A4: A,B3: A] :
% 0.16/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.45 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % less_asym'
% 0.16/0.45 thf(fact_205_less__asym,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A] :
% 0.16/0.45 ( ( ord_less @ A @ X @ Y )
% 0.16/0.45 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % less_asym
% 0.16/0.45 thf(fact_206_less__imp__neq,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A] :
% 0.16/0.45 ( ( ord_less @ A @ X @ Y )
% 0.16/0.45 => ( X != Y ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % less_imp_neq
% 0.16/0.45 thf(fact_207_dense,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A] :
% 0.16/0.45 ( ( ord_less @ A @ X @ Y )
% 0.16/0.45 => ? [Z2: A] :
% 0.16/0.45 ( ( ord_less @ A @ X @ Z2 )
% 0.16/0.45 & ( ord_less @ A @ Z2 @ Y ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % dense
% 0.16/0.45 thf(fact_208_order_Oasym,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [A4: A,B3: A] :
% 0.16/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.45 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % order.asym
% 0.16/0.45 thf(fact_209_neq__iff,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A] :
% 0.16/0.45 ( ( X != Y )
% 0.16/0.45 = ( ( ord_less @ A @ X @ Y )
% 0.16/0.45 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % neq_iff
% 0.16/0.45 thf(fact_210_neqE,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A,Y: A] :
% 0.16/0.45 ( ( X != Y )
% 0.16/0.45 => ( ~ ( ord_less @ A @ X @ Y )
% 0.16/0.45 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % neqE
% 0.16/0.45 thf(fact_211_gt__ex,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( no_top @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A] :
% 0.16/0.45 ? [X12: A] : ( ord_less @ A @ X @ X12 ) ) ).
% 0.16/0.45
% 0.16/0.45 % gt_ex
% 0.16/0.45 thf(fact_212_lt__ex,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.16/0.45 => ! [X: A] :
% 0.16/0.45 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.16/0.45
% 0.16/0.45 % lt_ex
% 0.16/0.45 thf(fact_213_order__less__subst2,axiom,
% 0.16/0.45 ! [A: $tType,C: $tType] :
% 0.16/0.45 ( ( ( order @ C @ ( type2 @ C ) )
% 0.16/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.45 => ! [A4: A,B3: A,F2: A > C,C2: C] :
% 0.16/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.45 => ( ( ord_less @ C @ ( F2 @ B3 ) @ C2 )
% 0.16/0.45 => ( ! [X3: A,Y2: A] :
% 0.16/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.16/0.45 => ( ord_less @ C @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 0.16/0.45 => ( ord_less @ C @ ( F2 @ A4 ) @ C2 ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % order_less_subst2
% 0.16/0.45 thf(fact_214_order__less__subst1,axiom,
% 0.16/0.45 ! [A: $tType,B: $tType] :
% 0.16/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.45 => ! [A4: A,F2: B > A,B3: B,C2: B] :
% 0.16/0.45 ( ( ord_less @ A @ A4 @ ( F2 @ B3 ) )
% 0.16/0.45 => ( ( ord_less @ B @ B3 @ C2 )
% 0.16/0.45 => ( ! [X3: B,Y2: B] :
% 0.16/0.45 ( ( ord_less @ B @ X3 @ Y2 )
% 0.16/0.45 => ( ord_less @ A @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 0.16/0.45 => ( ord_less @ A @ A4 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % order_less_subst1
% 0.16/0.45 thf(fact_215_ord__less__eq__subst,axiom,
% 0.16/0.45 ! [A: $tType,B: $tType] :
% 0.16/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.45 => ! [A4: A,B3: A,F2: A > B,C2: B] :
% 0.16/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.16/0.45 => ( ( ( F2 @ B3 )
% 0.16/0.45 = C2 )
% 0.16/0.45 => ( ! [X3: A,Y2: A] :
% 0.16/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.16/0.45 => ( ord_less @ B @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 0.16/0.45 => ( ord_less @ B @ ( F2 @ A4 ) @ C2 ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % ord_less_eq_subst
% 0.16/0.45 thf(fact_216_ord__eq__less__subst,axiom,
% 0.16/0.45 ! [A: $tType,B: $tType] :
% 0.16/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.45 => ! [A4: A,F2: B > A,B3: B,C2: B] :
% 0.16/0.45 ( ( A4
% 0.16/0.45 = ( F2 @ B3 ) )
% 0.16/0.45 => ( ( ord_less @ B @ B3 @ C2 )
% 0.16/0.45 => ( ! [X3: B,Y2: B] :
% 0.16/0.45 ( ( ord_less @ B @ X3 @ Y2 )
% 0.16/0.45 => ( ord_less @ A @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 0.16/0.45 => ( ord_less @ A @ A4 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % ord_eq_less_subst
% 0.16/0.45 thf(fact_217_bot__fun__def,axiom,
% 0.16/0.45 ! [B: $tType,A: $tType] :
% 0.16/0.45 ( ( bot @ B @ ( type2 @ B ) )
% 0.16/0.45 => ( ( bot_bot @ ( A > B ) )
% 0.16/0.45 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % bot_fun_def
% 0.16/0.45 thf(fact_218_bot__empty__eq,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( bot_bot @ ( A > $o ) )
% 0.16/0.45 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % bot_empty_eq
% 0.16/0.45 thf(fact_219_Collect__empty__eq__bot,axiom,
% 0.16/0.45 ! [A: $tType,P: A > $o] :
% 0.16/0.45 ( ( ( collect @ A @ P )
% 0.16/0.45 = ( bot_bot @ ( set @ A ) ) )
% 0.16/0.45 = ( P
% 0.16/0.45 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Collect_empty_eq_bot
% 0.16/0.45 thf(fact_220_map__tailrec__def,axiom,
% 0.16/0.45 ! [B: $tType,A: $tType] :
% 0.16/0.45 ( ( map_tailrec @ A @ B )
% 0.16/0.45 = ( ^ [F3: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F3 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % map_tailrec_def
% 0.16/0.45 thf(fact_221_rev__is__rev__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( ( rev @ A @ Xs )
% 0.16/0.45 = ( rev @ A @ Ys ) )
% 0.16/0.45 = ( Xs = Ys ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev_is_rev_conv
% 0.16/0.45 thf(fact_222_rev__rev__ident,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A] :
% 0.16/0.45 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 0.16/0.45 = Xs ) ).
% 0.16/0.45
% 0.16/0.45 % rev_rev_ident
% 0.16/0.45 thf(fact_223_rev__is__Nil__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A] :
% 0.16/0.45 ( ( ( rev @ A @ Xs )
% 0.16/0.45 = ( nil @ A ) )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev_is_Nil_conv
% 0.16/0.45 thf(fact_224_Nil__is__rev__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A] :
% 0.16/0.45 ( ( ( nil @ A )
% 0.16/0.45 = ( rev @ A @ Xs ) )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Nil_is_rev_conv
% 0.16/0.45 thf(fact_225_singleton__rev__conv,axiom,
% 0.16/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.16/0.45 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 0.16/0.45 = ( rev @ A @ Xs ) )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % singleton_rev_conv
% 0.16/0.45 thf(fact_226_rev__singleton__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,X: A] :
% 0.16/0.45 ( ( ( rev @ A @ Xs )
% 0.16/0.45 = ( cons @ A @ X @ ( nil @ A ) ) )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev_singleton_conv
% 0.16/0.45 thf(fact_227_rev_Osimps_I1_J,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( rev @ A @ ( nil @ A ) )
% 0.16/0.45 = ( nil @ A ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev.simps(1)
% 0.16/0.45 thf(fact_228_rev__map,axiom,
% 0.16/0.45 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.16/0.45 ( ( rev @ A @ ( map @ B @ A @ F2 @ Xs ) )
% 0.16/0.45 = ( map @ B @ A @ F2 @ ( rev @ B @ Xs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev_map
% 0.16/0.45 thf(fact_229_rev__swap,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( ( rev @ A @ Xs )
% 0.16/0.45 = Ys )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( rev @ A @ Ys ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev_swap
% 0.16/0.45 thf(fact_230_list__collect__set__map__simps_I4_J,axiom,
% 0.16/0.45 ! [A: $tType,B: $tType,C: $tType,F2: B > ( set @ A ),X: C > B,L3: list @ C,L4: list @ C] :
% 0.16/0.45 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( append @ C @ L3 @ L4 ) ) )
% 0.16/0.45 = ( sup_sup @ ( set @ A ) @ ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ L3 ) ) @ ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ L4 ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % list_collect_set_map_simps(4)
% 0.16/0.45 thf(fact_231_sorted__list__of__set__empty,axiom,
% 0.16/0.45 ! [A: $tType] :
% 0.16/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.45 => ( ( linord467138063of_set @ A @ ( bot_bot @ ( set @ A ) ) )
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % sorted_list_of_set_empty
% 0.16/0.45 thf(fact_232_append__assoc,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.16/0.45 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 0.16/0.45 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % append_assoc
% 0.16/0.45 thf(fact_233_append__same__eq,axiom,
% 0.16/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.16/0.45 ( ( ( append @ A @ Ys @ Xs )
% 0.16/0.45 = ( append @ A @ Zs @ Xs ) )
% 0.16/0.45 = ( Ys = Zs ) ) ).
% 0.16/0.45
% 0.16/0.45 % append_same_eq
% 0.16/0.45 thf(fact_234_same__append__eq,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.16/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.45 = ( append @ A @ Xs @ Zs ) )
% 0.16/0.45 = ( Ys = Zs ) ) ).
% 0.16/0.45
% 0.16/0.45 % same_append_eq
% 0.16/0.45 thf(fact_235_append__Nil2,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A] :
% 0.16/0.45 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.16/0.45 = Xs ) ).
% 0.16/0.45
% 0.16/0.45 % append_Nil2
% 0.16/0.45 thf(fact_236_append__self__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.45 = Xs )
% 0.16/0.45 = ( Ys
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % append_self_conv
% 0.16/0.45 thf(fact_237_self__append__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( Xs
% 0.16/0.45 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.45 = ( Ys
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % self_append_conv
% 0.16/0.45 thf(fact_238_append__self__conv2,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.45 = Ys )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % append_self_conv2
% 0.16/0.45 thf(fact_239_self__append__conv2,axiom,
% 0.16/0.45 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.16/0.45 ( ( Ys
% 0.16/0.45 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.45 = ( Xs
% 0.16/0.45 = ( nil @ A ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % self_append_conv2
% 0.16/0.45 thf(fact_240_Nil__is__append__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( ( nil @ A )
% 0.16/0.45 = ( append @ A @ Xs @ Ys ) )
% 0.16/0.45 = ( ( Xs
% 0.16/0.45 = ( nil @ A ) )
% 0.16/0.45 & ( Ys
% 0.16/0.45 = ( nil @ A ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % Nil_is_append_conv
% 0.16/0.45 thf(fact_241_append__is__Nil__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( ( append @ A @ Xs @ Ys )
% 0.16/0.45 = ( nil @ A ) )
% 0.16/0.45 = ( ( Xs
% 0.16/0.45 = ( nil @ A ) )
% 0.16/0.45 & ( Ys
% 0.16/0.45 = ( nil @ A ) ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % append_is_Nil_conv
% 0.16/0.45 thf(fact_242_map__append,axiom,
% 0.16/0.45 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Ys: list @ B] :
% 0.16/0.45 ( ( map @ B @ A @ F2 @ ( append @ B @ Xs @ Ys ) )
% 0.16/0.45 = ( append @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( map @ B @ A @ F2 @ Ys ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % map_append
% 0.16/0.45 thf(fact_243_rev__append,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.16/0.45 ( ( rev @ A @ ( append @ A @ Xs @ Ys ) )
% 0.16/0.45 = ( append @ A @ ( rev @ A @ Ys ) @ ( rev @ A @ Xs ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % rev_append
% 0.16/0.45 thf(fact_244_append1__eq__conv,axiom,
% 0.16/0.45 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.16/0.45 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.16/0.45 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.16/0.45 = ( ( Xs = Ys )
% 0.16/0.45 & ( X = Y ) ) ) ).
% 0.16/0.45
% 0.16/0.45 % append1_eq_conv
% 0.16/0.45 thf(fact_245_list__ee__eq__leel_I1_J,axiom,
% 0.16/0.45 ! [A: $tType,E1: A,E2: A,L1: list @ A,E12: A,E22: A,L2: list @ A] :
% 0.16/0.45 ( ( ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) )
% 0.16/0.45 = ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( nil @ A ) )
% 0.25/0.45 & ( E1 = E12 )
% 0.25/0.45 & ( E2 = E22 )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( nil @ A ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_ee_eq_leel(1)
% 0.25/0.45 thf(fact_246_list__ee__eq__leel_I2_J,axiom,
% 0.25/0.45 ! [A: $tType,L1: list @ A,E12: A,E22: A,L2: list @ A,E1: A,E2: A] :
% 0.25/0.45 ( ( ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) )
% 0.25/0.45 = ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( nil @ A ) )
% 0.25/0.45 & ( E1 = E12 )
% 0.25/0.45 & ( E2 = E22 )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( nil @ A ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_ee_eq_leel(2)
% 0.25/0.45 thf(fact_247_list__se__match_I1_J,axiom,
% 0.25/0.45 ! [A: $tType,L1: list @ A,L2: list @ A,A4: A] :
% 0.25/0.45 ( ( L1
% 0.25/0.45 != ( nil @ A ) )
% 0.25/0.45 => ( ( ( append @ A @ L1 @ L2 )
% 0.25/0.45 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( nil @ A ) ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_se_match(1)
% 0.25/0.45 thf(fact_248_list__se__match_I2_J,axiom,
% 0.25/0.45 ! [A: $tType,L2: list @ A,L1: list @ A,A4: A] :
% 0.25/0.45 ( ( L2
% 0.25/0.45 != ( nil @ A ) )
% 0.25/0.45 => ( ( ( append @ A @ L1 @ L2 )
% 0.25/0.45 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( nil @ A ) )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( cons @ A @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_se_match(2)
% 0.25/0.45 thf(fact_249_list__se__match_I3_J,axiom,
% 0.25/0.45 ! [A: $tType,L1: list @ A,A4: A,L2: list @ A] :
% 0.25/0.45 ( ( L1
% 0.25/0.45 != ( nil @ A ) )
% 0.25/0.45 => ( ( ( cons @ A @ A4 @ ( nil @ A ) )
% 0.25/0.45 = ( append @ A @ L1 @ L2 ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( nil @ A ) ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_se_match(3)
% 0.25/0.45 thf(fact_250_list__se__match_I4_J,axiom,
% 0.25/0.45 ! [A: $tType,L2: list @ A,A4: A,L1: list @ A] :
% 0.25/0.45 ( ( L2
% 0.25/0.45 != ( nil @ A ) )
% 0.25/0.45 => ( ( ( cons @ A @ A4 @ ( nil @ A ) )
% 0.25/0.45 = ( append @ A @ L1 @ L2 ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( nil @ A ) )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( cons @ A @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_se_match(4)
% 0.25/0.45 thf(fact_251_list__e__eq__lel_I1_J,axiom,
% 0.25/0.45 ! [A: $tType,E3: A,L1: list @ A,E4: A,L2: list @ A] :
% 0.25/0.45 ( ( ( cons @ A @ E3 @ ( nil @ A ) )
% 0.25/0.45 = ( append @ A @ L1 @ ( cons @ A @ E4 @ L2 ) ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( nil @ A ) )
% 0.25/0.45 & ( E4 = E3 )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( nil @ A ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_e_eq_lel(1)
% 0.25/0.45 thf(fact_252_list__e__eq__lel_I2_J,axiom,
% 0.25/0.45 ! [A: $tType,L1: list @ A,E4: A,L2: list @ A,E3: A] :
% 0.25/0.45 ( ( ( append @ A @ L1 @ ( cons @ A @ E4 @ L2 ) )
% 0.25/0.45 = ( cons @ A @ E3 @ ( nil @ A ) ) )
% 0.25/0.45 = ( ( L1
% 0.25/0.45 = ( nil @ A ) )
% 0.25/0.45 & ( E4 = E3 )
% 0.25/0.45 & ( L2
% 0.25/0.45 = ( nil @ A ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_e_eq_lel(2)
% 0.25/0.45 thf(fact_253_list__collect__set__simps_I4_J,axiom,
% 0.25/0.45 ! [A: $tType,B: $tType,F2: B > ( set @ A ),L3: list @ B,L4: list @ B] :
% 0.25/0.45 ( ( list_collect_set @ B @ A @ F2 @ ( append @ B @ L3 @ L4 ) )
% 0.25/0.45 = ( sup_sup @ ( set @ A ) @ ( list_collect_set @ B @ A @ F2 @ L3 ) @ ( list_collect_set @ B @ A @ F2 @ L4 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % list_collect_set_simps(4)
% 0.25/0.45 thf(fact_254_bind__simps_I2_J,axiom,
% 0.25/0.45 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F2: B > ( list @ A )] :
% 0.25/0.45 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F2 )
% 0.25/0.45 = ( append @ A @ ( F2 @ X ) @ ( bind @ B @ A @ Xs @ F2 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 % bind_simps(2)
% 0.25/0.45
% 0.25/0.45 %----Subclasses (4)
% 0.25/0.45 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 0.25/0.45 ! [A: $tType] :
% 0.25/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.25/0.45 => ( type @ A @ ( type2 @ A ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 0.25/0.45 ! [A: $tType] :
% 0.25/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.25/0.45 => ( ord @ A @ ( type2 @ A ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 0.25/0.45 ! [A: $tType] :
% 0.25/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.25/0.45 => ( order @ A @ ( type2 @ A ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 0.25/0.45 ! [A: $tType] :
% 0.25/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.25/0.45 => ( preorder @ A @ ( type2 @ A ) ) ) ).
% 0.25/0.45
% 0.25/0.45 %----Type constructors (31)
% 0.25/0.45 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.25/0.45 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.25/0.45 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( bounde1808546759up_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( bounded_lattice_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( order_bot @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( order_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Orderings_Oord,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_fun___Orderings_Obot,axiom,
% 0.25/0.45 ! [A8: $tType,A9: $tType] :
% 0.25/0.45 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 0.25/0.45 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 0.25/0.45 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_4,axiom,
% 0.25/0.45 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_5,axiom,
% 0.25/0.45 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 0.25/0.45 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 0.25/0.45 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Lattices_Olattice_8,axiom,
% 0.25/0.45 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 0.25/0.45 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 0.25/0.45 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 0.25/0.45 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 0.25/0.45 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_13,axiom,
% 0.25/0.45 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_14,axiom,
% 0.25/0.45 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15,axiom,
% 0.25/0.45 order_bot @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 0.25/0.45 preorder @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.25/0.45 linorder @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Lattices_Olattice_17,axiom,
% 0.25/0.45 lattice @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Orderings_Oorder_18,axiom,
% 0.25/0.45 order @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Orderings_Oord_19,axiom,
% 0.25/0.45 ord @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 thf(tcon_HOL_Obool___Orderings_Obot_20,axiom,
% 0.25/0.45 bot @ $o @ ( type2 @ $o ) ).
% 0.25/0.45
% 0.25/0.45 %----Free types (1)
% 0.25/0.45 thf(tfree_0,hypothesis,
% 0.25/0.45 linorder @ a @ ( type2 @ a ) ).
% 0.25/0.45
% 0.25/0.45 %----Conjectures (1)
% 0.25/0.45 thf(conj_0,conjecture,
% 0.25/0.45 ( ( ( cons @ a @ x1 @ l1 )
% 0.25/0.45 = l2a )
% 0.25/0.45 = ( ( sorted1061247458sorted @ a @ ( cons @ a @ x1 @ l1 ) @ l2a )
% 0.25/0.45 & ( sorted1061247458sorted @ a @ l2a @ ( cons @ a @ x1 @ l1 ) ) ) ) ).
% 0.25/0.45
% 0.25/0.45 %------------------------------------------------------------------------------
% 0.25/0.45 ------------------------
% 2.65/1.48 ---- Embedded in THF ---
% 2.65/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.65/1.48 %%% Generated on Tue Feb 24 06:10:55 EST 2026
% 2.65/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.65/1.48 %%% Logic specification used:
% 2.65/1.48 %%% thf(spec, logic, $$dhol).
% 2.65/1.48
% 2.65/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2DTF2830.p
% 2.65/1.48 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.65/1.48 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.65/1.48 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.65/1.48 thf(ty_tf_a, type, a: $tType).
% 2.65/1.48 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Lattices_Obounded__lattice__bot, type, bounded_lattice_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.65/1.48 thf(sy_c_BNF__Greatest__Fixpoint_Oshift, type, bNF_Greatest_shift: (!> [A:$tType,B:$tType]: ((((list @ A) > B) > (A > ((list @ A) > B)))))).
% 2.65/1.48 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.65/1.48 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.65/1.48 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_List_Olinorder__class_Osorted__list__of__set, type, linord467138063of_set: (!> [A:$tType]: (((set @ A) > (list @ A))))).
% 2.65/1.48 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.65/1.48 thf(sy_c_List_Olist_Omap, type, map: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((list @ A) > (list @ Aa)))))).
% 2.65/1.48 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.65/1.48 thf(sy_c_List_Olistrelp, type, listrelp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((list @ A) > ((list @ B) > $o)))))).
% 2.65/1.48 thf(sy_c_List_Omap__tailrec, type, map_tailrec: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > (list @ B)))))).
% 2.65/1.48 thf(sy_c_List_Omap__tailrec__rev, type, map_tailrec_rev: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > ((list @ B) > (list @ B))))))).
% 2.65/1.48 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.65/1.48 thf(sy_c_List_Oord__class_Olexordp__eq, type, ord_lexordp_eq: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.65/1.48 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.65/1.48 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.65/1.48 thf(sy_c_List_Osplice, type, splice: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.65/1.48 thf(sy_c_List__More_Ocombinatorial__product, type, list_c659805718roduct: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.65/1.48 thf(sy_c_Misc_Olist__collect__set, type, list_collect_set: (!> [B:$tType,A:$tType]: (((B > (set @ A)) > ((list @ B) > (set @ A)))))).
% 2.65/1.48 thf(sy_c_Misc_Omerge, type, merge: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_Misc_Omerge__list, type, merge_list: (!> [A:$tType]: (((list @ (list @ A)) > ((list @ (list @ A)) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_Misc_Orevg, type, revg: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.65/1.48 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.65/1.48 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.65/1.48 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.65/1.48 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.65/1.48 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Odiff__sorted, type, sorted1267110213sorted: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Ointer__sorted, type, sorted2037043510sorted: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.48 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Osubset__sorted, type, sorted1061247458sorted: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.65/1.48 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.65/1.48 thf(sy_v_l1_H____, type, l1: (list @ a)).
% 2.65/1.48 thf(sy_v_l2a____, type, l2a: (list @ a)).
% 2.65/1.48 thf(sy_v_x1____, type, x1: a).
% 2.65/1.48 thf(fact_0_local_ONil, axiom, (l2a = (nil @ a))).
% 2.65/1.48 thf(fact_1_ind__hyp, axiom, (! [L2:(list @ a)]: (((l1 = L2) = ((((sorted1061247458sorted @ a) @ l1) @ L2) & (((sorted1061247458sorted @ a) @ L2) @ l1)))))).
% 2.65/1.48 thf(fact_2_subset__sorted_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X1:A,L1:(list @ A)]: ((~ ((((sorted1061247458sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (nil @ A)))))))))).
% 2.65/1.48 thf(fact_3_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.65/1.48 thf(fact_4_subset__sorted_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(list @ A)]: ((((sorted1061247458sorted @ A) @ (nil @ A)) @ L2))))))).
% 2.65/1.48 thf(fact_5_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.65/1.48 thf(fact_6_list__tail__coinc, axiom, (! [A:$tType,N1:A,R1:(list @ A),N2:A,R2:(list @ A)]: ((((((cons @ A) @ N1) @ R1) = (((cons @ A) @ N2) @ R2)) => ((N1 = N2) & (R1 = R2)))))).
% 2.65/1.48 thf(fact_7_subset__sorted_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X1:A,L1:(list @ A),X2:A,L2:(list @ A)]: (((((sorted1061247458sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = ((~ ((((ord_less @ A) @ X1) @ X2))) & ((~ ((((ord_less @ A) @ X1) @ X2))) => (((X1 = X2) => (((sorted1061247458sorted @ A) @ L1) @ L2)) & ((X1 != X2) => (((sorted1061247458sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ L2)))))))))))).
% 2.65/1.48 thf(fact_8_shift__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Greatest_shift @ A) @ B) = (^ [Lab:((list @ A) > B),K:A,Kl:(list @ A)]: ((Lab @ (((cons @ A) @ K) @ Kl)))))))).
% 2.65/1.48 thf(fact_9_subset__sorted_Oelims_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A),Xa:(list @ A)]: (((~ ((((sorted1061247458sorted @ A) @ X) @ Xa))) => (((? [X12:A,L12:(list @ A)]: ((X = (((cons @ A) @ X12) @ L12)))) => (Xa != (nil @ A))) => (~ ((! [X12:A,L12:(list @ A)]: (((X = (((cons @ A) @ X12) @ L12)) => (! [X23:A,L22:(list @ A)]: (((Xa = (((cons @ A) @ X23) @ L22)) => ((~ ((((ord_less @ A) @ X12) @ X23))) & ((~ ((((ord_less @ A) @ X12) @ X23))) => (((X12 = X23) => (((sorted1061247458sorted @ A) @ L12) @ L22)) & ((X12 != X23) => (((sorted1061247458sorted @ A) @ (((cons @ A) @ X12) @ L12)) @ L22))))))))))))))))))))).
% 2.65/1.48 thf(fact_10_subset__sorted_Oelims_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A),Xa:(list @ A)]: (((((sorted1061247458sorted @ A) @ X) @ Xa) => (((X = (nil @ A)) => (! [L22:(list @ A)]: ((Xa != L22)))) => (~ ((! [X12:A,L12:(list @ A)]: (((X = (((cons @ A) @ X12) @ L12)) => (! [X23:A,L22:(list @ A)]: (((Xa = (((cons @ A) @ X23) @ L22)) => (~ (((~ ((((ord_less @ A) @ X12) @ X23))) & ((~ ((((ord_less @ A) @ X12) @ X23))) => (((X12 = X23) => (((sorted1061247458sorted @ A) @ L12) @ L22)) & ((X12 != X23) => (((sorted1061247458sorted @ A) @ (((cons @ A) @ X12) @ L12)) @ L22))))))))))))))))))))))).
% 2.65/1.48 thf(fact_11_subset__sorted_Oelims_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A),Xa:(list @ A),Y:$o]: ((((((sorted1061247458sorted @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (~ (Y))) => (((? [X12:A,L12:(list @ A)]: ((X = (((cons @ A) @ X12) @ L12)))) => ((Xa = (nil @ A)) => Y)) => (~ ((! [X12:A,L12:(list @ A)]: (((X = (((cons @ A) @ X12) @ L12)) => (! [X23:A,L22:(list @ A)]: (((Xa = (((cons @ A) @ X23) @ L22)) => (Y = (~ (((~ ((((ord_less @ A) @ X12) @ X23))) & ((~ ((((ord_less @ A) @ X12) @ X23))) => (((X12 = X23) => (((sorted1061247458sorted @ A) @ L12) @ L22)) & ((X12 != X23) => (((sorted1061247458sorted @ A) @ (((cons @ A) @ X12) @ L12)) @ L22))))))))))))))))))))))))).
% 2.65/1.48 thf(fact_12_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.65/1.48 thf(fact_13_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.65/1.48 thf(fact_14_transpose_Ocases, axiom, (! [A:$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))))))))))).
% 2.65/1.48 thf(fact_15_subset__sorted_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [X12:A,L12:(list @ A)]: (((P @ (((cons @ A) @ X12) @ L12)) @ (nil @ A)))) => ((! [X12:A,L12:(list @ A),X23:A,L22:(list @ A)]: ((((~ ((((ord_less @ A) @ X12) @ X23))) => ((X12 = X23) => ((P @ L12) @ L22))) => (((~ ((((ord_less @ A) @ X12) @ X23))) => ((X12 != X23) => ((P @ (((cons @ A) @ X12) @ L12)) @ L22))) => ((P @ (((cons @ A) @ X12) @ L12)) @ (((cons @ A) @ X23) @ L22)))))) => ((P @ A0) @ A1)))))))))).
% 2.65/1.48 thf(fact_16_inter__sorted_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [V:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V) @ Va)) @ (nil @ A)))) => ((! [X12:A,L12:(list @ A),X23:A,L22:(list @ A)]: ((((((ord_less @ A) @ X12) @ X23) => ((P @ L12) @ (((cons @ A) @ X23) @ L22))) => (((~ ((((ord_less @ A) @ X12) @ X23))) => ((X12 = X23) => ((P @ L12) @ L22))) => (((~ ((((ord_less @ A) @ X12) @ X23))) => ((X12 != X23) => ((P @ (((cons @ A) @ X12) @ L12)) @ L22))) => ((P @ (((cons @ A) @ X12) @ L12)) @ (((cons @ A) @ X23) @ L22))))))) => ((P @ A0) @ A1)))))))))).
% 2.65/1.48 thf(fact_17_mergesort__by__rel__merge__induct, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),R:(A > (B > $o)),Xs:(list @ A),Ys:(list @ B)]: (((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ B)))) => ((! [X12:(list @ B)]: (((P @ (nil @ A)) @ X12))) => ((! [X3:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: ((((R @ X3) @ Y2) => (((P @ Xs2) @ (((cons @ B) @ Y2) @ Ys2)) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2)))))) => ((! [X3:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: (((~ (((R @ X3) @ Y2))) => (((P @ (((cons @ A) @ X3) @ Xs2)) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2)))))) => ((P @ Xs) @ Ys)))))))).
% 2.65/1.48 thf(fact_18_mergesort__by__rel__merge_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > ((list @ A) > $o))),A0:(A > (A > $o)),A1:(list @ A),A2:(list @ A)]: (((! [R3:(A > (A > $o)),X3:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: (((((R3 @ X3) @ Y2) => (((P @ R3) @ Xs2) @ (((cons @ A) @ Y2) @ Ys2))) => (((~ (((R3 @ X3) @ Y2))) => (((P @ R3) @ (((cons @ A) @ X3) @ Xs2)) @ Ys2)) => (((P @ R3) @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))) => ((! [R3:(A > (A > $o)),Xs2:(list @ A)]: ((((P @ R3) @ Xs2) @ (nil @ A)))) => ((! [R3:(A > (A > $o)),V:A,Va:(list @ A)]: ((((P @ R3) @ (nil @ A)) @ (((cons @ A) @ V) @ Va)))) => (((P @ A0) @ A1) @ A2))))))).
% 2.65/1.48 thf(fact_19_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A2:(list @ B)]: (((! [F:(A > B),X12:(list @ B)]: ((((P @ F) @ (nil @ A)) @ X12))) => ((! [F:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F) @ As) @ (((cons @ B) @ (F @ A3)) @ Bs)) => (((P @ F) @ (((cons @ A) @ A3) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A2)))))).
% 2.65/1.48 thf(fact_20_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X3) @ Xs2)))))) => (P @ Xs))))))).
% 2.65/1.48 thf(fact_21_list__all__zip_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > (B > $o)) > ((list @ A) > ((list @ B) > $o))),A0:(A > (B > $o)),A1:(list @ A),A2:(list @ B)]: (((! [P2:(A > (B > $o))]: ((((P @ P2) @ (nil @ A)) @ (nil @ B)))) => ((! [P2:(A > (B > $o)),A3:A,As:(list @ A),B2:B,Bs:(list @ B)]: (((((P @ P2) @ As) @ Bs) => (((P @ P2) @ (((cons @ A) @ A3) @ As)) @ (((cons @ B) @ B2) @ Bs))))) => ((! [P2:(A > (B > $o)),V:A,Va:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ V) @ Va)) @ (nil @ B)))) => ((! [P2:(A > (B > $o)),V:B,Va:(list @ B)]: ((((P @ P2) @ (nil @ A)) @ (((cons @ B) @ V) @ Va)))) => (((P @ A0) @ A1) @ A2)))))))).
% 2.65/1.48 thf(fact_22_list__induct__first2, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X12:A,X23:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((cons @ A) @ X12) @ (((cons @ A) @ X23) @ Xs2)))))) => (P @ Xs))))))).
% 2.65/1.48 thf(fact_23_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X3:A]: ((P @ (((cons @ A) @ X3) @ (nil @ A))))) => ((! [X3:A,Y2:A,Xs2:(list @ A)]: ((((X3 = Y2) => (P @ (((cons @ A) @ X3) @ Xs2))) => (((X3 != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 2.65/1.48 thf(fact_24_remdups__adj_Ocases, axiom, (! [A:$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)))))))))))).
% 2.65/1.48 thf(fact_25_list__2pre__induct, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),W1:(list @ A),W2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [E:A,W12:(list @ A),W22:(list @ B)]: ((((P @ W12) @ W22) => ((P @ (((cons @ A) @ E) @ W12)) @ W22)))) => ((! [E:B,W13:(list @ A),W23:(list @ B)]: ((((P @ W13) @ W23) => ((P @ W13) @ (((cons @ B) @ E) @ W23))))) => ((P @ W1) @ W2))))))).
% 2.65/1.48 thf(fact_26_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [V:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V) @ Va)) @ (nil @ A)))) => ((! [X3:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((P @ A0) @ A1))))))).
% 2.65/1.48 thf(fact_27_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X3) @ Xs2)) @ (nil @ B)))) => ((! [Y2:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y2) @ Ys2)))) => ((! [X3:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.65/1.48 thf(fact_28_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys3)))))))).
% 2.65/1.48 thf(fact_29_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X12:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X12) @ X23))))) => (P @ List)))))).
% 2.65/1.48 thf(fact_30_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.65/1.48 thf(fact_31_zipf_Oinduct, axiom, (! [A:$tType,C:$tType,B:$tType,P:((A > (B > C)) > ((list @ A) > ((list @ B) > $o))),A0:(A > (B > C)),A1:(list @ A),A2:(list @ B)]: (((! [F:(A > (B > C))]: ((((P @ F) @ (nil @ A)) @ (nil @ B)))) => ((! [F:(A > (B > C)),A3:A,As:(list @ A),B2:B,Bs:(list @ B)]: (((((P @ F) @ As) @ Bs) => (((P @ F) @ (((cons @ A) @ A3) @ As)) @ (((cons @ B) @ B2) @ Bs))))) => ((! [A3:(A > (B > C)),V:A,Va:(list @ A)]: ((((P @ A3) @ (((cons @ A) @ V) @ Va)) @ (nil @ B)))) => ((! [A3:(A > (B > C)),V:B,Va:(list @ B)]: ((((P @ A3) @ (nil @ A)) @ (((cons @ B) @ V) @ Va)))) => (((P @ A0) @ A1) @ A2)))))))).
% 2.65/1.48 thf(fact_32_revg_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [A3:A,As:(list @ A),B2:(list @ A)]: ((((P @ As) @ (((cons @ A) @ A3) @ B2)) => ((P @ (((cons @ A) @ A3) @ As)) @ B2)))) => ((P @ A0) @ A1)))))).
% 2.65/1.48 thf(fact_33_quicksort_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X3:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X3) @ Xs2))))))))))))).
% 2.65/1.48 thf(fact_34_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.65/1.48 thf(fact_35_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 2.65/1.48 thf(fact_36_inter__sorted_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((sorted2037043510sorted @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != (nil @ A))) => (((? [V:A,Va:(list @ A)]: ((X = (((cons @ A) @ V) @ Va)))) => ((Xa = (nil @ A)) => (Y != (nil @ A)))) => (~ ((! [X12:A,L12:(list @ A)]: (((X = (((cons @ A) @ X12) @ L12)) => (! [X23:A,L22:(list @ A)]: (((Xa = (((cons @ A) @ X23) @ L22)) => (~ ((((((ord_less @ A) @ X12) @ X23) => (Y = (((sorted2037043510sorted @ A) @ L12) @ (((cons @ A) @ X23) @ L22)))) & ((~ ((((ord_less @ A) @ X12) @ X23))) => (((X12 = X23) => (Y = (((cons @ A) @ X12) @ (((sorted2037043510sorted @ A) @ L12) @ L22)))) & ((X12 != X23) => (Y = (((sorted2037043510sorted @ A) @ (((cons @ A) @ X12) @ L12)) @ L22))))))))))))))))))))))))).
% 2.65/1.48 thf(fact_37_diff__sorted_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((sorted1267110213sorted @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != (nil @ A))) => ((! [V:A,Va:(list @ A)]: (((X = (((cons @ A) @ V) @ Va)) => ((Xa = (nil @ A)) => (Y != (((cons @ A) @ V) @ Va)))))) => (~ ((! [X12:A,L12:(list @ A)]: (((X = (((cons @ A) @ X12) @ L12)) => (! [X23:A,L22:(list @ A)]: (((Xa = (((cons @ A) @ X23) @ L22)) => (~ ((((((ord_less @ A) @ X12) @ X23) => (Y = (((cons @ A) @ X12) @ (((sorted1267110213sorted @ A) @ L12) @ (((cons @ A) @ X23) @ L22))))) & ((~ ((((ord_less @ A) @ X12) @ X23))) => (((X12 = X23) => (Y = (((sorted1267110213sorted @ A) @ L12) @ L22))) & ((X12 != X23) => (Y = (((sorted1267110213sorted @ A) @ (((cons @ A) @ X12) @ L12)) @ L22))))))))))))))))))))))))).
% 2.65/1.48 thf(fact_38_merge_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((merge @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != Xa)) => ((! [V:A,Va:(list @ A)]: (((X = (((cons @ A) @ V) @ Va)) => ((Xa = (nil @ A)) => (Y != (((cons @ A) @ V) @ Va)))))) => (~ ((! [X12:A,L12:(list @ A)]: (((X = (((cons @ A) @ X12) @ L12)) => (! [X23:A,L22:(list @ A)]: (((Xa = (((cons @ A) @ X23) @ L22)) => (~ ((((((ord_less @ A) @ X12) @ X23) => (Y = (((cons @ A) @ X12) @ (((merge @ A) @ L12) @ (((cons @ A) @ X23) @ L22))))) & ((~ ((((ord_less @ A) @ X12) @ X23))) => (((X12 = X23) => (Y = (((cons @ A) @ X12) @ (((merge @ A) @ L12) @ L22)))) & ((X12 != X23) => (Y = (((cons @ A) @ X23) @ (((merge @ A) @ (((cons @ A) @ X12) @ L12)) @ L22)))))))))))))))))))))))))).
% 2.65/1.48 thf(fact_39_revg_Oelims, axiom, (! [A:$tType,X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((revg @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != Xa)) => (~ ((! [A3:A,As:(list @ A)]: (((X = (((cons @ A) @ A3) @ As)) => (Y != (((revg @ A) @ As) @ (((cons @ A) @ A3) @ Xa))))))))))))).
% 2.65/1.48 thf(fact_40_list__collect__set__simps_I2_J, axiom, (! [A:$tType,B:$tType,F2:(B > (set @ A)),A4:B]: ((((((list_collect_set @ B) @ A) @ F2) @ (((cons @ B) @ A4) @ (nil @ B))) = (F2 @ A4))))).
% 2.65/1.48 thf(fact_41_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A))))))).
% 2.65/1.48 thf(fact_42_lexordp__eq_Ocases, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A1:(list @ A),A2:(list @ A)]: (((((ord_lexordp_eq @ A) @ A1) @ A2) => (((A1 = (nil @ A)) => (! [Ys2:(list @ A)]: ((A2 != Ys2)))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y2:A]: (((? [Ys2:(list @ A)]: ((A2 = (((cons @ A) @ Y2) @ Ys2)))) => (~ ((((ord_less @ A) @ X3) @ Y2))))))))) => (~ ((! [X3:A,Y2:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A2 = (((cons @ A) @ Y2) @ Ys2)) => ((~ ((((ord_less @ A) @ X3) @ Y2))) => ((~ ((((ord_less @ A) @ Y2) @ X3))) => (~ ((((ord_lexordp_eq @ A) @ Xs2) @ Ys2)))))))))))))))))))))).
% 2.65/1.48 thf(fact_43_lexordp__eq_Osimps, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((ord_lexordp_eq @ A) = (^ [A12:(list @ A),A22:(list @ A)]: (((? [Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A22 = Ys3)))) | ((? [X4:A,Y3:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A22 = (((cons @ A) @ Y3) @ Ys3)) & (((ord_less @ A) @ X4) @ Y3))))) | (? [X4:A,Y3:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A22 = (((cons @ A) @ Y3) @ Ys3)) & ((~ ((((ord_less @ A) @ X4) @ Y3))) & ((~ ((((ord_less @ A) @ Y3) @ X4))) & (((ord_lexordp_eq @ A) @ Xs3) @ Ys3)))))))))))))))).
% 2.65/1.48 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 2.65/1.48 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A5)))) = A5)))).
% 2.65/1.48 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.65/1.48 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X3:A]: (((F2 @ X3) = (G @ X3)))) => (F2 = G))))).
% 2.65/1.48 thf(fact_48_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((Less @ X) @ Y) | ((~ (((Less @ Y) @ X))) & ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys))))))).
% 2.65/1.48 thf(fact_49_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys)))).
% 2.65/1.48 thf(fact_50_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.65/1.48 thf(fact_51_lexordp__eq__simps_I1_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys))))))).
% 2.65/1.48 thf(fact_52_lexordp__eq__simps_I2_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A))))))))).
% 2.65/1.48 thf(fact_53_lexordp__eq__simps_I4_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = ((((ord_less @ A) @ X) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X))) & (((ord_lexordp_eq @ A) @ Xs) @ Ys)))))))))).
% 2.65/1.48 thf(fact_54_lexordp__eq__simps_I3_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A)]: ((~ ((((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A)))))))))).
% 2.65/1.48 thf(fact_55_merge__list_Oinduct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:((list @ (list @ A)) > ((list @ (list @ A)) > $o)),A0:(list @ (list @ A)),A1:(list @ (list @ A))]: ((((P @ (nil @ (list @ A))) @ (nil @ (list @ A))) => ((! [L:(list @ A)]: (((P @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ L) @ (nil @ (list @ A)))))) => ((! [La:(list @ A),Acc2:(list @ (list @ A))]: ((((P @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ La) @ Acc2)) => ((P @ (((cons @ (list @ A)) @ La) @ Acc2)) @ (nil @ (list @ A)))))) => ((! [La:(list @ A),Acc2:(list @ (list @ A)),L:(list @ A)]: ((((P @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ L) @ (((cons @ (list @ A)) @ La) @ Acc2))) => ((P @ (((cons @ (list @ A)) @ La) @ Acc2)) @ (((cons @ (list @ A)) @ L) @ (nil @ (list @ A))))))) => ((! [Acc2:(list @ (list @ A)),L12:(list @ A),L22:(list @ A),Ls:(list @ (list @ A))]: ((((P @ (((cons @ (list @ A)) @ (((merge @ A) @ L12) @ L22)) @ Acc2)) @ Ls) => ((P @ Acc2) @ (((cons @ (list @ A)) @ L12) @ (((cons @ (list @ A)) @ L22) @ Ls)))))) => ((P @ A0) @ A1)))))))))))).
% 2.65/1.48 thf(fact_56_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ Xs) @ Xs)))).
% 2.65/1.48 thf(fact_57_lexordp__eq__refl, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: ((((ord_lexordp_eq @ A) @ Xs) @ Xs))))))).
% 2.65/1.48 thf(fact_58_lexordp__eq__trans, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) => ((((ord_lexordp_eq @ A) @ Ys) @ Zs) => (((ord_lexordp_eq @ A) @ Xs) @ Zs))))))))).
% 2.65/1.48 thf(fact_59_lexordp__eq__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) | (((ord_lexordp_eq @ A) @ Ys) @ Xs)))))))).
% 2.65/1.48 thf(fact_60_lexordp__eq__antisym, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) => ((((ord_lexordp_eq @ A) @ Ys) @ Xs) => (Xs = Ys))))))))).
% 2.65/1.48 thf(fact_61_lexordp__eq_ONil, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys))))))).
% 2.65/1.48 thf(fact_62_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: ((((Less @ X) @ Y) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))).
% 2.65/1.48 thf(fact_63_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ (((Less @ X) @ Y))) => ((~ (((Less @ Y) @ X))) => (((((lexordp_eq @ A) @ Less) @ Xs) @ Ys) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)))))))).
% 2.65/1.48 thf(fact_64_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys)))).
% 2.65/1.48 thf(fact_65_merge_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(list @ A)]: (((((merge @ A) @ (nil @ A)) @ L2) = L2))))))).
% 2.65/1.48 thf(fact_66_inter__sorted_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(list @ A)]: (((((sorted2037043510sorted @ A) @ (nil @ A)) @ L2) = (nil @ A)))))))).
% 2.65/1.48 thf(fact_67_diff__sorted_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L2:(list @ A)]: (((((sorted1267110213sorted @ A) @ (nil @ A)) @ L2) = (nil @ A)))))))).
% 2.65/1.48 thf(fact_68_revg_Osimps_I2_J, axiom, (! [A:$tType,A4:A,As2:(list @ A),B3:(list @ A)]: (((((revg @ A) @ (((cons @ A) @ A4) @ As2)) @ B3) = (((revg @ A) @ As2) @ (((cons @ A) @ A4) @ B3)))))).
% 2.65/1.48 thf(fact_69_revg_Osimps_I1_J, axiom, (! [A:$tType,B3:(list @ A)]: (((((revg @ A) @ (nil @ A)) @ B3) = B3)))).
% 2.65/1.48 thf(fact_70_lexordp__eq_OCons__eq, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X))) => ((((ord_lexordp_eq @ A) @ Xs) @ Ys) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys))))))))))).
% 2.65/1.48 thf(fact_71_lexordp__eq_OCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((((ord_less @ A) @ X) @ Y) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys))))))))).
% 2.65/1.48 thf(fact_72_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A2:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ A1) @ A2) => (((A1 = (nil @ A)) => (! [Ys2:(list @ A)]: ((A2 != Ys2)))) => ((! [X3:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X3) @ Xs2)))) => (! [Y2:A]: (((? [Ys2:(list @ A)]: ((A2 = (((cons @ A) @ Y2) @ Ys2)))) => (~ (((Less @ X3) @ Y2))))))))) => (~ ((! [X3:A,Y2:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ A)]: (((A2 = (((cons @ A) @ Y2) @ Ys2)) => ((~ (((Less @ X3) @ Y2))) => ((~ (((Less @ Y2) @ X3))) => (~ (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys2))))))))))))))))))).
% 2.65/1.48 thf(fact_73_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A22:(list @ A)]: (((? [Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A22 = Ys3)))) | ((? [X4:A,Y3:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A22 = (((cons @ A) @ Y3) @ Ys3)) & ((Less2 @ X4) @ Y3))))) | (? [X4:A,Y3:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A22 = (((cons @ A) @ Y3) @ Ys3)) & ((~ (((Less2 @ X4) @ Y3))) & ((~ (((Less2 @ Y3) @ X4))) & ((((lexordp_eq @ A) @ Less2) @ Xs3) @ Ys3))))))))))))))).
% 2.65/1.48 thf(fact_74_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X1:(list @ A),X2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less) @ X1) @ X2) => ((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [X3:A,Y2:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((Less @ X3) @ Y2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((! [X3:A,Y2:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X3) @ Y2))) => ((~ (((Less @ Y2) @ X3))) => (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))))) => ((P @ X1) @ X2)))))))).
% 2.65/1.48 thf(fact_75_merge_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X1:A,X2:A,L1:(list @ A),L2:(list @ A)]: ((((((ord_less @ A) @ X1) @ X2) => ((((merge @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((cons @ A) @ X1) @ (((merge @ A) @ L1) @ (((cons @ A) @ X2) @ L2))))) & ((~ ((((ord_less @ A) @ X1) @ X2))) => (((X1 = X2) => ((((merge @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((cons @ A) @ X1) @ (((merge @ A) @ L1) @ L2)))) & ((X1 != X2) => ((((merge @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((cons @ A) @ X2) @ (((merge @ A) @ (((cons @ A) @ X1) @ L1)) @ L2))))))))))))).
% 2.65/1.48 thf(fact_76_merge_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [V2:A,Va2:(list @ A)]: (((((merge @ A) @ (((cons @ A) @ V2) @ Va2)) @ (nil @ A)) = (((cons @ A) @ V2) @ Va2)))))))).
% 2.65/1.48 thf(fact_77_diff__sorted_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X1:A,X2:A,L1:(list @ A),L2:(list @ A)]: ((((((ord_less @ A) @ X1) @ X2) => ((((sorted1267110213sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((cons @ A) @ X1) @ (((sorted1267110213sorted @ A) @ L1) @ (((cons @ A) @ X2) @ L2))))) & ((~ ((((ord_less @ A) @ X1) @ X2))) => (((X1 = X2) => ((((sorted1267110213sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((sorted1267110213sorted @ A) @ L1) @ L2))) & ((X1 != X2) => ((((sorted1267110213sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((sorted1267110213sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ L2)))))))))))).
% 2.65/1.48 thf(fact_78_inter__sorted_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X1:A,X2:A,L1:(list @ A),L2:(list @ A)]: ((((((ord_less @ A) @ X1) @ X2) => ((((sorted2037043510sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((sorted2037043510sorted @ A) @ L1) @ (((cons @ A) @ X2) @ L2)))) & ((~ ((((ord_less @ A) @ X1) @ X2))) => (((X1 = X2) => ((((sorted2037043510sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((cons @ A) @ X1) @ (((sorted2037043510sorted @ A) @ L1) @ L2)))) & ((X1 != X2) => ((((sorted2037043510sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ (((cons @ A) @ X2) @ L2)) = (((sorted2037043510sorted @ A) @ (((cons @ A) @ X1) @ L1)) @ L2)))))))))))).
% 2.65/1.48 thf(fact_79_diff__sorted_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [V2:A,Va2:(list @ A)]: (((((sorted1267110213sorted @ A) @ (((cons @ A) @ V2) @ Va2)) @ (nil @ A)) = (((cons @ A) @ V2) @ Va2)))))))).
% 2.65/1.48 thf(fact_80_inter__sorted_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [V2:A,Va2:(list @ A)]: (((((sorted2037043510sorted @ A) @ (((cons @ A) @ V2) @ Va2)) @ (nil @ A)) = (nil @ A)))))))).
% 2.65/1.48 thf(fact_81_lexordp__eq_Oinducts, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X1:(list @ A),X2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp_eq @ A) @ X1) @ X2) => ((! [X12:(list @ A)]: (((P @ (nil @ A)) @ X12))) => ((! [X3:A,Y2:A,Xs2:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X3) @ Y2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((! [X3:A,Y2:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((~ ((((ord_less @ A) @ Y2) @ X3))) => ((((ord_lexordp_eq @ A) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2)))))))) => ((P @ X1) @ X2))))))))))).
% 2.65/1.48 thf(fact_82_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.65/1.48 thf(fact_83_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.65/1.48 thf(fact_84_merge__list_Oelims, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:(list @ (list @ A)),Xa:(list @ (list @ A)),Y:(list @ A)]: ((((((merge_list @ A) @ X) @ Xa) = Y) => (((X = (nil @ (list @ A))) => ((Xa = (nil @ (list @ A))) => (Y != (nil @ A)))) => (((X = (nil @ (list @ A))) => (! [L:(list @ A)]: (((Xa = (((cons @ (list @ A)) @ L) @ (nil @ (list @ A)))) => (Y != L))))) => ((! [La:(list @ A),Acc2:(list @ (list @ A))]: (((X = (((cons @ (list @ A)) @ La) @ Acc2)) => ((Xa = (nil @ (list @ A))) => (Y != (((merge_list @ A) @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ La) @ Acc2))))))) => ((! [La:(list @ A),Acc2:(list @ (list @ A))]: (((X = (((cons @ (list @ A)) @ La) @ Acc2)) => (! [L:(list @ A)]: (((Xa = (((cons @ (list @ A)) @ L) @ (nil @ (list @ A)))) => (Y != (((merge_list @ A) @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ L) @ (((cons @ (list @ A)) @ La) @ Acc2)))))))))) => (~ ((! [L12:(list @ A),L22:(list @ A),Ls:(list @ (list @ A))]: (((Xa = (((cons @ (list @ A)) @ L12) @ (((cons @ (list @ A)) @ L22) @ Ls))) => (Y != (((merge_list @ A) @ (((cons @ (list @ A)) @ (((merge @ A) @ L12) @ L22)) @ X)) @ Ls)))))))))))))))))).
% 2.65/1.48 thf(fact_85_combinatorial__product_Osimps_I1_J, axiom, (! [A:$tType]: ((((list_c659805718roduct @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.65/1.48 thf(fact_86_map__tailrec__rev_Oelims, axiom, (! [A:$tType,B:$tType,X:(A > B),Xa:(list @ A),Xb:(list @ B),Y:(list @ B)]: ((((((((map_tailrec_rev @ A) @ B) @ X) @ Xa) @ Xb) = Y) => (((Xa = (nil @ A)) => (Y != Xb)) => (~ ((! [A3:A,As:(list @ A)]: (((Xa = (((cons @ A) @ A3) @ As)) => (Y != (((((map_tailrec_rev @ A) @ B) @ X) @ As) @ (((cons @ B) @ (X @ A3)) @ Xb))))))))))))).
% 2.65/1.48 thf(fact_87_list__collect__set__map__simps_I2_J, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(B > (set @ A)),X:(C > B),A4:C]: ((((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ (((cons @ C) @ A4) @ (nil @ C)))) = (F2 @ (X @ A4)))))).
% 2.65/1.48 thf(fact_88_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F2:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F2) = (nil @ A))))).
% 2.65/1.48 thf(fact_89_splice_Osimps_I2_J, axiom, (! [A:$tType,V2:A,Va2:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ V2) @ Va2)) @ (nil @ A)) = (((cons @ A) @ V2) @ Va2))))).
% 2.65/1.48 thf(fact_90_Nil__is__map__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: ((((nil @ A) = ((((map @ B) @ A) @ F2) @ Xs)) = (Xs = (nil @ B)))))).
% 2.65/1.48 thf(fact_91_map__is__Nil__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: (((((((map @ B) @ A) @ F2) @ Xs) = (nil @ A)) = (Xs = (nil @ B)))))).
% 2.65/1.48 thf(fact_92_list_Omap__disc__iff, axiom, (! [B:$tType,A:$tType,F2:(A > B),A4:(list @ A)]: (((((((map @ A) @ B) @ F2) @ A4) = (nil @ B)) = (A4 = (nil @ A)))))).
% 2.65/1.48 thf(fact_93_splice__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((splice @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.65/1.48 thf(fact_94_map__eq__Cons__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),Y:A,Ys:(list @ A)]: (((((((map @ B) @ A) @ F2) @ Xs) = (((cons @ A) @ Y) @ Ys)) = (? [Z:B,Zs2:(list @ B)]: (((Xs = (((cons @ B) @ Z) @ Zs2)) & (((F2 @ Z) = Y) & (((((map @ B) @ A) @ F2) @ Zs2) = Ys))))))))).
% 2.65/1.48 thf(fact_95_Cons__eq__map__conv, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F2:(B > A),Ys:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F2) @ Ys)) = (? [Z:B,Zs2:(list @ B)]: (((Ys = (((cons @ B) @ Z) @ Zs2)) & ((X = (F2 @ Z)) & (Xs = ((((map @ B) @ A) @ F2) @ Zs2)))))))))).
% 2.65/1.48 thf(fact_96_map__eq__Cons__D, axiom, (! [B:$tType,A:$tType,F2:(B > A),Xs:(list @ B),Y:A,Ys:(list @ A)]: (((((((map @ B) @ A) @ F2) @ Xs) = (((cons @ A) @ Y) @ Ys)) => (? [Z2:B,Zs3:(list @ B)]: (((Xs = (((cons @ B) @ Z2) @ Zs3)) & (((F2 @ Z2) = Y) & (((((map @ B) @ A) @ F2) @ Zs3) = Ys))))))))).
% 2.65/1.48 thf(fact_97_Cons__eq__map__D, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F2:(B > A),Ys:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F2) @ Ys)) => (? [Z2:B,Zs3:(list @ B)]: (((Ys = (((cons @ B) @ Z2) @ Zs3)) & ((X = (F2 @ Z2)) & (Xs = ((((map @ B) @ A) @ F2) @ Zs3)))))))))).
% 2.65/1.48 thf(fact_98_map__eq__consE, axiom, (! [B:$tType,A:$tType,F2:(B > A),Ls2:(list @ B),Fa:A,Fl:(list @ A)]: (((((((map @ B) @ A) @ F2) @ Ls2) = (((cons @ A) @ Fa) @ Fl)) => (~ ((! [A3:B,L:(list @ B)]: (((Ls2 = (((cons @ B) @ A3) @ L)) => (((F2 @ A3) = Fa) => (((((map @ B) @ A) @ F2) @ L) != Fl))))))))))).
% 2.65/1.48 thf(fact_99_list_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),X21:A,X22:(list @ A)]: ((((((map @ A) @ B) @ F2) @ (((cons @ A) @ X21) @ X22)) = (((cons @ B) @ (F2 @ X21)) @ ((((map @ A) @ B) @ F2) @ X22)))))).
% 2.65/1.48 thf(fact_100_map__consI_I1_J, axiom, (! [A:$tType,B:$tType,W:(list @ A),F2:(B > A),Ww:(list @ B),A4:B]: (((W = ((((map @ B) @ A) @ F2) @ Ww)) => ((((cons @ A) @ (F2 @ A4)) @ W) = ((((map @ B) @ A) @ F2) @ (((cons @ B) @ A4) @ Ww))))))).
% 2.65/1.48 thf(fact_101_list_Osimps_I8_J, axiom, (! [A:$tType,B:$tType,F2:(A > B)]: ((((((map @ A) @ B) @ F2) @ (nil @ A)) = (nil @ B))))).
% 2.65/1.48 thf(fact_102_splice_Osimps_I3_J, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = (((cons @ A) @ X) @ (((cons @ A) @ Y) @ (((splice @ A) @ Xs) @ Ys))))))).
% 2.65/1.48 thf(fact_103_splice_Osimps_I1_J, axiom, (! [A:$tType,Ys:(list @ A)]: (((((splice @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.65/1.48 thf(fact_104_map__tailrec__rev_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,F2:(A > B),A4:A,As2:(list @ A),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F2) @ (((cons @ A) @ A4) @ As2)) @ Bs2) = (((((map_tailrec_rev @ A) @ B) @ F2) @ As2) @ (((cons @ B) @ (F2 @ A4)) @ Bs2)))))).
% 2.65/1.48 thf(fact_105_map__tailrec__rev_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,F2:(A > B),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F2) @ (nil @ A)) @ Bs2) = Bs2)))).
% 2.65/1.48 thf(fact_106_merge__list_Osimps_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((((merge_list @ A) @ (nil @ (list @ A))) @ (nil @ (list @ A))) = (nil @ A)))))).
% 2.65/1.48 thf(fact_107_merge__list_Osimps_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [L3:(list @ A)]: (((((merge_list @ A) @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ L3) @ (nil @ (list @ A)))) = L3))))))).
% 2.65/1.48 thf(fact_108_merge__list_Osimps_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [La2:(list @ A),Acc22:(list @ (list @ A))]: (((((merge_list @ A) @ (((cons @ (list @ A)) @ La2) @ Acc22)) @ (nil @ (list @ A))) = (((merge_list @ A) @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ La2) @ Acc22))))))))).
% 2.65/1.48 thf(fact_109_merge__list_Osimps_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [La2:(list @ A),Acc22:(list @ (list @ A)),L3:(list @ A)]: (((((merge_list @ A) @ (((cons @ (list @ A)) @ La2) @ Acc22)) @ (((cons @ (list @ A)) @ L3) @ (nil @ (list @ A)))) = (((merge_list @ A) @ (nil @ (list @ A))) @ (((cons @ (list @ A)) @ L3) @ (((cons @ (list @ A)) @ La2) @ Acc22)))))))))).
% 2.65/1.48 thf(fact_110_merge__list_Osimps_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Acc22:(list @ (list @ A)),L1:(list @ A),L2:(list @ A),Ls2:(list @ (list @ A))]: (((((merge_list @ A) @ Acc22) @ (((cons @ (list @ A)) @ L1) @ (((cons @ (list @ A)) @ L2) @ Ls2))) = (((merge_list @ A) @ (((cons @ (list @ A)) @ (((merge @ A) @ L1) @ L2)) @ Acc22)) @ Ls2)))))))).
% 2.65/1.48 thf(fact_111_splice_Oelims, axiom, (! [A:$tType,X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((splice @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != Xa)) => ((! [V:A,Va:(list @ A)]: (((X = (((cons @ A) @ V) @ Va)) => ((Xa = (nil @ A)) => (Y != (((cons @ A) @ V) @ Va)))))) => (~ ((! [X3:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X3) @ Xs2)) => (! [Y2:A,Ys2:(list @ A)]: (((Xa = (((cons @ A) @ Y2) @ Ys2)) => (Y != (((cons @ A) @ X3) @ (((cons @ A) @ Y2) @ (((splice @ A) @ Xs2) @ Ys2)))))))))))))))))).
% 2.65/1.48 thf(fact_112_map__eq__map__tailrec, axiom, (! [B:$tType,A:$tType]: ((((map @ A) @ B) = ((map_tailrec @ A) @ B))))).
% 2.65/1.48 thf(fact_113_list__collect__set__map__simps_I1_J, axiom, (! [C:$tType,B:$tType,A:$tType,F2:(B > (set @ A)),X:(C > B)]: ((((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ (nil @ C))) = (bot_bot @ (set @ A)))))).
% 2.65/1.48 thf(fact_114_list__collect__set__map__simps_I3_J, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(B > (set @ A)),X:(C > B),A4:C,L3:(list @ C)]: ((((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ (((cons @ C) @ A4) @ L3))) = (((sup_sup @ (set @ A)) @ (F2 @ (X @ A4))) @ ((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ L3))))))).
% 2.65/1.48 thf(fact_115_listrelp_Oinducts, axiom, (! [A:$tType,B:$tType,R4:(A > (B > $o)),X1:(list @ A),X2:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((((((listrelp @ A) @ B) @ R4) @ X1) @ X2) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X3:A,Y2:B,Xs2:(list @ A),Ys2:(list @ B)]: ((((R4 @ X3) @ Y2) => ((((((listrelp @ A) @ B) @ R4) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X3) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2))))))) => ((P @ X1) @ X2))))))).
% 2.65/1.48 thf(fact_116_listrelp_Osimps, axiom, (! [B:$tType,A:$tType]: ((((listrelp @ A) @ B) = (^ [R5:(A > (B > $o)),A12:(list @ A),A22:(list @ B)]: ((((A12 = (nil @ A)) & (A22 = (nil @ B))) | (? [X4:A,Y3:B,Xs3:(list @ A),Ys3:(list @ B)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A22 = (((cons @ B) @ Y3) @ Ys3)) & (((R5 @ X4) @ Y3) & (((((listrelp @ A) @ B) @ R5) @ Xs3) @ Ys3))))))))))))).
% 2.65/1.48 thf(fact_117_listrelp_Ocases, axiom, (! [A:$tType,B:$tType,R4:(A > (B > $o)),A1:(list @ A),A2:(list @ B)]: (((((((listrelp @ A) @ B) @ R4) @ A1) @ A2) => (((A1 = (nil @ A)) => (A2 != (nil @ B))) => (~ ((! [X3:A,Y2:B,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X3) @ Xs2)) => (! [Ys2:(list @ B)]: (((A2 = (((cons @ B) @ Y2) @ Ys2)) => (((R4 @ X3) @ Y2) => (~ ((((((listrelp @ A) @ B) @ R4) @ Xs2) @ Ys2))))))))))))))))).
% 2.65/1.48 thf(fact_118_list__collect__set__simps_I1_J, axiom, (! [B:$tType,A:$tType,F2:(B > (set @ A))]: ((((((list_collect_set @ B) @ A) @ F2) @ (nil @ B)) = (bot_bot @ (set @ A)))))).
% 2.65/1.48 thf(fact_119_list__collect__set__simps_I3_J, axiom, (! [A:$tType,B:$tType,F2:(B > (set @ A)),A4:B,L3:(list @ B)]: ((((((list_collect_set @ B) @ A) @ F2) @ (((cons @ B) @ A4) @ L3)) = (((sup_sup @ (set @ A)) @ (F2 @ A4)) @ ((((list_collect_set @ B) @ A) @ F2) @ L3)))))).
% 2.65/1.48 thf(fact_120_set__notEmptyE, axiom, (! [A:$tType,S:(set @ A)]: (((S != (bot_bot @ (set @ A))) => (~ ((! [X3:A]: ((~ ((((member @ A) @ X3) @ S))))))))))).
% 2.65/1.48 thf(fact_121_memb__imp__not__empty, axiom, (! [A:$tType,X:A,S:(set @ A)]: (((((member @ A) @ X) @ S) => (S != (bot_bot @ (set @ A))))))).
% 2.65/1.48 thf(fact_122_listrelp_OCons, axiom, (! [A:$tType,B:$tType,R4:(A > (B > $o)),X:A,Y:B,Xs:(list @ A),Ys:(list @ B)]: ((((R4 @ X) @ Y) => ((((((listrelp @ A) @ B) @ R4) @ Xs) @ Ys) => (((((listrelp @ A) @ B) @ R4) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ B) @ Y) @ Ys))))))).
% 2.65/1.48 thf(fact_123_listrelp_ONil, axiom, (! [A:$tType,B:$tType,R4:(A > (B > $o))]: ((((((listrelp @ A) @ B) @ R4) @ (nil @ A)) @ (nil @ B))))).
% 2.65/1.48 thf(fact_124_Un__empty, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A5) @ B4) = (bot_bot @ (set @ A))) = ((A5 = (bot_bot @ (set @ A))) & (B4 = (bot_bot @ (set @ A)))))))).
% 2.65/1.48 thf(fact_125_sup__bot_Oright__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ A4) @ (bot_bot @ A)) = A4))))))).
% 2.65/1.48 thf(fact_126_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: ((((bounde1808546759up_bot @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A4) = A4))))))).
% 2.65/1.48 thf(fact_127_sup__eq__bot__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.65/1.48 thf(fact_128_empty__iff, axiom, (! [A:$tType,C2:A]: ((~ ((((member @ A) @ C2) @ (bot_bot @ (set @ A)))))))).
% 2.65/1.48 thf(fact_129_all__not__in__conv, axiom, (! [A:$tType,A5:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A5))))) = (A5 = (bot_bot @ (set @ A))))))).
% 2.65/1.48 thf(fact_130_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.65/1.48 thf(fact_131_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 2.65/1.48 thf(fact_132_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X4:A]: ((((sup_sup @ B) @ (F3 @ X4)) @ (G2 @ X4))))))))).
% 2.65/1.48 thf(fact_133_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ A4) @ A4) = A4))))))).
% 2.65/1.48 thf(fact_134_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 2.65/1.48 thf(fact_135_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ A4) @ B3)) = (((sup_sup @ A) @ A4) @ B3)))))))).
% 2.65/1.48 thf(fact_136_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.65/1.48 thf(fact_137_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B3)) @ B3) = (((sup_sup @ A) @ A4) @ B3)))))))).
% 2.65/1.48 thf(fact_138_UnCI, axiom, (! [A:$tType,C2:A,B4:(set @ A),A5:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B4))) => (((member @ A) @ C2) @ A5)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.65/1.48 thf(fact_139_Un__iff, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) = ((((member @ A) @ C2) @ A5) | (((member @ A) @ C2) @ B4)))))).
% 2.65/1.48 thf(fact_140_bot__eq__sup__iff, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.65/1.48 thf(fact_141_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.65/1.48 thf(fact_142_emptyE, axiom, (! [A:$tType,A4:A]: ((~ ((((member @ A) @ A4) @ (bot_bot @ (set @ A)))))))).
% 2.65/1.48 thf(fact_143_equals0D, axiom, (! [A:$tType,A5:(set @ A),A4:A]: (((A5 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A4) @ A5))))))).
% 2.65/1.48 thf(fact_144_equals0I, axiom, (! [A:$tType,A5:(set @ A)]: (((! [Y2:A]: ((~ ((((member @ A) @ Y2) @ A5))))) => (A5 = (bot_bot @ (set @ A))))))).
% 2.65/1.48 thf(fact_145_ex__in__conv, axiom, (! [A:$tType,A5:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ A5))) = (A5 != (bot_bot @ (set @ A))))))).
% 2.65/1.48 thf(fact_146_not__psubset__empty, axiom, (! [A:$tType,A5:(set @ A)]: ((~ ((((ord_less @ (set @ A)) @ A5) @ (bot_bot @ (set @ A)))))))).
% 2.65/1.48 thf(fact_147_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.65/1.48 thf(fact_148_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z3)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z3))))))))).
% 2.65/1.48 thf(fact_149_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z3) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z3))))))))).
% 2.65/1.48 thf(fact_150_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X4:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X4)))))))).
% 2.65/1.48 thf(fact_151_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F3:(A > B),G2:(A > B),X4:A]: ((((sup_sup @ B) @ (F3 @ X4)) @ (G2 @ X4))))))))).
% 2.65/1.48 thf(fact_152_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B3)) @ C2) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B3) @ C2))))))))).
% 2.65/1.48 thf(fact_153_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z3) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z3))))))))).
% 2.65/1.48 thf(fact_154_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A6:A,B5:A]: ((((sup_sup @ A) @ B5) @ A6)))))))).
% 2.65/1.48 thf(fact_155_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X4:A,Y3:A]: ((((sup_sup @ A) @ Y3) @ X4)))))))).
% 2.65/1.48 thf(fact_156_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,A4:A,C2:A]: (((((sup_sup @ A) @ B3) @ (((sup_sup @ A) @ A4) @ C2)) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B3) @ C2))))))))).
% 2.65/1.48 thf(fact_157_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z3)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z3))))))))).
% 2.65/1.48 thf(fact_158_UnE, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) => ((~ ((((member @ A) @ C2) @ A5))) => (((member @ A) @ C2) @ B4)))))).
% 2.65/1.48 thf(fact_159_UnI1, axiom, (! [A:$tType,C2:A,A5:(set @ A),B4:(set @ A)]: (((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.65/1.48 thf(fact_160_UnI2, axiom, (! [A:$tType,C2:A,B4:(set @ A),A5:(set @ A)]: (((((member @ A) @ C2) @ B4) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A5) @ B4)))))).
% 2.65/1.48 thf(fact_161_bex__Un, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) & (P @ X4)))) = ((? [X4:A]: (((((member @ A) @ X4) @ A5) & (P @ X4)))) | (? [X4:A]: (((((member @ A) @ X4) @ B4) & (P @ X4))))))))).
% 2.65/1.48 thf(fact_162_ball__Un, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),P:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) => (P @ X4)))) = ((! [X4:A]: (((((member @ A) @ X4) @ A5) => (P @ X4)))) & (! [X4:A]: (((((member @ A) @ X4) @ B4) => (P @ X4))))))))).
% 2.65/1.48 thf(fact_163_Un__assoc, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) @ C3) = (((sup_sup @ (set @ A)) @ A5) @ (((sup_sup @ (set @ A)) @ B4) @ C3)))))).
% 2.65/1.48 thf(fact_164_Un__absorb, axiom, (! [A:$tType,A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ A5) = A5)))).
% 2.65/1.48 thf(fact_165_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((((sup_sup @ (set @ A)) @ B6) @ A7))))))).
% 2.65/1.48 thf(fact_166_Un__left__absorb, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (((sup_sup @ (set @ A)) @ A5) @ B4)) = (((sup_sup @ (set @ A)) @ A5) @ B4))))).
% 2.65/1.48 thf(fact_167_Un__left__commute, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (((sup_sup @ (set @ A)) @ B4) @ C3)) = (((sup_sup @ (set @ A)) @ B4) @ (((sup_sup @ (set @ A)) @ A5) @ C3)))))).
% 2.65/1.48 thf(fact_168_sup_Ostrict__coboundedI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,B3:A,A4:A]: (((((ord_less @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A4) @ B3))))))))).
% 2.65/1.48 thf(fact_169_sup_Ostrict__coboundedI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [C2:A,A4:A,B3:A]: (((((ord_less @ A) @ C2) @ A4) => (((ord_less @ A) @ C2) @ (((sup_sup @ A) @ A4) @ B3))))))))).
% 2.65/1.48 thf(fact_170_sup_Ostrict__order__iff, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [B5:A,A6:A]: (((A6 = (((sup_sup @ A) @ A6) @ B5)) & (A6 != B5))))))))).
% 2.65/1.48 thf(fact_171_sup_Ostrict__boundedE, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B3:A,C2:A,A4:A]: (((((ord_less @ A) @ (((sup_sup @ A) @ B3) @ C2)) @ A4) => (~ (((((ord_less @ A) @ B3) @ A4) => (~ ((((ord_less @ A) @ C2) @ A4))))))))))))).
% 2.65/1.48 thf(fact_172_less__supI2, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,B3:A,A4:A]: (((((ord_less @ A) @ X) @ B3) => (((ord_less @ A) @ X) @ (((sup_sup @ A) @ A4) @ B3))))))))).
% 2.65/1.48 thf(fact_173_less__supI1, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,A4:A,B3:A]: (((((ord_less @ A) @ X) @ A4) => (((ord_less @ A) @ X) @ (((sup_sup @ A) @ A4) @ B3))))))))).
% 2.65/1.48 thf(fact_174_sup__bot__left, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 2.65/1.48 thf(fact_175_sup__bot__right, axiom, (! [A:$tType]: ((((bounded_lattice_bot @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 2.65/1.48 thf(fact_176_Un__empty__left, axiom, (! [A:$tType,B4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B4) = B4)))).
% 2.65/1.48 thf(fact_177_Un__empty__right, axiom, (! [A:$tType,A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A5) @ (bot_bot @ (set @ A))) = A5)))).
% 2.65/1.48 thf(fact_178_bot__apply, axiom, (! [C:$tType,D:$tType]: ((((bot @ C) @ (type2 @ C)) => ((bot_bot @ (D > C)) = (^ [X4:D]: ((bot_bot @ C)))))))).
% 2.65/1.48 thf(fact_179_bot_Onot__eq__extremum, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A4:A]: (((A4 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A4)))))))).
% 2.65/1.48 thf(fact_180_bot_Oextremum__strict, axiom, (! [A:$tType]: ((((order_bot @ A) @ (type2 @ A)) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ (bot_bot @ A)))))))))).
% 2.65/1.48 thf(fact_181_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A7:(set @ A)]: ((A7 = (bot_bot @ (set @ A))))))))).
% 2.65/1.48 thf(fact_182_psubset__trans, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C3:(set @ A)]: (((((ord_less @ (set @ A)) @ A5) @ B4) => ((((ord_less @ (set @ A)) @ B4) @ C3) => (((ord_less @ (set @ A)) @ A5) @ C3)))))).
% 2.65/1.48 thf(fact_183_psubsetD, axiom, (! [A:$tType,A5:(set @ A),B4:(set @ A),C2:A]: (((((ord_less @ (set @ A)) @ A5) @ B4) => ((((member @ A) @ C2) @ A5) => (((member @ A) @ C2) @ B4)))))).
% 2.65/1.48 thf(fact_184_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (A4 != B3)))))))).
% 2.65/1.48 thf(fact_185_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (A4 != B3)))))))).
% 2.65/1.48 thf(fact_186_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 2.65/1.48 thf(fact_187_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A,C2:A]: (((((ord_less @ A) @ B3) @ A4) => ((((ord_less @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A4))))))))).
% 2.65/1.48 thf(fact_188_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.65/1.48 thf(fact_189_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.65/1.48 thf(fact_190_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))))))).
% 2.65/1.48 thf(fact_191_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.65/1.48 thf(fact_192_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 2.65/1.48 thf(fact_193_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 2.65/1.48 thf(fact_194_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 2.65/1.48 thf(fact_195_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A4:A]: (((! [X3:A]: (((! [Y4:A]: (((((ord_less @ A) @ Y4) @ X3) => (P @ Y4)))) => (P @ X3)))) => (P @ A4)))))))).
% 2.65/1.48 thf(fact_196_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.65/1.48 thf(fact_197_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.65/1.48 thf(fact_198_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (~ ((((ord_less @ A) @ A4) @ B3)))))))))).
% 2.65/1.48 thf(fact_199_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => ((B3 = C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.65/1.48 thf(fact_200_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C2:A]: (((A4 = B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.65/1.48 thf(fact_201_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 2.65/1.48 thf(fact_202_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.65/1.48 thf(fact_203_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z3:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X) @ Z3))))))))).
% 2.65/1.48 thf(fact_204_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (~ ((((ord_less @ A) @ B3) @ A4)))))))))).
% 2.65/1.48 thf(fact_205_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.65/1.48 thf(fact_206_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.65/1.48 thf(fact_207_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z2:A]: (((((ord_less @ A) @ X) @ Z2) & (((ord_less @ A) @ Z2) @ Y))))))))))).
% 2.65/1.48 thf(fact_208_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (~ ((((ord_less @ A) @ B3) @ A4)))))))))).
% 2.65/1.48 thf(fact_209_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.65/1.48 thf(fact_210_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.65/1.48 thf(fact_211_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X12:A]: ((((ord_less @ A) @ X) @ X12))))))))).
% 2.65/1.48 thf(fact_212_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X))))))))).
% 2.65/1.48 thf(fact_213_order__less__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F2:(A > C),C2:C]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ C) @ (F2 @ B3)) @ C2) => ((! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less @ C) @ (F2 @ X3)) @ (F2 @ Y2))))) => (((ord_less @ C) @ (F2 @ A4)) @ C2)))))))))).
% 2.65/1.48 thf(fact_214_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F2:(B > A),B3:B,C2:B]: (((((ord_less @ A) @ A4) @ (F2 @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X3:B,Y2:B]: (((((ord_less @ B) @ X3) @ Y2) => (((ord_less @ A) @ (F2 @ X3)) @ (F2 @ Y2))))) => (((ord_less @ A) @ A4) @ (F2 @ C2))))))))))).
% 2.65/1.48 thf(fact_215_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F2:(A > B),C2:B]: (((((ord_less @ A) @ A4) @ B3) => (((F2 @ B3) = C2) => ((! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less @ B) @ (F2 @ X3)) @ (F2 @ Y2))))) => (((ord_less @ B) @ (F2 @ A4)) @ C2)))))))))).
% 2.65/1.48 thf(fact_216_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,F2:(B > A),B3:B,C2:B]: (((A4 = (F2 @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X3:B,Y2:B]: (((((ord_less @ B) @ X3) @ Y2) => (((ord_less @ A) @ (F2 @ X3)) @ (F2 @ Y2))))) => (((ord_less @ A) @ A4) @ (F2 @ C2))))))))))).
% 2.65/1.48 thf(fact_217_bot__fun__def, axiom, (! [B:$tType,A:$tType]: ((((bot @ B) @ (type2 @ B)) => ((bot_bot @ (A > B)) = (^ [X4:A]: ((bot_bot @ B)))))))).
% 2.65/1.48 thf(fact_218_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 2.65/1.48 thf(fact_219_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.65/1.48 thf(fact_220_map__tailrec__def, axiom, (! [B:$tType,A:$tType]: ((((map_tailrec @ A) @ B) = (^ [F3:(A > B),As3:(list @ A)]: (((rev @ B) @ (((((map_tailrec_rev @ A) @ B) @ F3) @ As3) @ (nil @ B))))))))).
% 2.65/1.48 thf(fact_221_rev__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((rev @ A) @ Xs) = ((rev @ A) @ Ys)) = (Xs = Ys))))).
% 2.65/1.48 thf(fact_222_rev__rev__ident, axiom, (! [A:$tType,Xs:(list @ A)]: ((((rev @ A) @ ((rev @ A) @ Xs)) = Xs)))).
% 2.65/1.48 thf(fact_223_rev__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rev @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.65/1.48 thf(fact_224_Nil__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((rev @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.65/1.48 thf(fact_225_singleton__rev__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((((cons @ A) @ X) @ (nil @ A)) = ((rev @ A) @ Xs)) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.65/1.48 thf(fact_226_rev__singleton__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((((rev @ A) @ Xs) = (((cons @ A) @ X) @ (nil @ A))) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.65/1.48 thf(fact_227_rev_Osimps_I1_J, axiom, (! [A:$tType]: ((((rev @ A) @ (nil @ A)) = (nil @ A))))).
% 2.65/1.48 thf(fact_228_rev__map, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: ((((rev @ A) @ ((((map @ B) @ A) @ F2) @ Xs)) = ((((map @ B) @ A) @ F2) @ ((rev @ B) @ Xs)))))).
% 2.65/1.48 thf(fact_229_rev__swap, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((rev @ A) @ Xs) = Ys) = (Xs = ((rev @ A) @ Ys)))))).
% 2.65/1.48 thf(fact_230_list__collect__set__map__simps_I4_J, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(B > (set @ A)),X:(C > B),L3:(list @ C),L4:(list @ C)]: ((((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ (((append @ C) @ L3) @ L4))) = (((sup_sup @ (set @ A)) @ ((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ L3))) @ ((((list_collect_set @ B) @ A) @ F2) @ ((((map @ C) @ B) @ X) @ L4))))))).
% 2.65/1.48 thf(fact_231_sorted__list__of__set__empty, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (((linord467138063of_set @ A) @ (bot_bot @ (set @ A))) = (nil @ A)))))).
% 2.65/1.48 thf(fact_232_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs)))))).
% 2.65/1.48 thf(fact_233_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys = Zs))))).
% 2.65/1.48 thf(fact_234_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs)) = (Ys = Zs))))).
% 2.65/1.48 thf(fact_235_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.65/1.48 thf(fact_236_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.65/1.48 thf(fact_237_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.65/1.48 thf(fact_238_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.65/1.48 thf(fact_239_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.65/1.48 thf(fact_240_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.65/1.48 thf(fact_241_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.65/1.48 thf(fact_242_map__append, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),Ys:(list @ B)]: ((((((map @ B) @ A) @ F2) @ (((append @ B) @ Xs) @ Ys)) = (((append @ A) @ ((((map @ B) @ A) @ F2) @ Xs)) @ ((((map @ B) @ A) @ F2) @ Ys)))))).
% 2.65/1.48 thf(fact_243_rev__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((rev @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((rev @ A) @ Ys)) @ ((rev @ A) @ Xs)))))).
% 2.65/1.48 thf(fact_244_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.65/1.48 thf(fact_245_list__ee__eq__leel_I1_J, axiom, (! [A:$tType,E1:A,E2:A,L1:(list @ A),E12:A,E22:A,L2:(list @ A)]: ((((((cons @ A) @ E1) @ (((cons @ A) @ E2) @ (nil @ A))) = (((append @ A) @ L1) @ (((cons @ A) @ E12) @ (((cons @ A) @ E22) @ L2)))) = ((L1 = (nil @ A)) & ((E1 = E12) & ((E2 = E22) & (L2 = (nil @ A))))))))).
% 2.65/1.48 thf(fact_246_list__ee__eq__leel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E12:A,E22:A,L2:(list @ A),E1:A,E2:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E12) @ (((cons @ A) @ E22) @ L2))) = (((cons @ A) @ E1) @ (((cons @ A) @ E2) @ (nil @ A)))) = ((L1 = (nil @ A)) & ((E1 = E12) & ((E2 = E22) & (L2 = (nil @ A))))))))).
% 2.65/1.48 thf(fact_247_list__se__match_I1_J, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),A4:A]: (((L1 != (nil @ A)) => (((((append @ A) @ L1) @ L2) = (((cons @ A) @ A4) @ (nil @ A))) = ((L1 = (((cons @ A) @ A4) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.65/1.48 thf(fact_248_list__se__match_I2_J, axiom, (! [A:$tType,L2:(list @ A),L1:(list @ A),A4:A]: (((L2 != (nil @ A)) => (((((append @ A) @ L1) @ L2) = (((cons @ A) @ A4) @ (nil @ A))) = ((L1 = (nil @ A)) & (L2 = (((cons @ A) @ A4) @ (nil @ A))))))))).
% 2.65/1.48 thf(fact_249_list__se__match_I3_J, axiom, (! [A:$tType,L1:(list @ A),A4:A,L2:(list @ A)]: (((L1 != (nil @ A)) => (((((cons @ A) @ A4) @ (nil @ A)) = (((append @ A) @ L1) @ L2)) = ((L1 = (((cons @ A) @ A4) @ (nil @ A))) & (L2 = (nil @ A)))))))).
% 2.65/1.48 thf(fact_250_list__se__match_I4_J, axiom, (! [A:$tType,L2:(list @ A),A4:A,L1:(list @ A)]: (((L2 != (nil @ A)) => (((((cons @ A) @ A4) @ (nil @ A)) = (((append @ A) @ L1) @ L2)) = ((L1 = (nil @ A)) & (L2 = (((cons @ A) @ A4) @ (nil @ A))))))))).
% 2.65/1.48 thf(fact_251_list__e__eq__lel_I1_J, axiom, (! [A:$tType,E3:A,L1:(list @ A),E4:A,L2:(list @ A)]: ((((((cons @ A) @ E3) @ (nil @ A)) = (((append @ A) @ L1) @ (((cons @ A) @ E4) @ L2))) = ((L1 = (nil @ A)) & ((E4 = E3) & (L2 = (nil @ A)))))))).
% 2.65/1.48 thf(fact_252_list__e__eq__lel_I2_J, axiom, (! [A:$tType,L1:(list @ A),E4:A,L2:(list @ A),E3:A]: ((((((append @ A) @ L1) @ (((cons @ A) @ E4) @ L2)) = (((cons @ A) @ E3) @ (nil @ A))) = ((L1 = (nil @ A)) & ((E4 = E3) & (L2 = (nil @ A)))))))).
% 2.65/1.48 thf(fact_253_list__collect__set__simps_I4_J, axiom, (! [A:$tType,B:$tType,F2:(B > (set @ A)),L3:(list @ B),L4:(list @ B)]: ((((((list_collect_set @ B) @ A) @ F2) @ (((append @ B) @ L3) @ L4)) = (((sup_sup @ (set @ A)) @ ((((list_collect_set @ B) @ A) @ F2) @ L3)) @ ((((list_collect_set @ B) @ A) @ F2) @ L4)))))).
% 2.65/1.48 thf(fact_254_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F2:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F2) = (((append @ A) @ (F2 @ X)) @ ((((bind @ B) @ A) @ Xs) @ F2)))))).
% 2.65/1.48 thf(subcl_Orderings_Olinorder___HOL_Otype, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((type @ A) @ (type2 @ A)))))).
% 2.65/1.48 thf(subcl_Orderings_Olinorder___Orderings_Oord, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord @ A) @ (type2 @ A)))))).
% 2.65/1.48 thf(subcl_Orderings_Olinorder___Orderings_Oorder, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((order @ A) @ (type2 @ A)))))).
% 2.65/1.48 thf(subcl_Orderings_Olinorder___Orderings_Opreorder, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((preorder @ A) @ (type2 @ A)))))).
% 2.65/1.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: (((bounded_lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounde1808546759up_bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Lattices_Obounded__lattice__bot, axiom, (! [A8:$tType,A9:$tType]: ((((bounded_lattice @ A9) @ (type2 @ A9)) => ((bounded_lattice_bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_sup @ A9) @ (type2 @ A9)) => ((semilattice_sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A8:$tType,A9:$tType]: ((((order_bot @ A9) @ (type2 @ A9)) => ((order_bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Lattices_Olattice, axiom, (! [A8:$tType,A9:$tType]: ((((lattice @ A9) @ (type2 @ A9)) => ((lattice @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: ((((bot @ A9) @ (type2 @ A9)) => ((bot @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.65/1.48 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3, axiom, (! [A8:$tType]: (((bounde1808546759up_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_4, axiom, (! [A8:$tType]: (((bounded_lattice_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_5, axiom, (! [A8:$tType]: (((semilattice_sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Orderings_Oorder__bot_6, axiom, (! [A8:$tType]: (((order_bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Orderings_Opreorder_7, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Lattices_Olattice_8, axiom, (! [A8:$tType]: (((lattice @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Orderings_Oorder_9, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Orderings_Oord_10, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_Set_Oset___Orderings_Obot_11, axiom, (! [A8:$tType]: (((bot @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.65/1.48 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, axiom, ((bounde1808546759up_bot @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_13, axiom, ((bounded_lattice_bot @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_14, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15, axiom, ((order_bot @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Orderings_Opreorder_16, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Lattices_Olattice_17, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Orderings_Oorder_18, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Orderings_Oord_19, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tcon_HOL_Obool___Orderings_Obot_20, axiom, ((bot @ $o) @ (type2 @ $o))).
% 2.65/1.48 thf(tfree_0, hypothesis, ((linorder @ a) @ (type2 @ a))).
% 2.65/1.48 thf(conj_0, conjecture, (((((cons @ a) @ x1) @ l1) = l2a) = ((((sorted1061247458sorted @ a) @ (((cons @ a) @ x1) @ l1)) @ l2a) & (((sorted1061247458sorted @ a) @ l2a) @ (((cons @ a) @ x1) @ l1))))).
% 2.65/1.48 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2DTF2830.p
% 2.65/1.48 ------------------------
% 2.86/1.52 ---- Cleaned THF ---
% 2.86/1.52 thf(ty_t_List_Olist,type,
% 2.86/1.52 list: $tType > $tType ).
% 2.86/1.52
% 2.86/1.52 thf(ty_t_Set_Oset,type,
% 2.86/1.52 set: $tType > $tType ).
% 2.86/1.52
% 2.86/1.52 thf(ty_t_itself,type,
% 2.86/1.52 itself: $tType > $tType ).
% 2.86/1.52
% 2.86/1.52 thf(ty_tf_a,type,
% 2.86/1.52 a: $tType ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.86/1.52 bounded_lattice:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_HOL_Otype,type,
% 2.86/1.52 type:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Obot,type,
% 2.86/1.52 bot:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Oord,type,
% 2.86/1.52 ord:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Oorder,type,
% 2.86/1.52 order:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Lattices_Olattice,type,
% 2.86/1.52 lattice:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Ono__bot,type,
% 2.86/1.52 no_bot:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Ono__top,type,
% 2.86/1.52 no_top:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Olinorder,type,
% 2.86/1.52 linorder:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Opreorder,type,
% 2.86/1.52 preorder:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.86/1.52 order_bot:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Owellorder,type,
% 2.86/1.52 wellorder:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Orderings_Odense__order,type,
% 2.86/1.52 dense_order:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.86/1.52 semilattice_sup:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Lattices_Obounded__lattice__bot,type,
% 2.86/1.52 bounded_lattice_bot:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.86/1.52 bounde1808546759up_bot:
% 2.86/1.52 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 2.86/1.52 bNF_Greatest_shift:
% 2.86/1.52 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.86/1.52 sup_sup:
% 2.86/1.52 !>[A: $tType] : ( A > A > A ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Oappend,type,
% 2.86/1.52 append:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Obind,type,
% 2.86/1.52 bind:
% 2.86/1.52 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Oinsert,type,
% 2.86/1.52 insert:
% 2.86/1.52 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set,type,
% 2.86/1.52 linord467138063of_set:
% 2.86/1.52 !>[A: $tType] : ( ( set @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Olist_OCons,type,
% 2.86/1.52 cons:
% 2.86/1.52 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Olist_ONil,type,
% 2.86/1.52 nil:
% 2.86/1.52 !>[A: $tType] : ( list @ A ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Olist_Omap,type,
% 2.86/1.52 map:
% 2.86/1.52 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Olist__ex1,type,
% 2.86/1.52 list_ex1:
% 2.86/1.52 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Olistrelp,type,
% 2.86/1.52 listrelp:
% 2.86/1.52 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Omap__tailrec,type,
% 2.86/1.52 map_tailrec:
% 2.86/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Omap__tailrec__rev,type,
% 2.86/1.52 map_tailrec_rev:
% 2.86/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Oord_Olexordp__eq,type,
% 2.86/1.52 lexordp_eq:
% 2.86/1.52 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 2.86/1.52 ord_lexordp_eq:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Oproduct__lists,type,
% 2.86/1.52 product_lists:
% 2.86/1.52 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Orev,type,
% 2.86/1.52 rev:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Osplice,type,
% 2.86/1.52 splice:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List_Osublists,type,
% 2.86/1.52 sublists:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_List__More_Ocombinatorial__product,type,
% 2.86/1.52 list_c659805718roduct:
% 2.86/1.52 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Misc_Olist__collect__set,type,
% 2.86/1.52 list_collect_set:
% 2.86/1.52 !>[B: $tType,A: $tType] : ( ( B > ( set @ A ) ) > ( list @ B ) > ( set @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Misc_Omerge,type,
% 2.86/1.52 merge:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Misc_Omerge__list,type,
% 2.86/1.52 merge_list:
% 2.86/1.52 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Misc_Orevg,type,
% 2.86/1.52 revg:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.86/1.52 bot_bot:
% 2.86/1.52 !>[A: $tType] : A ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.86/1.52 ord_less:
% 2.86/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Pure_Otype,type,
% 2.86/1.52 type2:
% 2.86/1.52 !>[A: $tType] : ( itself @ A ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Set_OCollect,type,
% 2.86/1.52 collect:
% 2.86/1.52 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Set_Ois__empty,type,
% 2.86/1.52 is_empty:
% 2.86/1.52 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Odiff__sorted,type,
% 2.86/1.52 sorted1267110213sorted:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Ointer__sorted,type,
% 2.86/1.52 sorted2037043510sorted:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_Sorted__List__Operations__Mirabelle__fineeiboro_Osubset__sorted,type,
% 2.86/1.52 sorted1061247458sorted:
% 2.86/1.52 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_c_member,type,
% 2.86/1.52 member:
% 2.86/1.52 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.86/1.52
% 2.86/1.52 thf(sy_v_l1_H____,type,
% 2.86/1.52 l1: list @ a ).
% 2.86/1.52
% 2.86/1.52 thf(sy_v_l2a____,type,
% 2.86/1.52 l2a: list @ a ).
% 2.86/1.52
% 2.86/1.52 thf(sy_v_x1____,type,
% 2.86/1.52 x1: a ).
% 2.86/1.52
% 2.86/1.52 thf(fact_0_local_ONil,axiom,
% 2.86/1.52 ( l2a
% 2.86/1.52 = ( nil @ a ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_1_ind__hyp,axiom,
% 2.86/1.52 ! [L2: list @ a] :
% 2.86/1.52 ( ( l1 = L2 )
% 2.86/1.52 = ( ( sorted1061247458sorted @ a @ l1 @ L2 )
% 2.86/1.52 & ( sorted1061247458sorted @ a @ L2 @ l1 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_2_subset__sorted_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X1: A,L1: list @ A] :
% 2.86/1.52 ~ ( sorted1061247458sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_3_list_Oinject,axiom,
% 2.86/1.52 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.86/1.52 ( ( ( cons @ A @ X21 @ X22 )
% 2.86/1.52 = ( cons @ A @ Y21 @ Y22 ) )
% 2.86/1.52 = ( ( X21 = Y21 )
% 2.86/1.52 & ( X22 = Y22 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_4_subset__sorted_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [L2: list @ A] : ( sorted1061247458sorted @ A @ ( nil @ A ) @ L2 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_5_not__Cons__self2,axiom,
% 2.86/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.86/1.52 ( ( cons @ A @ X @ Xs )
% 2.86/1.52 != Xs ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_6_list__tail__coinc,axiom,
% 2.86/1.52 ! [A: $tType,N1: A,R1: list @ A,N2: A,R2: list @ A] :
% 2.86/1.52 ( ( ( cons @ A @ N1 @ R1 )
% 2.86/1.52 = ( cons @ A @ N2 @ R2 ) )
% 2.86/1.52 => ( ( N1 = N2 )
% 2.86/1.52 & ( R1 = R2 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_7_subset__sorted_Osimps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X1: A,L1: list @ A,X2: A,L2: list @ A] :
% 2.86/1.52 ( ( sorted1061247458sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( ~ ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( ( X1 = X2 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ L1 @ L2 ) )
% 2.86/1.52 & ( ( X1 != X2 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_8_shift__def,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( bNF_Greatest_shift @ A @ B )
% 2.86/1.52 = ( ^ [Lab: ( list @ A ) > B,K: A,Kl: list @ A] : ( Lab @ ( cons @ A @ K @ Kl ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_9_subset__sorted_Oelims_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A,Xa: list @ A] :
% 2.86/1.52 ( ~ ( sorted1061247458sorted @ A @ X @ Xa )
% 2.86/1.52 => ( ( ? [X12: A,L12: list @ A] :
% 2.86/1.52 ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ( Xa
% 2.86/1.52 != ( nil @ A ) ) )
% 2.86/1.52 => ~ ! [X12: A,L12: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ! [X23: A,L22: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ X23 @ L22 ) )
% 2.86/1.52 => ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( ( X12 = X23 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ L12 @ L22 ) )
% 2.86/1.52 & ( ( X12 != X23 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_10_subset__sorted_Oelims_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A,Xa: list @ A] :
% 2.86/1.52 ( ( sorted1061247458sorted @ A @ X @ Xa )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ! [L22: list @ A] : ( Xa != L22 ) )
% 2.86/1.52 => ~ ! [X12: A,L12: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ! [X23: A,L22: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ X23 @ L22 ) )
% 2.86/1.52 => ~ ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( ( X12 = X23 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ L12 @ L22 ) )
% 2.86/1.52 & ( ( X12 != X23 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_11_subset__sorted_Oelims_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A,Xa: list @ A,Y: $o] :
% 2.86/1.52 ( ( ( sorted1061247458sorted @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ~ Y )
% 2.86/1.52 => ( ( ? [X12: A,L12: list @ A] :
% 2.86/1.52 ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => Y ) )
% 2.86/1.52 => ~ ! [X12: A,L12: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ! [X23: A,L22: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ X23 @ L22 ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( ~ ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( ( X12 = X23 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ L12 @ L22 ) )
% 2.86/1.52 & ( ( X12 != X23 )
% 2.86/1.52 => ( sorted1061247458sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_12_list_Odistinct_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,X21: A,X22: list @ A] :
% 2.86/1.52 ( ( nil @ A )
% 2.86/1.52 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_13_list_OdiscI,axiom,
% 2.86/1.52 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.86/1.52 ( ( List
% 2.86/1.52 = ( cons @ A @ X21 @ X22 ) )
% 2.86/1.52 => ( List
% 2.86/1.52 != ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_14_transpose_Ocases,axiom,
% 2.86/1.52 ! [A: $tType,X: list @ ( list @ A )] :
% 2.86/1.52 ( ( X
% 2.86/1.52 != ( nil @ ( list @ A ) ) )
% 2.86/1.52 => ( ! [Xss: list @ ( list @ A )] :
% 2.86/1.52 ( X
% 2.86/1.52 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.86/1.52 => ~ ! [X3: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.86/1.52 ( X
% 2.86/1.52 != ( cons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_15_subset__sorted_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.86/1.52 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [X12: A,L12: list @ A] : ( P @ ( cons @ A @ X12 @ L12 ) @ ( nil @ A ) )
% 2.86/1.52 => ( ! [X12: A,L12: list @ A,X23: A,L22: list @ A] :
% 2.86/1.52 ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( X12 = X23 )
% 2.86/1.52 => ( P @ L12 @ L22 ) ) )
% 2.86/1.52 => ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( X12 != X23 )
% 2.86/1.52 => ( P @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) )
% 2.86/1.52 => ( P @ ( cons @ A @ X12 @ L12 ) @ ( cons @ A @ X23 @ L22 ) ) ) )
% 2.86/1.52 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_16_inter__sorted_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.86/1.52 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 2.86/1.52 => ( ! [X12: A,L12: list @ A,X23: A,L22: list @ A] :
% 2.86/1.52 ( ( ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( P @ L12 @ ( cons @ A @ X23 @ L22 ) ) )
% 2.86/1.52 => ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( X12 = X23 )
% 2.86/1.52 => ( P @ L12 @ L22 ) ) )
% 2.86/1.52 => ( ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( X12 != X23 )
% 2.86/1.52 => ( P @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) )
% 2.86/1.52 => ( P @ ( cons @ A @ X12 @ L12 ) @ ( cons @ A @ X23 @ L22 ) ) ) ) )
% 2.86/1.52 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_17_mergesort__by__rel__merge__induct,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,R: A > B > $o,Xs: list @ A,Ys: list @ B] :
% 2.86/1.52 ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ B ) )
% 2.86/1.52 => ( ! [X12: list @ B] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 2.86/1.52 ( ( R @ X3 @ Y2 )
% 2.86/1.52 => ( ( P @ Xs2 @ ( cons @ B @ Y2 @ Ys2 ) )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) )
% 2.86/1.52 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 2.86/1.52 ( ~ ( R @ X3 @ Y2 )
% 2.86/1.52 => ( ( P @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) )
% 2.86/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_18_mergesort__by__rel__merge_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A,A2: list @ A] :
% 2.86/1.52 ( ! [R3: A > A > $o,X3: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.86/1.52 ( ( ( R3 @ X3 @ Y2 )
% 2.86/1.52 => ( P @ R3 @ Xs2 @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.86/1.52 => ( ( ~ ( R3 @ X3 @ Y2 )
% 2.86/1.52 => ( P @ R3 @ ( cons @ A @ X3 @ Xs2 ) @ Ys2 ) )
% 2.86/1.52 => ( P @ R3 @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) )
% 2.86/1.52 => ( ! [R3: A > A > $o,Xs2: list @ A] : ( P @ R3 @ Xs2 @ ( nil @ A ) )
% 2.86/1.52 => ( ! [R3: A > A > $o,V: A,Va: list @ A] : ( P @ R3 @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 2.86/1.52 => ( P @ A0 @ A1 @ A2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_19_map__tailrec__rev_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A2: list @ B] :
% 2.86/1.52 ( ! [F: A > B,X12: list @ B] : ( P @ F @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [F: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 2.86/1.52 ( ( P @ F @ As @ ( cons @ B @ ( F @ A3 ) @ Bs ) )
% 2.86/1.52 => ( P @ F @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 2.86/1.52 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_20_list__nonempty__induct,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.86/1.52 ( ( Xs
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.86/1.52 => ( ! [X3: A,Xs2: list @ A] :
% 2.86/1.52 ( ( Xs2
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ( P @ Xs2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) ) )
% 2.86/1.52 => ( P @ Xs ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_21_list__all__zip_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,P: ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > $o,A1: list @ A,A2: list @ B] :
% 2.86/1.52 ( ! [P2: A > B > $o] : ( P @ P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [P2: A > B > $o,A3: A,As: list @ A,B2: B,Bs: list @ B] :
% 2.86/1.52 ( ( P @ P2 @ As @ Bs )
% 2.86/1.52 => ( P @ P2 @ ( cons @ A @ A3 @ As ) @ ( cons @ B @ B2 @ Bs ) ) )
% 2.86/1.52 => ( ! [P2: A > B > $o,V: A,Va: list @ A] : ( P @ P2 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [P2: A > B > $o,V: B,Va: list @ B] : ( P @ P2 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 2.86/1.52 => ( P @ A0 @ A1 @ A2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_22_list__induct__first2,axiom,
% 2.86/1.52 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.86/1.52 ( ( P @ ( nil @ A ) )
% 2.86/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.86/1.52 => ( ! [X12: A,X23: A,Xs2: list @ A] :
% 2.86/1.52 ( ( P @ Xs2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X12 @ ( cons @ A @ X23 @ Xs2 ) ) ) )
% 2.86/1.52 => ( P @ Xs ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_23_remdups__adj_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.86/1.52 ( ( P @ ( nil @ A ) )
% 2.86/1.52 => ( ! [X3: A] : ( P @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.86/1.52 => ( ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.86/1.52 ( ( ( X3 = Y2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) ) )
% 2.86/1.52 => ( ( ( X3 != Y2 )
% 2.86/1.52 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.86/1.52 => ( P @ A0 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_24_remdups__adj_Ocases,axiom,
% 2.86/1.52 ! [A: $tType,X: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ! [X3: A] :
% 2.86/1.52 ( X
% 2.86/1.52 != ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.86/1.52 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.86/1.52 ( X
% 2.86/1.52 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_25_list__2pre__induct,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,W1: list @ A,W2: list @ B] :
% 2.86/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [E: A,W12: list @ A,W22: list @ B] :
% 2.86/1.52 ( ( P @ W12 @ W22 )
% 2.86/1.52 => ( P @ ( cons @ A @ E @ W12 ) @ W22 ) )
% 2.86/1.52 => ( ! [E: B,W13: list @ A,W23: list @ B] :
% 2.86/1.52 ( ( P @ W13 @ W23 )
% 2.86/1.52 => ( P @ W13 @ ( cons @ B @ E @ W23 ) ) )
% 2.86/1.52 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_26_splice_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.86/1.52 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 2.86/1.52 => ( ! [X3: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.86/1.52 ( ( P @ Xs2 @ Ys2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.86/1.52 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_27_list__induct2_H,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.86/1.52 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [X3: A,Xs2: list @ A] : ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 2.86/1.52 => ( ! [X3: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 2.86/1.52 ( ( P @ Xs2 @ Ys2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 2.86/1.52 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_28_neq__Nil__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A] :
% 2.86/1.52 ( ( Xs
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 = ( ? [Y3: A,Ys3: list @ A] :
% 2.86/1.52 ( Xs
% 2.86/1.52 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_29_list_Oinducts,axiom,
% 2.86/1.52 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.86/1.52 ( ( P @ ( nil @ A ) )
% 2.86/1.52 => ( ! [X12: A,X23: list @ A] :
% 2.86/1.52 ( ( P @ X23 )
% 2.86/1.52 => ( P @ ( cons @ A @ X12 @ X23 ) ) )
% 2.86/1.52 => ( P @ List ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_30_list_Oexhaust,axiom,
% 2.86/1.52 ! [A: $tType,Y: list @ A] :
% 2.86/1.52 ( ( Y
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ~ ! [X212: A,X222: list @ A] :
% 2.86/1.52 ( Y
% 2.86/1.52 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_31_zipf_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,C: $tType,B: $tType,P: ( A > B > C ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B > C,A1: list @ A,A2: list @ B] :
% 2.86/1.52 ( ! [F: A > B > C] : ( P @ F @ ( nil @ A ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [F: A > B > C,A3: A,As: list @ A,B2: B,Bs: list @ B] :
% 2.86/1.52 ( ( P @ F @ As @ Bs )
% 2.86/1.52 => ( P @ F @ ( cons @ A @ A3 @ As ) @ ( cons @ B @ B2 @ Bs ) ) )
% 2.86/1.52 => ( ! [A3: A > B > C,V: A,Va: list @ A] : ( P @ A3 @ ( cons @ A @ V @ Va ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [A3: A > B > C,V: B,Va: list @ B] : ( P @ A3 @ ( nil @ A ) @ ( cons @ B @ V @ Va ) )
% 2.86/1.52 => ( P @ A0 @ A1 @ A2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_32_revg_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.86/1.52 ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [A3: A,As: list @ A,B2: list @ A] :
% 2.86/1.52 ( ( P @ As @ ( cons @ A @ A3 @ B2 ) )
% 2.86/1.52 => ( P @ ( cons @ A @ A3 @ As ) @ B2 ) )
% 2.86/1.52 => ( P @ A0 @ A1 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_33_quicksort_Ocases,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ~ ! [X3: A,Xs2: list @ A] :
% 2.86/1.52 ( X
% 2.86/1.52 != ( cons @ A @ X3 @ Xs2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_34_insert__Nil,axiom,
% 2.86/1.52 ! [A: $tType,X: A] :
% 2.86/1.52 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.86/1.52 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_35_list__ex1__simps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,P: A > $o] :
% 2.86/1.52 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_36_inter__sorted_Oelims,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A,Xa: list @ A,Y: list @ A] :
% 2.86/1.52 ( ( ( sorted2037043510sorted @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( nil @ A ) ) )
% 2.86/1.52 => ( ( ? [V: A,Va: list @ A] :
% 2.86/1.52 ( X
% 2.86/1.52 = ( cons @ A @ V @ Va ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( nil @ A ) ) ) )
% 2.86/1.52 => ~ ! [X12: A,L12: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ! [X23: A,L22: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ X23 @ L22 ) )
% 2.86/1.52 => ~ ( ( ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( sorted2037043510sorted @ A @ L12 @ ( cons @ A @ X23 @ L22 ) ) ) )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( ( X12 = X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( cons @ A @ X12 @ ( sorted2037043510sorted @ A @ L12 @ L22 ) ) ) )
% 2.86/1.52 & ( ( X12 != X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( sorted2037043510sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_37_diff__sorted_Oelims,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A,Xa: list @ A,Y: list @ A] :
% 2.86/1.52 ( ( ( sorted1267110213sorted @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( nil @ A ) ) )
% 2.86/1.52 => ( ! [V: A,Va: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ V @ Va ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( cons @ A @ V @ Va ) ) ) )
% 2.86/1.52 => ~ ! [X12: A,L12: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ! [X23: A,L22: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ X23 @ L22 ) )
% 2.86/1.52 => ~ ( ( ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( cons @ A @ X12 @ ( sorted1267110213sorted @ A @ L12 @ ( cons @ A @ X23 @ L22 ) ) ) ) )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( ( X12 = X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( sorted1267110213sorted @ A @ L12 @ L22 ) ) )
% 2.86/1.52 & ( ( X12 != X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( sorted1267110213sorted @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_38_merge_Oelims,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ A,Xa: list @ A,Y: list @ A] :
% 2.86/1.52 ( ( ( merge @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y != Xa ) )
% 2.86/1.52 => ( ! [V: A,Va: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ V @ Va ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( cons @ A @ V @ Va ) ) ) )
% 2.86/1.52 => ~ ! [X12: A,L12: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X12 @ L12 ) )
% 2.86/1.52 => ! [X23: A,L22: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ X23 @ L22 ) )
% 2.86/1.52 => ~ ( ( ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( cons @ A @ X12 @ ( merge @ A @ L12 @ ( cons @ A @ X23 @ L22 ) ) ) ) )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X12 @ X23 )
% 2.86/1.52 => ( ( ( X12 = X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( cons @ A @ X12 @ ( merge @ A @ L12 @ L22 ) ) ) )
% 2.86/1.52 & ( ( X12 != X23 )
% 2.86/1.52 => ( Y
% 2.86/1.52 = ( cons @ A @ X23 @ ( merge @ A @ ( cons @ A @ X12 @ L12 ) @ L22 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_39_revg_Oelims,axiom,
% 2.86/1.52 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 2.86/1.52 ( ( ( revg @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y != Xa ) )
% 2.86/1.52 => ~ ! [A3: A,As: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ A3 @ As ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( revg @ A @ As @ ( cons @ A @ A3 @ Xa ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_40_list__collect__set__simps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > ( set @ A ),A4: B] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( cons @ B @ A4 @ ( nil @ B ) ) )
% 2.86/1.52 = ( F2 @ A4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_41_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 2.86/1.52 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_42_lexordp__eq_Ocases,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A1: list @ A,A2: list @ A] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ A1 @ A2 )
% 2.86/1.52 => ( ( ( A1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ! [Ys2: list @ A] : ( A2 != Ys2 ) )
% 2.86/1.52 => ( ! [X3: A] :
% 2.86/1.52 ( ? [Xs2: list @ A] :
% 2.86/1.52 ( A1
% 2.86/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.86/1.52 => ! [Y2: A] :
% 2.86/1.52 ( ? [Ys2: list @ A] :
% 2.86/1.52 ( A2
% 2.86/1.52 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.86/1.52 => ~ ( ord_less @ A @ X3 @ Y2 ) ) )
% 2.86/1.52 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.86/1.52 ( ( A1
% 2.86/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.86/1.52 => ! [Ys2: list @ A] :
% 2.86/1.52 ( ( A2
% 2.86/1.52 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.86/1.52 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.86/1.52 => ( ~ ( ord_less @ A @ Y2 @ X3 )
% 2.86/1.52 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_43_lexordp__eq_Osimps,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( ord_lexordp_eq @ A )
% 2.86/1.52 = ( ^ [A12: list @ A,A22: list @ A] :
% 2.86/1.52 ( ? [Ys3: list @ A] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( A22 = Ys3 ) )
% 2.86/1.52 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( cons @ A @ X4 @ Xs3 ) )
% 2.86/1.52 & ( A22
% 2.86/1.52 = ( cons @ A @ Y3 @ Ys3 ) )
% 2.86/1.52 & ( ord_less @ A @ X4 @ Y3 ) )
% 2.86/1.52 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( cons @ A @ X4 @ Xs3 ) )
% 2.86/1.52 & ( A22
% 2.86/1.52 = ( cons @ A @ Y3 @ Ys3 ) )
% 2.86/1.52 & ~ ( ord_less @ A @ X4 @ Y3 )
% 2.86/1.52 & ~ ( ord_less @ A @ Y3 @ X4 )
% 2.86/1.52 & ( ord_lexordp_eq @ A @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_44_mem__Collect__eq,axiom,
% 2.86/1.52 ! [A: $tType,A4: A,P: A > $o] :
% 2.86/1.52 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 2.86/1.52 = ( P @ A4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_45_Collect__mem__eq,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ( ( collect @ A
% 2.86/1.52 @ ^ [X4: A] : ( member @ A @ X4 @ A5 ) )
% 2.86/1.52 = A5 ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_46_Collect__cong,axiom,
% 2.86/1.52 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.86/1.52 ( ! [X3: A] :
% 2.86/1.52 ( ( P @ X3 )
% 2.86/1.52 = ( Q @ X3 ) )
% 2.86/1.52 => ( ( collect @ A @ P )
% 2.86/1.52 = ( collect @ A @ Q ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_47_ext,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 2.86/1.52 ( ! [X3: A] :
% 2.86/1.52 ( ( F2 @ X3 )
% 2.86/1.52 = ( G @ X3 ) )
% 2.86/1.52 => ( F2 = G ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_48_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.86/1.52 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.86/1.52 = ( ( Less @ X @ Y )
% 2.86/1.52 | ( ~ ( Less @ Y @ X )
% 2.86/1.52 & ( lexordp_eq @ A @ Less @ Xs @ Ys ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_49_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_50_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.86/1.52 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_51_lexordp__eq__simps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_52_lexordp__eq__simps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Xs: list @ A] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_53_lexordp__eq__simps_I4_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.86/1.52 = ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 | ( ~ ( ord_less @ A @ Y @ X )
% 2.86/1.52 & ( ord_lexordp_eq @ A @ Xs @ Ys ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_54_lexordp__eq__simps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Xs: list @ A] :
% 2.86/1.52 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_55_merge__list_Oinduct,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [P: ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) > $o,A0: list @ ( list @ A ),A1: list @ ( list @ A )] :
% 2.86/1.52 ( ( P @ ( nil @ ( list @ A ) ) @ ( nil @ ( list @ A ) ) )
% 2.86/1.52 => ( ! [L: list @ A] : ( P @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) )
% 2.86/1.52 => ( ! [La: list @ A,Acc2: list @ ( list @ A )] :
% 2.86/1.52 ( ( P @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ La @ Acc2 ) )
% 2.86/1.52 => ( P @ ( cons @ ( list @ A ) @ La @ Acc2 ) @ ( nil @ ( list @ A ) ) ) )
% 2.86/1.52 => ( ! [La: list @ A,Acc2: list @ ( list @ A ),L: list @ A] :
% 2.86/1.52 ( ( P @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L @ ( cons @ ( list @ A ) @ La @ Acc2 ) ) )
% 2.86/1.52 => ( P @ ( cons @ ( list @ A ) @ La @ Acc2 ) @ ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) ) )
% 2.86/1.52 => ( ! [Acc2: list @ ( list @ A ),L12: list @ A,L22: list @ A,Ls: list @ ( list @ A )] :
% 2.86/1.52 ( ( P @ ( cons @ ( list @ A ) @ ( merge @ A @ L12 @ L22 ) @ Acc2 ) @ Ls )
% 2.86/1.52 => ( P @ Acc2 @ ( cons @ ( list @ A ) @ L12 @ ( cons @ ( list @ A ) @ L22 @ Ls ) ) ) )
% 2.86/1.52 => ( P @ A0 @ A1 ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_56_ord_Olexordp__eq__refl,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_57_lexordp__eq__refl,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_58_lexordp__eq__trans,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.86/1.52 => ( ( ord_lexordp_eq @ A @ Ys @ Zs )
% 2.86/1.52 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_59_lexordp__eq__linear,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.86/1.52 | ( ord_lexordp_eq @ A @ Ys @ Xs ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_60_lexordp__eq__antisym,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.86/1.52 => ( ( ord_lexordp_eq @ A @ Ys @ Xs )
% 2.86/1.52 => ( Xs = Ys ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_61_lexordp__eq_ONil,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_62_ord_Olexordp__eq_OCons,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( Less @ X @ Y )
% 2.86/1.52 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_63_ord_Olexordp__eq_OCons__eq,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ~ ( Less @ X @ Y )
% 2.86/1.52 => ( ~ ( Less @ Y @ X )
% 2.86/1.52 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys )
% 2.86/1.52 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_64_ord_Olexordp__eq_ONil,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,Ys: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_65_merge_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [L2: list @ A] :
% 2.86/1.52 ( ( merge @ A @ ( nil @ A ) @ L2 )
% 2.86/1.52 = L2 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_66_inter__sorted_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [L2: list @ A] :
% 2.86/1.52 ( ( sorted2037043510sorted @ A @ ( nil @ A ) @ L2 )
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_67_diff__sorted_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [L2: list @ A] :
% 2.86/1.52 ( ( sorted1267110213sorted @ A @ ( nil @ A ) @ L2 )
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_68_revg_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,A4: A,As2: list @ A,B3: list @ A] :
% 2.86/1.52 ( ( revg @ A @ ( cons @ A @ A4 @ As2 ) @ B3 )
% 2.86/1.52 = ( revg @ A @ As2 @ ( cons @ A @ A4 @ B3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_69_revg_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,B3: list @ A] :
% 2.86/1.52 ( ( revg @ A @ ( nil @ A ) @ B3 )
% 2.86/1.52 = B3 ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_70_lexordp__eq_OCons__eq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ~ ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( ~ ( ord_less @ A @ Y @ X )
% 2.86/1.52 => ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 2.86/1.52 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_71_lexordp__eq_OCons,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_72_ord_Olexordp__eq_Ocases,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,A1: list @ A,A2: list @ A] :
% 2.86/1.52 ( ( lexordp_eq @ A @ Less @ A1 @ A2 )
% 2.86/1.52 => ( ( ( A1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ! [Ys2: list @ A] : ( A2 != Ys2 ) )
% 2.86/1.52 => ( ! [X3: A] :
% 2.86/1.52 ( ? [Xs2: list @ A] :
% 2.86/1.52 ( A1
% 2.86/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.86/1.52 => ! [Y2: A] :
% 2.86/1.52 ( ? [Ys2: list @ A] :
% 2.86/1.52 ( A2
% 2.86/1.52 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.86/1.52 => ~ ( Less @ X3 @ Y2 ) ) )
% 2.86/1.52 => ~ ! [X3: A,Y2: A,Xs2: list @ A] :
% 2.86/1.52 ( ( A1
% 2.86/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.86/1.52 => ! [Ys2: list @ A] :
% 2.86/1.52 ( ( A2
% 2.86/1.52 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.86/1.52 => ( ~ ( Less @ X3 @ Y2 )
% 2.86/1.52 => ( ~ ( Less @ Y2 @ X3 )
% 2.86/1.52 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_73_ord_Olexordp__eq_Osimps,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( lexordp_eq @ A )
% 2.86/1.52 = ( ^ [Less2: A > A > $o,A12: list @ A,A22: list @ A] :
% 2.86/1.52 ( ? [Ys3: list @ A] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( A22 = Ys3 ) )
% 2.86/1.52 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( cons @ A @ X4 @ Xs3 ) )
% 2.86/1.52 & ( A22
% 2.86/1.52 = ( cons @ A @ Y3 @ Ys3 ) )
% 2.86/1.52 & ( Less2 @ X4 @ Y3 ) )
% 2.86/1.52 | ? [X4: A,Y3: A,Xs3: list @ A,Ys3: list @ A] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( cons @ A @ X4 @ Xs3 ) )
% 2.86/1.52 & ( A22
% 2.86/1.52 = ( cons @ A @ Y3 @ Ys3 ) )
% 2.86/1.52 & ~ ( Less2 @ X4 @ Y3 )
% 2.86/1.52 & ~ ( Less2 @ Y3 @ X4 )
% 2.86/1.52 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_74_ord_Olexordp__eq_Oinducts,axiom,
% 2.86/1.52 ! [A: $tType,Less: A > A > $o,X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.86/1.52 ( ( lexordp_eq @ A @ Less @ X1 @ X2 )
% 2.86/1.52 => ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.86/1.52 ( ( Less @ X3 @ Y2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.86/1.52 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.86/1.52 ( ~ ( Less @ X3 @ Y2 )
% 2.86/1.52 => ( ~ ( Less @ Y2 @ X3 )
% 2.86/1.52 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys2 )
% 2.86/1.52 => ( ( P @ Xs2 @ Ys2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) )
% 2.86/1.52 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_75_merge_Osimps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X1: A,X2: A,L1: list @ A,L2: list @ A] :
% 2.86/1.52 ( ( ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( cons @ A @ X1 @ ( merge @ A @ L1 @ ( cons @ A @ X2 @ L2 ) ) ) ) )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( ( X1 = X2 )
% 2.86/1.52 => ( ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( cons @ A @ X1 @ ( merge @ A @ L1 @ L2 ) ) ) )
% 2.86/1.52 & ( ( X1 != X2 )
% 2.86/1.52 => ( ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( cons @ A @ X2 @ ( merge @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_76_merge_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [V2: A,Va2: list @ A] :
% 2.86/1.52 ( ( merge @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 2.86/1.52 = ( cons @ A @ V2 @ Va2 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_77_diff__sorted_Osimps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X1: A,X2: A,L1: list @ A,L2: list @ A] :
% 2.86/1.52 ( ( ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( cons @ A @ X1 @ ( sorted1267110213sorted @ A @ L1 @ ( cons @ A @ X2 @ L2 ) ) ) ) )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( ( X1 = X2 )
% 2.86/1.52 => ( ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( sorted1267110213sorted @ A @ L1 @ L2 ) ) )
% 2.86/1.52 & ( ( X1 != X2 )
% 2.86/1.52 => ( ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( sorted1267110213sorted @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_78_inter__sorted_Osimps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X1: A,X2: A,L1: list @ A,L2: list @ A] :
% 2.86/1.52 ( ( ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( sorted2037043510sorted @ A @ L1 @ ( cons @ A @ X2 @ L2 ) ) ) )
% 2.86/1.52 & ( ~ ( ord_less @ A @ X1 @ X2 )
% 2.86/1.52 => ( ( ( X1 = X2 )
% 2.86/1.52 => ( ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( cons @ A @ X1 @ ( sorted2037043510sorted @ A @ L1 @ L2 ) ) ) )
% 2.86/1.52 & ( ( X1 != X2 )
% 2.86/1.52 => ( ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ ( cons @ A @ X2 @ L2 ) )
% 2.86/1.52 = ( sorted2037043510sorted @ A @ ( cons @ A @ X1 @ L1 ) @ L2 ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_79_diff__sorted_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [V2: A,Va2: list @ A] :
% 2.86/1.52 ( ( sorted1267110213sorted @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 2.86/1.52 = ( cons @ A @ V2 @ Va2 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_80_inter__sorted_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [V2: A,Va2: list @ A] :
% 2.86/1.52 ( ( sorted2037043510sorted @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_81_lexordp__eq_Oinducts,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.86/1.52 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 2.86/1.52 => ( ! [X12: list @ A] : ( P @ ( nil @ A ) @ X12 )
% 2.86/1.52 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.86/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.86/1.52 => ( ! [X3: A,Y2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.86/1.52 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.86/1.52 => ( ~ ( ord_less @ A @ Y2 @ X3 )
% 2.86/1.52 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys2 )
% 2.86/1.52 => ( ( P @ Xs2 @ Ys2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) ) ) ) )
% 2.86/1.52 => ( P @ X1 @ X2 ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_82_sublists_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( sublists @ A @ ( nil @ A ) )
% 2.86/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_83_product__lists_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.86/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_84_merge__list_Oelims,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: list @ ( list @ A ),Xa: list @ ( list @ A ),Y: list @ A] :
% 2.86/1.52 ( ( ( merge_list @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ ( list @ A ) ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ ( list @ A ) ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( nil @ A ) ) ) )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ ( list @ A ) ) )
% 2.86/1.52 => ! [L: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) )
% 2.86/1.52 => ( Y != L ) ) )
% 2.86/1.52 => ( ! [La: list @ A,Acc2: list @ ( list @ A )] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ ( list @ A ) @ La @ Acc2 ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ ( list @ A ) ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ La @ Acc2 ) ) ) ) )
% 2.86/1.52 => ( ! [La: list @ A,Acc2: list @ ( list @ A )] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ ( list @ A ) @ La @ Acc2 ) )
% 2.86/1.52 => ! [L: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ ( list @ A ) @ L @ ( nil @ ( list @ A ) ) ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L @ ( cons @ ( list @ A ) @ La @ Acc2 ) ) ) ) ) )
% 2.86/1.52 => ~ ! [L12: list @ A,L22: list @ A,Ls: list @ ( list @ A )] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ ( list @ A ) @ L12 @ ( cons @ ( list @ A ) @ L22 @ Ls ) ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( merge_list @ A @ ( cons @ ( list @ A ) @ ( merge @ A @ L12 @ L22 ) @ X ) @ Ls ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_85_combinatorial__product_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( list_c659805718roduct @ A @ ( nil @ ( list @ A ) ) )
% 2.86/1.52 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_86_map__tailrec__rev_Oelims,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,X: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 2.86/1.52 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa @ Xb )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( Xa
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y != Xb ) )
% 2.86/1.52 => ~ ! [A3: A,As: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ A3 @ As ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A3 ) @ Xb ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_87_list__collect__set__map__simps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,C: $tType,F2: B > ( set @ A ),X: C > B,A4: C] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( cons @ C @ A4 @ ( nil @ C ) ) ) )
% 2.86/1.52 = ( F2 @ ( X @ A4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_88_bind__simps_I1_J,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: B > ( list @ A )] :
% 2.86/1.52 ( ( bind @ B @ A @ ( nil @ B ) @ F2 )
% 2.86/1.52 = ( nil @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_89_splice_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,V2: A,Va2: list @ A] :
% 2.86/1.52 ( ( splice @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 2.86/1.52 = ( cons @ A @ V2 @ Va2 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_90_Nil__is__map__conv,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.86/1.52 ( ( ( nil @ A )
% 2.86/1.52 = ( map @ B @ A @ F2 @ Xs ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ B ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_91_map__is__Nil__conv,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.86/1.52 ( ( ( map @ B @ A @ F2 @ Xs )
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ B ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_92_list_Omap__disc__iff,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: A > B,A4: list @ A] :
% 2.86/1.52 ( ( ( map @ A @ B @ F2 @ A4 )
% 2.86/1.52 = ( nil @ B ) )
% 2.86/1.52 = ( A4
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_93_splice__Nil2,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A] :
% 2.86/1.52 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 2.86/1.52 = Xs ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_94_map__eq__Cons__conv,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 2.86/1.52 ( ( ( map @ B @ A @ F2 @ Xs )
% 2.86/1.52 = ( cons @ A @ Y @ Ys ) )
% 2.86/1.52 = ( ? [Z: B,Zs2: list @ B] :
% 2.86/1.52 ( ( Xs
% 2.86/1.52 = ( cons @ B @ Z @ Zs2 ) )
% 2.86/1.52 & ( ( F2 @ Z )
% 2.86/1.52 = Y )
% 2.86/1.52 & ( ( map @ B @ A @ F2 @ Zs2 )
% 2.86/1.52 = Ys ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_95_Cons__eq__map__conv,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys: list @ B] :
% 2.86/1.52 ( ( ( cons @ A @ X @ Xs )
% 2.86/1.52 = ( map @ B @ A @ F2 @ Ys ) )
% 2.86/1.52 = ( ? [Z: B,Zs2: list @ B] :
% 2.86/1.52 ( ( Ys
% 2.86/1.52 = ( cons @ B @ Z @ Zs2 ) )
% 2.86/1.52 & ( X
% 2.86/1.52 = ( F2 @ Z ) )
% 2.86/1.52 & ( Xs
% 2.86/1.52 = ( map @ B @ A @ F2 @ Zs2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_96_map__eq__Cons__D,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 2.86/1.52 ( ( ( map @ B @ A @ F2 @ Xs )
% 2.86/1.52 = ( cons @ A @ Y @ Ys ) )
% 2.86/1.52 => ? [Z2: B,Zs3: list @ B] :
% 2.86/1.52 ( ( Xs
% 2.86/1.52 = ( cons @ B @ Z2 @ Zs3 ) )
% 2.86/1.52 & ( ( F2 @ Z2 )
% 2.86/1.52 = Y )
% 2.86/1.52 & ( ( map @ B @ A @ F2 @ Zs3 )
% 2.86/1.52 = Ys ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_97_Cons__eq__map__D,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys: list @ B] :
% 2.86/1.52 ( ( ( cons @ A @ X @ Xs )
% 2.86/1.52 = ( map @ B @ A @ F2 @ Ys ) )
% 2.86/1.52 => ? [Z2: B,Zs3: list @ B] :
% 2.86/1.52 ( ( Ys
% 2.86/1.52 = ( cons @ B @ Z2 @ Zs3 ) )
% 2.86/1.52 & ( X
% 2.86/1.52 = ( F2 @ Z2 ) )
% 2.86/1.52 & ( Xs
% 2.86/1.52 = ( map @ B @ A @ F2 @ Zs3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_98_map__eq__consE,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: B > A,Ls2: list @ B,Fa: A,Fl: list @ A] :
% 2.86/1.52 ( ( ( map @ B @ A @ F2 @ Ls2 )
% 2.86/1.52 = ( cons @ A @ Fa @ Fl ) )
% 2.86/1.52 => ~ ! [A3: B,L: list @ B] :
% 2.86/1.52 ( ( Ls2
% 2.86/1.52 = ( cons @ B @ A3 @ L ) )
% 2.86/1.52 => ( ( ( F2 @ A3 )
% 2.86/1.52 = Fa )
% 2.86/1.52 => ( ( map @ B @ A @ F2 @ L )
% 2.86/1.52 != Fl ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_99_list_Osimps_I9_J,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: A > B,X21: A,X22: list @ A] :
% 2.86/1.52 ( ( map @ A @ B @ F2 @ ( cons @ A @ X21 @ X22 ) )
% 2.86/1.52 = ( cons @ B @ ( F2 @ X21 ) @ ( map @ A @ B @ F2 @ X22 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_100_map__consI_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,W: list @ A,F2: B > A,Ww: list @ B,A4: B] :
% 2.86/1.52 ( ( W
% 2.86/1.52 = ( map @ B @ A @ F2 @ Ww ) )
% 2.86/1.52 => ( ( cons @ A @ ( F2 @ A4 ) @ W )
% 2.86/1.52 = ( map @ B @ A @ F2 @ ( cons @ B @ A4 @ Ww ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_101_list_Osimps_I8_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: A > B] :
% 2.86/1.52 ( ( map @ A @ B @ F2 @ ( nil @ A ) )
% 2.86/1.52 = ( nil @ B ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_102_splice_Osimps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.86/1.52 ( ( splice @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 2.86/1.52 = ( cons @ A @ X @ ( cons @ A @ Y @ ( splice @ A @ Xs @ Ys ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_103_splice_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,Ys: list @ A] :
% 2.86/1.52 ( ( splice @ A @ ( nil @ A ) @ Ys )
% 2.86/1.52 = Ys ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_104_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: A > B,A4: A,As2: list @ A,Bs2: list @ B] :
% 2.86/1.52 ( ( map_tailrec_rev @ A @ B @ F2 @ ( cons @ A @ A4 @ As2 ) @ Bs2 )
% 2.86/1.52 = ( map_tailrec_rev @ A @ B @ F2 @ As2 @ ( cons @ B @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_105_map__tailrec__rev_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: A > B,Bs2: list @ B] :
% 2.86/1.52 ( ( map_tailrec_rev @ A @ B @ F2 @ ( nil @ A ) @ Bs2 )
% 2.86/1.52 = Bs2 ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_106_merge__list_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( nil @ ( list @ A ) ) )
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_107_merge__list_Osimps_I2_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [L3: list @ A] :
% 2.86/1.52 ( ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L3 @ ( nil @ ( list @ A ) ) ) )
% 2.86/1.52 = L3 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_108_merge__list_Osimps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [La2: list @ A,Acc22: list @ ( list @ A )] :
% 2.86/1.52 ( ( merge_list @ A @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) @ ( nil @ ( list @ A ) ) )
% 2.86/1.52 = ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_109_merge__list_Osimps_I4_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [La2: list @ A,Acc22: list @ ( list @ A ),L3: list @ A] :
% 2.86/1.52 ( ( merge_list @ A @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) @ ( cons @ ( list @ A ) @ L3 @ ( nil @ ( list @ A ) ) ) )
% 2.86/1.52 = ( merge_list @ A @ ( nil @ ( list @ A ) ) @ ( cons @ ( list @ A ) @ L3 @ ( cons @ ( list @ A ) @ La2 @ Acc22 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_110_merge__list_Osimps_I5_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Acc22: list @ ( list @ A ),L1: list @ A,L2: list @ A,Ls2: list @ ( list @ A )] :
% 2.86/1.52 ( ( merge_list @ A @ Acc22 @ ( cons @ ( list @ A ) @ L1 @ ( cons @ ( list @ A ) @ L2 @ Ls2 ) ) )
% 2.86/1.52 = ( merge_list @ A @ ( cons @ ( list @ A ) @ ( merge @ A @ L1 @ L2 ) @ Acc22 ) @ Ls2 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_111_splice_Oelims,axiom,
% 2.86/1.52 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 2.86/1.52 ( ( ( splice @ A @ X @ Xa )
% 2.86/1.52 = Y )
% 2.86/1.52 => ( ( ( X
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y != Xa ) )
% 2.86/1.52 => ( ! [V: A,Va: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ V @ Va ) )
% 2.86/1.52 => ( ( Xa
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( cons @ A @ V @ Va ) ) ) )
% 2.86/1.52 => ~ ! [X3: A,Xs2: list @ A] :
% 2.86/1.52 ( ( X
% 2.86/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.86/1.52 => ! [Y2: A,Ys2: list @ A] :
% 2.86/1.52 ( ( Xa
% 2.86/1.52 = ( cons @ A @ Y2 @ Ys2 ) )
% 2.86/1.52 => ( Y
% 2.86/1.52 != ( cons @ A @ X3 @ ( cons @ A @ Y2 @ ( splice @ A @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_112_map__eq__map__tailrec,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( map @ A @ B )
% 2.86/1.52 = ( map_tailrec @ A @ B ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_113_list__collect__set__map__simps_I1_J,axiom,
% 2.86/1.52 ! [C: $tType,B: $tType,A: $tType,F2: B > ( set @ A ),X: C > B] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( nil @ C ) ) )
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_114_list__collect__set__map__simps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,C: $tType,F2: B > ( set @ A ),X: C > B,A4: C,L3: list @ C] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( cons @ C @ A4 @ L3 ) ) )
% 2.86/1.52 = ( sup_sup @ ( set @ A ) @ ( F2 @ ( X @ A4 ) ) @ ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ L3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_115_listrelp_Oinducts,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,R4: A > B > $o,X1: list @ A,X2: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 2.86/1.52 ( ( listrelp @ A @ B @ R4 @ X1 @ X2 )
% 2.86/1.52 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.86/1.52 => ( ! [X3: A,Y2: B,Xs2: list @ A,Ys2: list @ B] :
% 2.86/1.52 ( ( R4 @ X3 @ Y2 )
% 2.86/1.52 => ( ( listrelp @ A @ B @ R4 @ Xs2 @ Ys2 )
% 2.86/1.52 => ( ( P @ Xs2 @ Ys2 )
% 2.86/1.52 => ( P @ ( cons @ A @ X3 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) ) ) )
% 2.86/1.52 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_116_listrelp_Osimps,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( listrelp @ A @ B )
% 2.86/1.52 = ( ^ [R5: A > B > $o,A12: list @ A,A22: list @ B] :
% 2.86/1.52 ( ( ( A12
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( A22
% 2.86/1.52 = ( nil @ B ) ) )
% 2.86/1.52 | ? [X4: A,Y3: B,Xs3: list @ A,Ys3: list @ B] :
% 2.86/1.52 ( ( A12
% 2.86/1.52 = ( cons @ A @ X4 @ Xs3 ) )
% 2.86/1.52 & ( A22
% 2.86/1.52 = ( cons @ B @ Y3 @ Ys3 ) )
% 2.86/1.52 & ( R5 @ X4 @ Y3 )
% 2.86/1.52 & ( listrelp @ A @ B @ R5 @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_117_listrelp_Ocases,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,R4: A > B > $o,A1: list @ A,A2: list @ B] :
% 2.86/1.52 ( ( listrelp @ A @ B @ R4 @ A1 @ A2 )
% 2.86/1.52 => ( ( ( A1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 => ( A2
% 2.86/1.52 != ( nil @ B ) ) )
% 2.86/1.52 => ~ ! [X3: A,Y2: B,Xs2: list @ A] :
% 2.86/1.52 ( ( A1
% 2.86/1.52 = ( cons @ A @ X3 @ Xs2 ) )
% 2.86/1.52 => ! [Ys2: list @ B] :
% 2.86/1.52 ( ( A2
% 2.86/1.52 = ( cons @ B @ Y2 @ Ys2 ) )
% 2.86/1.52 => ( ( R4 @ X3 @ Y2 )
% 2.86/1.52 => ~ ( listrelp @ A @ B @ R4 @ Xs2 @ Ys2 ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_118_list__collect__set__simps_I1_J,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType,F2: B > ( set @ A )] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( nil @ B ) )
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_119_list__collect__set__simps_I3_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > ( set @ A ),A4: B,L3: list @ B] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( cons @ B @ A4 @ L3 ) )
% 2.86/1.52 = ( sup_sup @ ( set @ A ) @ ( F2 @ A4 ) @ ( list_collect_set @ B @ A @ F2 @ L3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_120_set__notEmptyE,axiom,
% 2.86/1.52 ! [A: $tType,S: set @ A] :
% 2.86/1.52 ( ( S
% 2.86/1.52 != ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 => ~ ! [X3: A] :
% 2.86/1.52 ~ ( member @ A @ X3 @ S ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_121_memb__imp__not__empty,axiom,
% 2.86/1.52 ! [A: $tType,X: A,S: set @ A] :
% 2.86/1.52 ( ( member @ A @ X @ S )
% 2.86/1.52 => ( S
% 2.86/1.52 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_122_listrelp_OCons,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,R4: A > B > $o,X: A,Y: B,Xs: list @ A,Ys: list @ B] :
% 2.86/1.52 ( ( R4 @ X @ Y )
% 2.86/1.52 => ( ( listrelp @ A @ B @ R4 @ Xs @ Ys )
% 2.86/1.52 => ( listrelp @ A @ B @ R4 @ ( cons @ A @ X @ Xs ) @ ( cons @ B @ Y @ Ys ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_123_listrelp_ONil,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,R4: A > B > $o] : ( listrelp @ A @ B @ R4 @ ( nil @ A ) @ ( nil @ B ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_124_Un__empty,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 2.86/1.52 ( ( ( sup_sup @ ( set @ A ) @ A5 @ B4 )
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 = ( ( A5
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 & ( B4
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_125_sup__bot_Oright__neutral,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A] :
% 2.86/1.52 ( ( sup_sup @ A @ A4 @ ( bot_bot @ A ) )
% 2.86/1.52 = A4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_126_sup__bot_Oleft__neutral,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bounde1808546759up_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A] :
% 2.86/1.52 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A4 )
% 2.86/1.52 = A4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_127_sup__eq__bot__iff,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ( sup_sup @ A @ X @ Y )
% 2.86/1.52 = ( bot_bot @ A ) )
% 2.86/1.52 = ( ( X
% 2.86/1.52 = ( bot_bot @ A ) )
% 2.86/1.52 & ( Y
% 2.86/1.52 = ( bot_bot @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_128_empty__iff,axiom,
% 2.86/1.52 ! [A: $tType,C2: A] :
% 2.86/1.52 ~ ( member @ A @ C2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_129_all__not__in__conv,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ( ( ! [X4: A] :
% 2.86/1.52 ~ ( member @ A @ X4 @ A5 ) )
% 2.86/1.52 = ( A5
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_130_Collect__empty__eq,axiom,
% 2.86/1.52 ! [A: $tType,P: A > $o] :
% 2.86/1.52 ( ( ( collect @ A @ P )
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 = ( ! [X4: A] :
% 2.86/1.52 ~ ( P @ X4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_131_empty__Collect__eq,axiom,
% 2.86/1.52 ! [A: $tType,P: A > $o] :
% 2.86/1.52 ( ( ( bot_bot @ ( set @ A ) )
% 2.86/1.52 = ( collect @ A @ P ) )
% 2.86/1.52 = ( ! [X4: A] :
% 2.86/1.52 ~ ( P @ X4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_132_sup__apply,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.86/1.52 => ( ( sup_sup @ ( A > B ) )
% 2.86/1.52 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( sup_sup @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_133_sup_Oidem,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A] :
% 2.86/1.52 ( ( sup_sup @ A @ A4 @ A4 )
% 2.86/1.52 = A4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_134_sup__idem,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A] :
% 2.86/1.52 ( ( sup_sup @ A @ X @ X )
% 2.86/1.52 = X ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_135_sup_Oleft__idem,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A] :
% 2.86/1.52 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B3 ) )
% 2.86/1.52 = ( sup_sup @ A @ A4 @ B3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_136_sup__left__idem,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.86/1.52 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_137_sup_Oright__idem,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A] :
% 2.86/1.52 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B3 ) @ B3 )
% 2.86/1.52 = ( sup_sup @ A @ A4 @ B3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_138_UnCI,axiom,
% 2.86/1.52 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 2.86/1.52 ( ( ~ ( member @ A @ C2 @ B4 )
% 2.86/1.52 => ( member @ A @ C2 @ A5 ) )
% 2.86/1.52 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_139_Un__iff,axiom,
% 2.86/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.86/1.52 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.86/1.52 = ( ( member @ A @ C2 @ A5 )
% 2.86/1.52 | ( member @ A @ C2 @ B4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_140_bot__eq__sup__iff,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ( bot_bot @ A )
% 2.86/1.52 = ( sup_sup @ A @ X @ Y ) )
% 2.86/1.52 = ( ( X
% 2.86/1.52 = ( bot_bot @ A ) )
% 2.86/1.52 & ( Y
% 2.86/1.52 = ( bot_bot @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_141_bot__set__def,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bot_bot @ ( set @ A ) )
% 2.86/1.52 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_142_emptyE,axiom,
% 2.86/1.52 ! [A: $tType,A4: A] :
% 2.86/1.52 ~ ( member @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_143_equals0D,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,A4: A] :
% 2.86/1.52 ( ( A5
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 => ~ ( member @ A @ A4 @ A5 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_144_equals0I,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ( ! [Y2: A] :
% 2.86/1.52 ~ ( member @ A @ Y2 @ A5 )
% 2.86/1.52 => ( A5
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_145_ex__in__conv,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ( ( ? [X4: A] : ( member @ A @ X4 @ A5 ) )
% 2.86/1.52 = ( A5
% 2.86/1.52 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_146_not__psubset__empty,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ~ ( ord_less @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_147_inf__sup__aci_I8_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( lattice @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.86/1.52 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_148_inf__sup__aci_I7_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( lattice @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Z3: A] :
% 2.86/1.52 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) )
% 2.86/1.52 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_149_inf__sup__aci_I6_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( lattice @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Z3: A] :
% 2.86/1.52 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z3 )
% 2.86/1.52 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_150_inf__sup__aci_I5_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( lattice @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( sup_sup @ A )
% 2.86/1.52 = ( ^ [X4: A,Y3: A] : ( sup_sup @ A @ Y3 @ X4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_151_sup__fun__def,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.86/1.52 => ( ( sup_sup @ ( A > B ) )
% 2.86/1.52 = ( ^ [F3: A > B,G2: A > B,X4: A] : ( sup_sup @ B @ ( F3 @ X4 ) @ ( G2 @ X4 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_152_sup_Oassoc,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A,C2: A] :
% 2.86/1.52 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B3 ) @ C2 )
% 2.86/1.52 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_153_sup__assoc,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Z3: A] :
% 2.86/1.52 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z3 )
% 2.86/1.52 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_154_sup_Ocommute,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( sup_sup @ A )
% 2.86/1.52 = ( ^ [A6: A,B5: A] : ( sup_sup @ A @ B5 @ A6 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_155_sup__commute,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( sup_sup @ A )
% 2.86/1.52 = ( ^ [X4: A,Y3: A] : ( sup_sup @ A @ Y3 @ X4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_156_sup_Oleft__commute,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [B3: A,A4: A,C2: A] :
% 2.86/1.52 ( ( sup_sup @ A @ B3 @ ( sup_sup @ A @ A4 @ C2 ) )
% 2.86/1.52 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B3 @ C2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_157_sup__left__commute,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Z3: A] :
% 2.86/1.52 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z3 ) )
% 2.86/1.52 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_158_UnE,axiom,
% 2.86/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.86/1.52 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.86/1.52 => ( ~ ( member @ A @ C2 @ A5 )
% 2.86/1.52 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_159_UnI1,axiom,
% 2.86/1.52 ! [A: $tType,C2: A,A5: set @ A,B4: set @ A] :
% 2.86/1.52 ( ( member @ A @ C2 @ A5 )
% 2.86/1.52 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_160_UnI2,axiom,
% 2.86/1.52 ! [A: $tType,C2: A,B4: set @ A,A5: set @ A] :
% 2.86/1.52 ( ( member @ A @ C2 @ B4 )
% 2.86/1.52 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_161_bex__Un,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 2.86/1.52 ( ( ? [X4: A] :
% 2.86/1.52 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.86/1.52 & ( P @ X4 ) ) )
% 2.86/1.52 = ( ? [X4: A] :
% 2.86/1.52 ( ( member @ A @ X4 @ A5 )
% 2.86/1.52 & ( P @ X4 ) )
% 2.86/1.52 | ? [X4: A] :
% 2.86/1.52 ( ( member @ A @ X4 @ B4 )
% 2.86/1.52 & ( P @ X4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_162_ball__Un,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,P: A > $o] :
% 2.86/1.52 ( ( ! [X4: A] :
% 2.86/1.52 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.86/1.52 => ( P @ X4 ) ) )
% 2.86/1.52 = ( ! [X4: A] :
% 2.86/1.52 ( ( member @ A @ X4 @ A5 )
% 2.86/1.52 => ( P @ X4 ) )
% 2.86/1.52 & ! [X4: A] :
% 2.86/1.52 ( ( member @ A @ X4 @ B4 )
% 2.86/1.52 => ( P @ X4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_163_Un__assoc,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C3: set @ A] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) @ C3 )
% 2.86/1.52 = ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_164_Un__absorb,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ A5 )
% 2.86/1.52 = A5 ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_165_Un__commute,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) )
% 2.86/1.52 = ( ^ [A7: set @ A,B6: set @ A] : ( sup_sup @ ( set @ A ) @ B6 @ A7 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_166_Un__left__absorb,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ A5 @ B4 ) )
% 2.86/1.52 = ( sup_sup @ ( set @ A ) @ A5 @ B4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_167_Un__left__commute,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C3: set @ A] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( sup_sup @ ( set @ A ) @ B4 @ C3 ) )
% 2.86/1.52 = ( sup_sup @ ( set @ A ) @ B4 @ ( sup_sup @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_168_sup_Ostrict__coboundedI2,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [C2: A,B3: A,A4: A] :
% 2.86/1.52 ( ( ord_less @ A @ C2 @ B3 )
% 2.86/1.52 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_169_sup_Ostrict__coboundedI1,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [C2: A,A4: A,B3: A] :
% 2.86/1.52 ( ( ord_less @ A @ C2 @ A4 )
% 2.86/1.52 => ( ord_less @ A @ C2 @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_170_sup_Ostrict__order__iff,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( ord_less @ A )
% 2.86/1.52 = ( ^ [B5: A,A6: A] :
% 2.86/1.52 ( ( A6
% 2.86/1.52 = ( sup_sup @ A @ A6 @ B5 ) )
% 2.86/1.52 & ( A6 != B5 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_171_sup_Ostrict__boundedE,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [B3: A,C2: A,A4: A] :
% 2.86/1.52 ( ( ord_less @ A @ ( sup_sup @ A @ B3 @ C2 ) @ A4 )
% 2.86/1.52 => ~ ( ( ord_less @ A @ B3 @ A4 )
% 2.86/1.52 => ~ ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_172_less__supI2,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,B3: A,A4: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ B3 )
% 2.86/1.52 => ( ord_less @ A @ X @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_173_less__supI1,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,A4: A,B3: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ A4 )
% 2.86/1.52 => ( ord_less @ A @ X @ ( sup_sup @ A @ A4 @ B3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_174_sup__bot__left,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A] :
% 2.86/1.52 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 2.86/1.52 = X ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_175_sup__bot__right,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bounded_lattice_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A] :
% 2.86/1.52 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 2.86/1.52 = X ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_176_Un__empty__left,axiom,
% 2.86/1.52 ! [A: $tType,B4: set @ A] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B4 )
% 2.86/1.52 = B4 ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_177_Un__empty__right,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A] :
% 2.86/1.52 ( ( sup_sup @ ( set @ A ) @ A5 @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 = A5 ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_178_bot__apply,axiom,
% 2.86/1.52 ! [C: $tType,D: $tType] :
% 2.86/1.52 ( ( bot @ C @ ( type2 @ C ) )
% 2.86/1.52 => ( ( bot_bot @ ( D > C ) )
% 2.86/1.52 = ( ^ [X4: D] : ( bot_bot @ C ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_179_bot_Onot__eq__extremum,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A] :
% 2.86/1.52 ( ( A4
% 2.86/1.52 != ( bot_bot @ A ) )
% 2.86/1.52 = ( ord_less @ A @ ( bot_bot @ A ) @ A4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_180_bot_Oextremum__strict,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A] :
% 2.86/1.52 ~ ( ord_less @ A @ A4 @ ( bot_bot @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_181_Set_Ois__empty__def,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( is_empty @ A )
% 2.86/1.52 = ( ^ [A7: set @ A] :
% 2.86/1.52 ( A7
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_182_psubset__trans,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C3: set @ A] :
% 2.86/1.52 ( ( ord_less @ ( set @ A ) @ A5 @ B4 )
% 2.86/1.52 => ( ( ord_less @ ( set @ A ) @ B4 @ C3 )
% 2.86/1.52 => ( ord_less @ ( set @ A ) @ A5 @ C3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_183_psubsetD,axiom,
% 2.86/1.52 ! [A: $tType,A5: set @ A,B4: set @ A,C2: A] :
% 2.86/1.52 ( ( ord_less @ ( set @ A ) @ A5 @ B4 )
% 2.86/1.52 => ( ( member @ A @ C2 @ A5 )
% 2.86/1.52 => ( member @ A @ C2 @ B4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_184_dual__order_Ostrict__implies__not__eq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [B3: A,A4: A] :
% 2.86/1.52 ( ( ord_less @ A @ B3 @ A4 )
% 2.86/1.52 => ( A4 != B3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_185_order_Ostrict__implies__not__eq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ( A4 != B3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_186_not__less__iff__gr__or__eq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.86/1.52 = ( ( ord_less @ A @ Y @ X )
% 2.86/1.52 | ( X = Y ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_187_dual__order_Ostrict__trans,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [B3: A,A4: A,C2: A] :
% 2.86/1.52 ( ( ord_less @ A @ B3 @ A4 )
% 2.86/1.52 => ( ( ord_less @ A @ C2 @ B3 )
% 2.86/1.52 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_188_less__imp__not__less,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_189_order_Ostrict__trans,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A,C2: A] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ( ( ord_less @ A @ B3 @ C2 )
% 2.86/1.52 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_190_dual__order_Oirrefl,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A] :
% 2.86/1.52 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_191_linorder__cases,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ~ ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( ( X != Y )
% 2.86/1.52 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_192_less__imp__triv,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,P: $o] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( ( ord_less @ A @ Y @ X )
% 2.86/1.52 => P ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_193_less__imp__not__eq2,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( Y != X ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_194_antisym__conv3,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [Y: A,X: A] :
% 2.86/1.52 ( ~ ( ord_less @ A @ Y @ X )
% 2.86/1.52 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.86/1.52 = ( X = Y ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_195_less__induct,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [P: A > $o,A4: A] :
% 2.86/1.52 ( ! [X3: A] :
% 2.86/1.52 ( ! [Y4: A] :
% 2.86/1.52 ( ( ord_less @ A @ Y4 @ X3 )
% 2.86/1.52 => ( P @ Y4 ) )
% 2.86/1.52 => ( P @ X3 ) )
% 2.86/1.52 => ( P @ A4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_196_less__not__sym,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_197_less__imp__not__eq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( X != Y ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_198_dual__order_Oasym,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [B3: A,A4: A] :
% 2.86/1.52 ( ( ord_less @ A @ B3 @ A4 )
% 2.86/1.52 => ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_199_ord__less__eq__trans,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A,C2: A] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ( ( B3 = C2 )
% 2.86/1.52 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_200_ord__eq__less__trans,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( ord @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A,C2: A] :
% 2.86/1.52 ( ( A4 = B3 )
% 2.86/1.52 => ( ( ord_less @ A @ B3 @ C2 )
% 2.86/1.52 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_201_less__irrefl,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A] :
% 2.86/1.52 ~ ( ord_less @ A @ X @ X ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_202_less__linear,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 | ( X = Y )
% 2.86/1.52 | ( ord_less @ A @ Y @ X ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_203_less__trans,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A,Z3: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( ( ord_less @ A @ Y @ Z3 )
% 2.86/1.52 => ( ord_less @ A @ X @ Z3 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_204_less__asym_H,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_205_less__asym,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_206_less__imp__neq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( X != Y ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_207_dense,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( dense_order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ? [Z2: A] :
% 2.86/1.52 ( ( ord_less @ A @ X @ Z2 )
% 2.86/1.52 & ( ord_less @ A @ Z2 @ Y ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_208_order_Oasym,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( order @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [A4: A,B3: A] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_209_neq__iff,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( X != Y )
% 2.86/1.52 = ( ( ord_less @ A @ X @ Y )
% 2.86/1.52 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_210_neqE,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A,Y: A] :
% 2.86/1.52 ( ( X != Y )
% 2.86/1.52 => ( ~ ( ord_less @ A @ X @ Y )
% 2.86/1.52 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_211_gt__ex,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( no_top @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A] :
% 2.86/1.52 ? [X12: A] : ( ord_less @ A @ X @ X12 ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_212_lt__ex,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( no_bot @ A @ ( type2 @ A ) )
% 2.86/1.52 => ! [X: A] :
% 2.86/1.52 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_213_order__less__subst2,axiom,
% 2.86/1.52 ! [A: $tType,C: $tType] :
% 2.86/1.52 ( ( ( order @ C @ ( type2 @ C ) )
% 2.86/1.52 & ( order @ A @ ( type2 @ A ) ) )
% 2.86/1.52 => ! [A4: A,B3: A,F2: A > C,C2: C] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ( ( ord_less @ C @ ( F2 @ B3 ) @ C2 )
% 2.86/1.52 => ( ! [X3: A,Y2: A] :
% 2.86/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 2.86/1.52 => ( ord_less @ C @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 2.86/1.52 => ( ord_less @ C @ ( F2 @ A4 ) @ C2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_214_order__less__subst1,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType] :
% 2.86/1.52 ( ( ( order @ B @ ( type2 @ B ) )
% 2.86/1.52 & ( order @ A @ ( type2 @ A ) ) )
% 2.86/1.52 => ! [A4: A,F2: B > A,B3: B,C2: B] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ ( F2 @ B3 ) )
% 2.86/1.52 => ( ( ord_less @ B @ B3 @ C2 )
% 2.86/1.52 => ( ! [X3: B,Y2: B] :
% 2.86/1.52 ( ( ord_less @ B @ X3 @ Y2 )
% 2.86/1.52 => ( ord_less @ A @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 2.86/1.52 => ( ord_less @ A @ A4 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_215_ord__less__eq__subst,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType] :
% 2.86/1.52 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.52 & ( ord @ A @ ( type2 @ A ) ) )
% 2.86/1.52 => ! [A4: A,B3: A,F2: A > B,C2: B] :
% 2.86/1.52 ( ( ord_less @ A @ A4 @ B3 )
% 2.86/1.52 => ( ( ( F2 @ B3 )
% 2.86/1.52 = C2 )
% 2.86/1.52 => ( ! [X3: A,Y2: A] :
% 2.86/1.52 ( ( ord_less @ A @ X3 @ Y2 )
% 2.86/1.52 => ( ord_less @ B @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 2.86/1.52 => ( ord_less @ B @ ( F2 @ A4 ) @ C2 ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_216_ord__eq__less__subst,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType] :
% 2.86/1.52 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.86/1.52 & ( ord @ A @ ( type2 @ A ) ) )
% 2.86/1.52 => ! [A4: A,F2: B > A,B3: B,C2: B] :
% 2.86/1.52 ( ( A4
% 2.86/1.52 = ( F2 @ B3 ) )
% 2.86/1.52 => ( ( ord_less @ B @ B3 @ C2 )
% 2.86/1.52 => ( ! [X3: B,Y2: B] :
% 2.86/1.52 ( ( ord_less @ B @ X3 @ Y2 )
% 2.86/1.52 => ( ord_less @ A @ ( F2 @ X3 ) @ ( F2 @ Y2 ) ) )
% 2.86/1.52 => ( ord_less @ A @ A4 @ ( F2 @ C2 ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_217_bot__fun__def,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( bot @ B @ ( type2 @ B ) )
% 2.86/1.52 => ( ( bot_bot @ ( A > B ) )
% 2.86/1.52 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_218_bot__empty__eq,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( bot_bot @ ( A > $o ) )
% 2.86/1.52 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_219_Collect__empty__eq__bot,axiom,
% 2.86/1.52 ! [A: $tType,P: A > $o] :
% 2.86/1.52 ( ( ( collect @ A @ P )
% 2.86/1.52 = ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 = ( P
% 2.86/1.52 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_220_map__tailrec__def,axiom,
% 2.86/1.52 ! [B: $tType,A: $tType] :
% 2.86/1.52 ( ( map_tailrec @ A @ B )
% 2.86/1.52 = ( ^ [F3: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F3 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_221_rev__is__rev__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ( rev @ A @ Xs )
% 2.86/1.52 = ( rev @ A @ Ys ) )
% 2.86/1.52 = ( Xs = Ys ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_222_rev__rev__ident,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A] :
% 2.86/1.52 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 2.86/1.52 = Xs ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_223_rev__is__Nil__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A] :
% 2.86/1.52 ( ( ( rev @ A @ Xs )
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_224_Nil__is__rev__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A] :
% 2.86/1.52 ( ( ( nil @ A )
% 2.86/1.52 = ( rev @ A @ Xs ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_225_singleton__rev__conv,axiom,
% 2.86/1.52 ! [A: $tType,X: A,Xs: list @ A] :
% 2.86/1.52 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 2.86/1.52 = ( rev @ A @ Xs ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_226_rev__singleton__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,X: A] :
% 2.86/1.52 ( ( ( rev @ A @ Xs )
% 2.86/1.52 = ( cons @ A @ X @ ( nil @ A ) ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_227_rev_Osimps_I1_J,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( rev @ A @ ( nil @ A ) )
% 2.86/1.52 = ( nil @ A ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_228_rev__map,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.86/1.52 ( ( rev @ A @ ( map @ B @ A @ F2 @ Xs ) )
% 2.86/1.52 = ( map @ B @ A @ F2 @ ( rev @ B @ Xs ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_229_rev__swap,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ( rev @ A @ Xs )
% 2.86/1.52 = Ys )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( rev @ A @ Ys ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_230_list__collect__set__map__simps_I4_J,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,C: $tType,F2: B > ( set @ A ),X: C > B,L3: list @ C,L4: list @ C] :
% 2.86/1.52 ( ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ ( append @ C @ L3 @ L4 ) ) )
% 2.86/1.52 = ( sup_sup @ ( set @ A ) @ ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ L3 ) ) @ ( list_collect_set @ B @ A @ F2 @ ( map @ C @ B @ X @ L4 ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_231_sorted__list__of__set__empty,axiom,
% 2.86/1.52 ! [A: $tType] :
% 2.86/1.52 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.52 => ( ( linord467138063of_set @ A @ ( bot_bot @ ( set @ A ) ) )
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_232_append__assoc,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.86/1.52 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs )
% 2.86/1.52 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_233_append__same__eq,axiom,
% 2.86/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.86/1.52 ( ( ( append @ A @ Ys @ Xs )
% 2.86/1.52 = ( append @ A @ Zs @ Xs ) )
% 2.86/1.52 = ( Ys = Zs ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_234_same__append__eq,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 2.86/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.86/1.52 = ( append @ A @ Xs @ Zs ) )
% 2.86/1.52 = ( Ys = Zs ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_235_append__Nil2,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A] :
% 2.86/1.52 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.86/1.52 = Xs ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_236_append__self__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.86/1.52 = Xs )
% 2.86/1.52 = ( Ys
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_237_self__append__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( Xs
% 2.86/1.52 = ( append @ A @ Xs @ Ys ) )
% 2.86/1.52 = ( Ys
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_238_append__self__conv2,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.86/1.52 = Ys )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_239_self__append__conv2,axiom,
% 2.86/1.52 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.86/1.52 ( ( Ys
% 2.86/1.52 = ( append @ A @ Xs @ Ys ) )
% 2.86/1.52 = ( Xs
% 2.86/1.52 = ( nil @ A ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_240_Nil__is__append__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ( nil @ A )
% 2.86/1.52 = ( append @ A @ Xs @ Ys ) )
% 2.86/1.52 = ( ( Xs
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( Ys
% 2.86/1.52 = ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_241_append__is__Nil__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( ( append @ A @ Xs @ Ys )
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 = ( ( Xs
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( Ys
% 2.86/1.52 = ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_242_map__append,axiom,
% 2.86/1.52 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Ys: list @ B] :
% 2.86/1.52 ( ( map @ B @ A @ F2 @ ( append @ B @ Xs @ Ys ) )
% 2.86/1.52 = ( append @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( map @ B @ A @ F2 @ Ys ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_243_rev__append,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.86/1.52 ( ( rev @ A @ ( append @ A @ Xs @ Ys ) )
% 2.86/1.52 = ( append @ A @ ( rev @ A @ Ys ) @ ( rev @ A @ Xs ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_244_append1__eq__conv,axiom,
% 2.86/1.52 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.86/1.52 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.86/1.52 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.86/1.52 = ( ( Xs = Ys )
% 2.86/1.52 & ( X = Y ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_245_list__ee__eq__leel_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,E1: A,E2: A,L1: list @ A,E12: A,E22: A,L2: list @ A] :
% 2.86/1.52 ( ( ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) )
% 2.86/1.52 = ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) ) )
% 2.86/1.52 = ( ( L1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( E1 = E12 )
% 2.86/1.52 & ( E2 = E22 )
% 2.86/1.52 & ( L2
% 2.86/1.52 = ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_246_list__ee__eq__leel_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,L1: list @ A,E12: A,E22: A,L2: list @ A,E1: A,E2: A] :
% 2.86/1.52 ( ( ( append @ A @ L1 @ ( cons @ A @ E12 @ ( cons @ A @ E22 @ L2 ) ) )
% 2.86/1.52 = ( cons @ A @ E1 @ ( cons @ A @ E2 @ ( nil @ A ) ) ) )
% 2.86/1.52 = ( ( L1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( E1 = E12 )
% 2.86/1.52 & ( E2 = E22 )
% 2.86/1.52 & ( L2
% 2.86/1.52 = ( nil @ A ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_247_list__se__match_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,L1: list @ A,L2: list @ A,A4: A] :
% 2.86/1.52 ( ( L1
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ( ( append @ A @ L1 @ L2 )
% 2.86/1.52 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 2.86/1.52 = ( ( L1
% 2.86/1.52 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 2.86/1.52 & ( L2
% 2.86/1.52 = ( nil @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_248_list__se__match_I2_J,axiom,
% 2.86/1.52 ! [A: $tType,L2: list @ A,L1: list @ A,A4: A] :
% 2.86/1.52 ( ( L2
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ( ( append @ A @ L1 @ L2 )
% 2.86/1.52 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 2.86/1.52 = ( ( L1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( L2
% 2.86/1.52 = ( cons @ A @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_249_list__se__match_I3_J,axiom,
% 2.86/1.52 ! [A: $tType,L1: list @ A,A4: A,L2: list @ A] :
% 2.86/1.52 ( ( L1
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ( ( cons @ A @ A4 @ ( nil @ A ) )
% 2.86/1.52 = ( append @ A @ L1 @ L2 ) )
% 2.86/1.52 = ( ( L1
% 2.86/1.52 = ( cons @ A @ A4 @ ( nil @ A ) ) )
% 2.86/1.52 & ( L2
% 2.86/1.52 = ( nil @ A ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_250_list__se__match_I4_J,axiom,
% 2.86/1.52 ! [A: $tType,L2: list @ A,A4: A,L1: list @ A] :
% 2.86/1.52 ( ( L2
% 2.86/1.52 != ( nil @ A ) )
% 2.86/1.52 => ( ( ( cons @ A @ A4 @ ( nil @ A ) )
% 2.86/1.52 = ( append @ A @ L1 @ L2 ) )
% 2.86/1.52 = ( ( L1
% 2.86/1.52 = ( nil @ A ) )
% 2.86/1.52 & ( L2
% 2.86/1.52 = ( cons @ A @ A4 @ ( nil @ A ) ) ) ) ) ) ).
% 2.86/1.52
% 2.86/1.52 thf(fact_251_list__e__eq__lel_I1_J,axiom,
% 2.86/1.52 ! [A: $tType,E3: A,L1: list @ A,E4: A,L2: list @ A] :
% 2.86/1.52 ( ( ( cons @ A @ E3 @ ( nil @ A ) )
% 2.86/1.52 = ( append @ A @ L1 @ ( cons @ A @ E4 @ L2 ) ) )
% 2.86/1.53 = ( ( L1
% 2.86/1.53 = ( nil @ A ) )
% 2.86/1.53 & ( E4 = E3 )
% 2.86/1.53 & ( L2
% 2.86/1.53 = ( nil @ A ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(fact_252_list__e__eq__lel_I2_J,axiom,
% 2.86/1.53 ! [A: $tType,L1: list @ A,E4: A,L2: list @ A,E3: A] :
% 2.86/1.53 ( ( ( append @ A @ L1 @ ( cons @ A @ E4 @ L2 ) )
% 2.86/1.53 = ( cons @ A @ E3 @ ( nil @ A ) ) )
% 2.86/1.53 = ( ( L1
% 2.86/1.53 = ( nil @ A ) )
% 2.86/1.53 & ( E4 = E3 )
% 2.86/1.53 & ( L2
% 2.86/1.53 = ( nil @ A ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(fact_253_list__collect__set__simps_I4_J,axiom,
% 2.86/1.53 ! [A: $tType,B: $tType,F2: B > ( set @ A ),L3: list @ B,L4: list @ B] :
% 2.86/1.53 ( ( list_collect_set @ B @ A @ F2 @ ( append @ B @ L3 @ L4 ) )
% 2.86/1.53 = ( sup_sup @ ( set @ A ) @ ( list_collect_set @ B @ A @ F2 @ L3 ) @ ( list_collect_set @ B @ A @ F2 @ L4 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(fact_254_bind__simps_I2_J,axiom,
% 2.86/1.53 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F2: B > ( list @ A )] :
% 2.86/1.53 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F2 )
% 2.86/1.53 = ( append @ A @ ( F2 @ X ) @ ( bind @ B @ A @ Xs @ F2 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(subcl_Orderings_Olinorder___HOL_Otype,axiom,
% 2.86/1.53 ! [A: $tType] :
% 2.86/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.53 => ( type @ A @ ( type2 @ A ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(subcl_Orderings_Olinorder___Orderings_Oord,axiom,
% 2.86/1.53 ! [A: $tType] :
% 2.86/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.53 => ( ord @ A @ ( type2 @ A ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(subcl_Orderings_Olinorder___Orderings_Oorder,axiom,
% 2.86/1.53 ! [A: $tType] :
% 2.86/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.53 => ( order @ A @ ( type2 @ A ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(subcl_Orderings_Olinorder___Orderings_Opreorder,axiom,
% 2.86/1.53 ! [A: $tType] :
% 2.86/1.53 ( ( linorder @ A @ ( type2 @ A ) )
% 2.86/1.53 => ( preorder @ A @ ( type2 @ A ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.86/1.53 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.86/1.53 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( bounded_lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( bounde1808546759up_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Lattices_Obounded__lattice__bot,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( bounded_lattice @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( bounded_lattice_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( order_bot @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( order_bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( lattice @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( lattice @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( order @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Orderings_Oord,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_fun___Orderings_Obot,axiom,
% 2.86/1.53 ! [A8: $tType,A9: $tType] :
% 2.86/1.53 ( ( bot @ A9 @ ( type2 @ A9 ) )
% 2.86/1.53 => ( bot @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_3,axiom,
% 2.86/1.53 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Lattices_Obounded__lattice__bot_4,axiom,
% 2.86/1.53 ! [A8: $tType] : ( bounded_lattice_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_5,axiom,
% 2.86/1.53 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder__bot_6,axiom,
% 2.86/1.53 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Opreorder_7,axiom,
% 2.86/1.53 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Lattices_Olattice_8,axiom,
% 2.86/1.53 ! [A8: $tType] : ( lattice @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 2.86/1.53 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 2.86/1.53 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 2.86/1.53 ! [A8: $tType] : ( bot @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 2.86/1.53 bounde1808546759up_bot @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__bot_13,axiom,
% 2.86/1.53 bounded_lattice_bot @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_14,axiom,
% 2.86/1.53 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15,axiom,
% 2.86/1.53 order_bot @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 2.86/1.53 preorder @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.86/1.53 linorder @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Lattices_Olattice_17,axiom,
% 2.86/1.53 lattice @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_18,axiom,
% 2.86/1.53 order @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Oord_19,axiom,
% 2.86/1.53 ord @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tcon_HOL_Obool___Orderings_Obot_20,axiom,
% 2.86/1.53 bot @ $o @ ( type2 @ $o ) ).
% 2.86/1.53
% 2.86/1.53 thf(tfree_0,hypothesis,
% 2.86/1.53 linorder @ a @ ( type2 @ a ) ).
% 2.86/1.53
% 2.86/1.53 thf(conj_0,conjecture,
% 2.86/1.53 ( ( ( cons @ a @ x1 @ l1 )
% 2.86/1.53 = l2a )
% 2.86/1.53 = ( ( sorted1061247458sorted @ a @ ( cons @ a @ x1 @ l1 ) @ l2a )
% 2.86/1.53 & ( sorted1061247458sorted @ a @ l2a @ ( cons @ a @ x1 @ l1 ) ) ) ) ).
% 2.86/1.53 ------------------------
% 2.86/1.55 % (2931)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2830 for (2999ds/183Mi)
% 2.86/1.55 % (2934)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2830 for (2999ds/2Mi)
% 2.86/1.55 % (2933)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_2830 for (2999ds/27Mi)
% 2.86/1.55 % (2935)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_2830 for (2999ds/2Mi)
% 2.86/1.55 % (2937)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2830 for (2999ds/18Mi)
% 2.86/1.55 % (2932)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_2830 for (2999ds/4Mi)
% 2.86/1.55 % (2936)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_2830 for (2999ds/275Mi)
% 2.86/1.55 % (2934)Instruction limit reached!
% 2.86/1.55 % (2934)------------------------------
% 2.86/1.55 % (2934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.55 % (2934)Termination reason: Unknown
% 2.86/1.55 % (2935)Instruction limit reached!
% 2.86/1.55 % (2935)------------------------------
% 2.86/1.55 % (2935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.55 % (2934)Termination phase: shuffling
% 2.86/1.55
% 2.86/1.55 % (2934)Memory used [KB]: 1407
% 2.86/1.55 % (2934)Time elapsed: 0.003 s
% 2.86/1.55 % (2934)Instructions burned: 3 (million)
% 2.86/1.55 % (2934)------------------------------
% 2.86/1.55 % (2934)------------------------------
% 2.86/1.55 % (2935)Termination reason: Unknown
% 2.86/1.55 % (2935)Termination phase: shuffling
% 2.86/1.55
% 2.86/1.55 % (2935)Memory used [KB]: 1407
% 2.86/1.55 % (2935)Time elapsed: 0.003 s
% 2.86/1.55 % (2935)Instructions burned: 3 (million)
% 2.86/1.55 % (2935)------------------------------
% 2.86/1.55 % (2935)------------------------------
% 2.86/1.55 % (2932)Instruction limit reached!
% 2.86/1.55 % (2932)------------------------------
% 2.86/1.55 % (2932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.55 % (2932)Termination reason: Unknown
% 2.86/1.55 % (2932)Termination phase: shuffling
% 2.86/1.55
% 2.86/1.55 % (2932)Memory used [KB]: 1535
% 2.86/1.55 % (2932)Time elapsed: 0.004 s
% 2.86/1.55 % (2932)Instructions burned: 5 (million)
% 2.86/1.55 % (2932)------------------------------
% 2.86/1.55 % (2932)------------------------------
% 2.86/1.56 % (2937)Instruction limit reached!
% 2.86/1.56 % (2937)------------------------------
% 2.86/1.56 % (2937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.56 % (2937)Termination reason: Unknown
% 2.86/1.56 % (2937)Termination phase: shuffling
% 2.86/1.56
% 2.86/1.56 % (2937)Memory used [KB]: 1791
% 2.86/1.56 % (2937)Time elapsed: 0.011 s
% 2.86/1.56 % (2937)Instructions burned: 19 (million)
% 2.86/1.56 % (2937)------------------------------
% 2.86/1.56 % (2937)------------------------------
% 2.86/1.56 % (2933)Instruction limit reached!
% 2.86/1.56 % (2933)------------------------------
% 2.86/1.56 % (2933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.56 % (2933)Termination reason: Unknown
% 2.86/1.56 % (2933)Termination phase: shuffling
% 2.86/1.56
% 2.86/1.56 % (2933)Memory used [KB]: 2046
% 2.86/1.56 % (2933)Time elapsed: 0.015 s
% 2.86/1.56 % (2933)Instructions burned: 27 (million)
% 2.86/1.56 % (2933)------------------------------
% 2.86/1.56 % (2933)------------------------------
% 2.86/1.57 % (2939)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_2830 for (2999ds/37Mi)
% 2.86/1.57 % (2938)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2830 for (2999ds/3Mi)
% 2.86/1.57 % (2940)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_2830 for (2999ds/15Mi)
% 2.86/1.57 % (2938)Instruction limit reached!
% 2.86/1.57 % (2938)------------------------------
% 2.86/1.57 % (2938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.57 % (2938)Termination reason: Unknown
% 2.86/1.57 % (2938)Termination phase: shuffling
% 2.86/1.57
% 2.86/1.57 % (2938)Memory used [KB]: 1407
% 2.86/1.57 % (2938)Time elapsed: 0.003 s
% 2.86/1.57 % (2938)Instructions burned: 3 (million)
% 2.86/1.57 % (2938)------------------------------
% 2.86/1.57 % (2938)------------------------------
% 2.86/1.58 % (2941)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_2830 for (2999ds/3Mi)
% 2.86/1.58 % (2940)Instruction limit reached!
% 2.86/1.58 % (2940)------------------------------
% 2.86/1.58 % (2940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.58 % (2940)Termination reason: Unknown
% 2.86/1.58 % (2940)Termination phase: shuffling
% 2.86/1.58
% 2.86/1.58 % (2940)Memory used [KB]: 1663
% 2.86/1.58 % (2940)Time elapsed: 0.009 s
% 2.86/1.58 % (2940)Instructions burned: 15 (million)
% 2.86/1.58 % (2940)------------------------------
% 2.86/1.58 % (2940)------------------------------
% 2.86/1.58 % (2941)Instruction limit reached!
% 2.86/1.58 % (2941)------------------------------
% 2.86/1.58 % (2941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.58 % (2941)Termination reason: Unknown
% 2.86/1.58 % (2941)Termination phase: shuffling
% 2.86/1.58
% 2.86/1.58 % (2941)Memory used [KB]: 1407
% 2.86/1.58 % (2941)Time elapsed: 0.003 s
% 2.86/1.58 % (2941)Instructions burned: 4 (million)
% 2.86/1.58 % (2941)------------------------------
% 2.86/1.58 % (2941)------------------------------
% 2.86/1.58 % (2942)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_2830 for (2999ds/1041Mi)
% 2.86/1.59 % (2939)Instruction limit reached!
% 2.86/1.59 % (2939)------------------------------
% 2.86/1.59 % (2939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.59 % (2939)Termination reason: Unknown
% 2.86/1.59 % (2939)Termination phase: shuffling
% 2.86/1.59
% 2.86/1.59 % (2939)Memory used [KB]: 2174
% 2.86/1.59 % (2939)Time elapsed: 0.018 s
% 2.86/1.59 % (2939)Instructions burned: 37 (million)
% 2.86/1.59 % (2939)------------------------------
% 2.86/1.59 % (2939)------------------------------
% 2.86/1.59 % (2943)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2830 for (2999ds/7Mi)
% 2.86/1.59 % (2943)Instruction limit reached!
% 2.86/1.59 % (2943)------------------------------
% 2.86/1.59 % (2943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.59 % (2943)Termination reason: Unknown
% 2.86/1.59 % (2943)Termination phase: shuffling
% 2.86/1.59
% 2.86/1.59 % (2943)Memory used [KB]: 1535
% 2.86/1.59 % (2943)Time elapsed: 0.005 s
% 2.86/1.59 % (2943)Instructions burned: 8 (million)
% 2.86/1.59 % (2943)------------------------------
% 2.86/1.59 % (2943)------------------------------
% 2.86/1.59 % (2945)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_2830 for (2999ds/3Mi)
% 2.86/1.59 % (2944)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2830 for (2999ds/16Mi)
% 2.86/1.60 % (2945)Instruction limit reached!
% 2.86/1.60 % (2945)------------------------------
% 2.86/1.60 % (2945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.60 % (2945)Termination reason: Unknown
% 2.86/1.60 % (2945)Termination phase: shuffling
% 2.86/1.60
% 2.86/1.60 % (2945)Memory used [KB]: 1407
% 2.86/1.60 % (2945)Time elapsed: 0.003 s
% 2.86/1.60 % (2945)Instructions burned: 4 (million)
% 2.86/1.60 % (2945)------------------------------
% 2.86/1.60 % (2945)------------------------------
% 2.90/1.60 % (2931)Instruction limit reached!
% 2.90/1.60 % (2931)------------------------------
% 2.90/1.60 % (2931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (2931)Termination reason: Unknown
% 2.90/1.60 % (2931)Termination phase: Saturation
% 2.90/1.60
% 2.90/1.60 % (2931)Memory used [KB]: 7547
% 2.90/1.60 % (2931)Time elapsed: 0.054 s
% 2.90/1.60 % (2931)Instructions burned: 184 (million)
% 2.90/1.60 % (2931)------------------------------
% 2.90/1.60 % (2931)------------------------------
% 2.90/1.60 % (2946)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_2830 for (2999ds/3Mi)
% 2.90/1.60 % (2936)First to succeed.
% 2.90/1.60 % (2946)Instruction limit reached!
% 2.90/1.60 % (2946)------------------------------
% 2.90/1.60 % (2946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (2946)Termination reason: Unknown
% 2.90/1.60 % (2946)Termination phase: shuffling
% 2.90/1.60
% 2.90/1.60 % (2946)Memory used [KB]: 1407
% 2.90/1.60 % (2946)Time elapsed: 0.003 s
% 2.90/1.60 % (2946)Instructions burned: 3 (million)
% 2.90/1.60 % (2946)------------------------------
% 2.90/1.60 % (2946)------------------------------
% 2.90/1.60 % (2944)Instruction limit reached!
% 2.90/1.60 % (2944)------------------------------
% 2.90/1.60 % (2944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (2944)Termination reason: Unknown
% 2.90/1.60 % (2944)Termination phase: shuffling
% 2.90/1.60
% 2.90/1.60 % (2944)Memory used [KB]: 1791
% 2.90/1.60 % (2944)Time elapsed: 0.010 s
% 2.90/1.60 % (2944)Instructions burned: 17 (million)
% 2.90/1.60 % (2944)------------------------------
% 2.90/1.60 % (2944)------------------------------
% 2.90/1.61 % (2936)Refutation found. Thanks to Tanya!
% 2.90/1.61 % SZS status Theorem for DTF2THF_2830
% 2.90/1.61 % SZS output start Proof for DTF2THF_2830
% 2.90/1.61 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.90/1.61 thf(type_def_7, type, list: ($tType) > $tType).
% 2.90/1.61 thf(type_def_8, type, set: ($tType) > $tType).
% 2.90/1.61 thf(type_def_9, type, a: $tType).
% 2.90/1.61 thf(func_def_0, type, list: ($tType) > $tType).
% 2.90/1.61 thf(func_def_1, type, set: ($tType) > $tType).
% 2.90/1.61 thf(func_def_2, type, itself: ($tType) > $tType).
% 2.90/1.61 thf(func_def_3, type, a: $tType).
% 2.90/1.61 thf(func_def_4, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_6, type, bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_7, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_8, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_9, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_10, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_11, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_12, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_13, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_14, type, order_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_15, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_16, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_17, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_18, type, bounded_lattice_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_19, type, bounde1808546759up_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.90/1.61 thf(func_def_20, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > X0 > list @ X0 > X1)).
% 2.90/1.61 thf(func_def_21, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.90/1.61 thf(func_def_22, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_23, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 2.90/1.61 thf(func_def_24, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_25, type, linord467138063of_set: !>[X0: $tType]:(set @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_26, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_27, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.90/1.61 thf(func_def_28, type, map: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 2.90/1.61 thf(func_def_29, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_30, type, listrelp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > list @ X0 > list @ X1 > $o)).
% 2.90/1.61 thf(func_def_31, type, map_tailrec: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 2.90/1.61 thf(func_def_32, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1 > list @ X1)).
% 2.90/1.61 thf(func_def_33, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_34, type, ord_lexordp_eq: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_35, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.90/1.61 thf(func_def_36, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_37, type, splice: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_38, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.90/1.61 thf(func_def_39, type, list_c659805718roduct: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.90/1.61 thf(func_def_40, type, list_collect_set: !>[X0: $tType, X1: $tType]:((X0 > set @ X1) > list @ X0 > set @ X1)).
% 2.90/1.61 thf(func_def_41, type, merge: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_42, type, merge_list: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_43, type, revg: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_44, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.90/1.61 thf(func_def_45, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.90/1.61 thf(func_def_46, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.90/1.61 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.90/1.61 thf(func_def_48, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 2.90/1.61 thf(func_def_49, type, sorted1267110213sorted: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_50, type, sorted2037043510sorted: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_51, type, sorted1061247458sorted: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_52, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.90/1.61 thf(func_def_53, type, l1: list @ a).
% 2.90/1.61 thf(func_def_54, type, l2a: list @ a).
% 2.90/1.61 thf(func_def_55, type, x1: a).
% 2.90/1.61 thf(func_def_72, type, sP0: !>[X0: $tType]:($o > list @ X0 > list @ X0 > X0 > X0 > $o)).
% 2.90/1.61 thf(func_def_73, type, sP1: !>[X0: $tType]:($o > list @ X0 > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_74, type, sP2: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_75, type, sP3: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > $o)).
% 2.90/1.61 thf(func_def_76, type, sP4: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.90/1.61 thf(func_def_77, type, sK5: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.90/1.61 thf(func_def_78, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_79, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.90/1.61 thf(func_def_80, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_81, type, sK9: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_82, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_83, type, sK11: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_84, type, sK12: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_85, type, sK13: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.90/1.61 thf(func_def_86, type, sK14: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 2.90/1.61 thf(func_def_87, type, sK15: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_88, type, sK16: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.90/1.61 thf(func_def_89, type, sK17: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_90, type, sK18: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_91, type, sK19: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_92, type, sK20: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_93, type, sK21: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_94, type, sK22: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_95, type, sK23: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_96, type, sK24: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_97, type, sK25: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_98, type, sK26: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_99, type, sK27: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_100, type, sK28: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_101, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.90/1.61 thf(func_def_102, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.90/1.61 thf(func_def_103, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0)).
% 2.90/1.61 thf(func_def_104, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_105, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X2)).
% 2.90/1.61 thf(func_def_106, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X2)).
% 2.90/1.61 thf(func_def_107, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.90/1.61 thf(func_def_108, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0)).
% 2.90/1.61 thf(func_def_109, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_110, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X0 > X2 > X1)).
% 2.90/1.61 thf(func_def_111, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > X2)).
% 2.90/1.61 thf(func_def_112, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2 > X1) > list @ X0 > list @ X2 > $o) > list @ X2)).
% 2.90/1.61 thf(func_def_113, type, sK41: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_114, type, sK42: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_115, type, sK43: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_116, type, sK44: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_117, type, sK45: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_118, type, sK46: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_119, type, sK47: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_120, type, sK48: !>[X0: $tType]:($o > list @ X0 > list @ X0 > X0)).
% 2.90/1.61 thf(func_def_121, type, sK49: !>[X0: $tType]:($o > list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_122, type, sK50: !>[X0: $tType]:($o > list @ X0 > list @ X0 > X0)).
% 2.90/1.61 thf(func_def_123, type, sK51: !>[X0: $tType]:($o > list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_124, type, sK52: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_125, type, sK53: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_126, type, sK54: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_127, type, sK55: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_128, type, sK56: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_129, type, sK57: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_130, type, sK58: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_131, type, sK59: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_132, type, sK60: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_133, type, sK61: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_134, type, sK62: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_135, type, sK63: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.90/1.61 thf(func_def_136, type, sK64: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_137, type, sK65: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.90/1.61 thf(func_def_138, type, sK66: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_139, type, sK67: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_140, type, sK68: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_141, type, sK69: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_142, type, sK70: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_143, type, sK71: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_144, type, sK72: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_145, type, sK73: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_146, type, sK74: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_147, type, sK75: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_148, type, sK76: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_149, type, sK77: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_150, type, sK78: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_151, type, sK79: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_152, type, sK80: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_153, type, sK81: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_154, type, sK82: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_155, type, sK83: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_156, type, sK84: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_157, type, sK85: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_158, type, sK86: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_159, type, sK87: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_160, type, sK88: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_161, type, sK89: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_162, type, sK90: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_163, type, sK91: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_164, type, sK92: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_165, type, sK93: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_166, type, sK94: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_167, type, sK95: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_168, type, sK96: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_169, type, sK97: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_170, type, sK98: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_171, type, sK99: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_172, type, sK100: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_173, type, sK101: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_174, type, sK102: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_175, type, sK103: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_176, type, sK104: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_177, type, sK105: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_178, type, sK106: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_179, type, sK107: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_180, type, sK108: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_181, type, sK109: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_182, type, sK110: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.90/1.61 thf(func_def_183, type, sK111: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.90/1.61 thf(func_def_184, type, sK112: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_185, type, sK113: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_186, type, sK114: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.90/1.61 thf(func_def_187, type, sK115: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.90/1.61 thf(func_def_188, type, sK116: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_189, type, sK117: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_190, type, sK118: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0 > X1 > $o)).
% 2.90/1.61 thf(func_def_191, type, sK119: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X0)).
% 2.90/1.61 thf(func_def_192, type, sK120: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_193, type, sK121: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > X1)).
% 2.90/1.61 thf(func_def_194, type, sK122: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.90/1.61 thf(func_def_195, type, sK123: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 2.90/1.61 thf(func_def_196, type, sK124: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_197, type, sK125: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_198, type, sK126: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 2.90/1.61 thf(func_def_199, type, sK127: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_200, type, sK128: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_201, type, sK129: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0)).
% 2.90/1.61 thf(func_def_202, type, sK130: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_203, type, sK131: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > X0 > X0 > $o)).
% 2.90/1.61 thf(func_def_204, type, sK132: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.90/1.61 thf(func_def_205, type, sK133: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.90/1.61 thf(func_def_206, type, sK134: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_207, type, sK135: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.90/1.61 thf(func_def_208, type, sK136: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_209, type, sK137: !>[X0: $tType]:(list @ X0 > X0)).
% 2.90/1.61 thf(func_def_210, type, sK138: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.90/1.61 thf(func_def_212, type, ph140: !>[X0: $tType]:(X0)).
% 2.90/1.61 thf(f1139,plain,(
% 2.90/1.61 $false),
% 2.90/1.61 inference(subsumption_resolution,[status(thm)],[f1138,f1028])).
% 2.90/1.61 thf(f1028,plain,(
% 2.90/1.61 ((linorder @ a @ type2 @ a) = $true)),
% 2.90/1.61 inference(cnf_transformation,[status(thm)],[f686])).
% 2.90/1.61 thf(f686,plain,(
% 2.90/1.61 ((linorder @ a @ type2 @ a) = $true)),
% 2.90/1.61 inference(fool_elimination,[status(thm)],[f685])).
% 2.90/1.61 thf(f685,plain,(
% 2.90/1.61 (linorder @ a @ type2 @ a)),
% 2.90/1.61 inference(rectify,[status(thm)],[f291])).
% 2.90/1.61 thf(f291,axiom,(
% 2.90/1.61 (linorder @ a @ type2 @ a)),
% 2.90/1.61 file('/export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2THF_2830.p',tfree_0)).
% 2.90/1.61 thf(f1138,plain,(
% 2.90/1.61 ((linorder @ a @ type2 @ a) != $true)),
% 2.90/1.61 inference(trivial_inequality_removal,[status(thm)],[f1131])).
% 2.90/1.61 thf(f1131,plain,(
% 2.90/1.61 ($true != $true) | ((linorder @ a @ type2 @ a) != $true)),
% 2.90/1.61 inference(superposition,[status(thm)],[f1050,f1124])).
% 2.90/1.61 thf(f1124,plain,(
% 2.90/1.61 ($true = (sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ nil @ a))),
% 2.90/1.61 inference(subsumption_resolution,[status(thm)],[f1095,f1116])).
% 2.90/1.61 thf(f1116,plain,(
% 2.90/1.61 ( ! [X0 : $tType,X2 : X0,X3 : list @ X0] : ((nil @ X0 != (cons @ X0 @ X2 @ X3))) )),
% 2.90/1.61 inference(equality_resolution,[status(thm)],[f1051])).
% 2.90/1.61 thf(f1051,plain,(
% 2.90/1.61 ( ! [X0 : $tType,X2 : X0,X3 : list @ X0,X1 : list @ X0] : (((cons @ X0 @ X2 @ X3) != X1) | (nil @ X0 != X1)) )),
% 2.90/1.61 inference(cnf_transformation,[status(thm)],[f792])).
% 2.90/1.61 thf(f792,plain,(
% 2.90/1.61 ! [X0 : $tType,X1 : list @ X0,X2 : X0,X3 : list @ X0] : (((cons @ X0 @ X2 @ X3) != X1) | (nil @ X0 != X1))),
% 2.90/1.61 inference(ennf_transformation,[status(thm)],[f766])).
% 2.90/1.61 thf(f766,plain,(
% 2.90/1.61 ! [X0 : $tType,X1 : list @ X0,X2 : X0,X3 : list @ X0] : (((cons @ X0 @ X2 @ X3) = X1) => (nil @ X0 != X1))),
% 2.90/1.61 inference(rectify,[status(thm)],[f14])).
% 2.90/1.61 thf(f14,axiom,(
% 2.90/1.61 ! [X0 : $tType,X26 : list @ X0,X6 : X0,X7 : list @ X0] : (((cons @ X0 @ X6 @ X7) = X26) => (nil @ X0 != X26))),
% 2.90/1.61 file('/export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2THF_2830.p',fact_13_list_OdiscI)).
% 2.90/1.61 thf(f1095,plain,(
% 2.90/1.61 (nil @ a = (cons @ a @ x1 @ l1)) | ($true = (sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ nil @ a))),
% 2.90/1.61 inference(definition_unfolding,[status(thm)],[f995,f977,f977])).
% 2.90/1.61 thf(f977,plain,(
% 2.90/1.61 (l2a = nil @ a)),
% 2.90/1.61 inference(cnf_transformation,[status(thm)],[f1])).
% 2.90/1.61 thf(f1,axiom,(
% 2.90/1.61 (l2a = nil @ a)),
% 2.90/1.61 file('/export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2THF_2830.p',fact_0_local_ONil)).
% 2.90/1.61 thf(f995,plain,(
% 2.90/1.61 (l2a = (cons @ a @ x1 @ l1)) | ((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) = $true)),
% 2.90/1.61 inference(cnf_transformation,[status(thm)],[f872])).
% 2.90/1.61 thf(f872,plain,(
% 2.90/1.61 ((l2a != (cons @ a @ x1 @ l1)) | ((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) != $true) | ((sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) != $true)) & ((l2a = (cons @ a @ x1 @ l1)) | (((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) = $true) & ((sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = $true)))),
% 2.90/1.61 inference(flattening,[status(thm)],[f871])).
% 2.90/1.61 thf(f871,plain,(
% 2.90/1.61 ((l2a != (cons @ a @ x1 @ l1)) | (((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) != $true) | ((sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) != $true))) & ((l2a = (cons @ a @ x1 @ l1)) | (((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) = $true) & ((sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = $true)))),
% 2.90/1.61 inference(nnf_transformation,[status(thm)],[f790])).
% 2.90/1.61 thf(f790,plain,(
% 2.90/1.61 (((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) = $true) & ((sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = $true)) <~> (l2a = (cons @ a @ x1 @ l1))),
% 2.90/1.61 inference(ennf_transformation,[status(thm)],[f644])).
% 2.90/1.61 thf(f644,plain,(
% 2.90/1.61 ~((((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) = $true) & ((sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = $true)) <=> (l2a = (cons @ a @ x1 @ l1)))),
% 2.90/1.61 inference(fool_elimination,[status(thm)],[f643])).
% 2.90/1.61 thf(f643,plain,(
% 2.90/1.61 ~((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) & (sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = (l2a = (cons @ a @ x1 @ l1)))),
% 2.90/1.61 inference(rectify,[status(thm)],[f293])).
% 2.90/1.61 thf(f293,negated_conjecture,(
% 2.90/1.61 ~((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) & (sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = (l2a = (cons @ a @ x1 @ l1)))),
% 2.90/1.61 inference(negated_conjecture,[status(cth)],[f292])).
% 2.90/1.61 thf(f292,conjecture,(
% 2.90/1.61 ((sorted1061247458sorted @ a @ (cons @ a @ x1 @ l1) @ l2a) & (sorted1061247458sorted @ a @ l2a @ (cons @ a @ x1 @ l1)) = (l2a = (cons @ a @ x1 @ l1)))),
% 2.90/1.61 file('/export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2THF_2830.p',conj_0)).
% 2.90/1.61 thf(f1050,plain,(
% 2.90/1.61 ( ! [X0 : $tType,X2 : list @ X0,X1 : X0] : (($true != (sorted1061247458sorted @ X0 @ (cons @ X0 @ X1 @ X2) @ nil @ X0)) | ((linorder @ X0 @ type2 @ X0) != $true)) )),
% 2.90/1.61 inference(cnf_transformation,[status(thm)],[f821])).
% 2.90/1.61 thf(f821,plain,(
% 2.90/1.61 ! [X0 : $tType] : (! [X1 : X0,X2 : list @ X0] : ($true != (sorted1061247458sorted @ X0 @ (cons @ X0 @ X1 @ X2) @ nil @ X0)) | ((linorder @ X0 @ type2 @ X0) != $true))),
% 2.90/1.61 inference(ennf_transformation,[status(thm)],[f778])).
% 2.90/1.61 thf(f778,plain,(
% 2.90/1.61 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : list @ X0] : ($true != (sorted1061247458sorted @ X0 @ (cons @ X0 @ X1 @ X2) @ nil @ X0)))),
% 2.90/1.61 inference(flattening,[status(thm)],[f338])).
% 2.90/1.61 thf(f338,plain,(
% 2.90/1.61 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : list @ X0] : ~($true = (sorted1061247458sorted @ X0 @ (cons @ X0 @ X1 @ X2) @ nil @ X0)))),
% 2.90/1.61 inference(fool_elimination,[status(thm)],[f337])).
% 2.90/1.61 thf(f337,plain,(
% 2.90/1.61 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : list @ X0] : ~(sorted1061247458sorted @ X0 @ (cons @ X0 @ X1 @ X2) @ nil @ X0))),
% 2.90/1.61 inference(rectify,[status(thm)],[f3])).
% 2.90/1.61 thf(f3,axiom,(
% 2.90/1.61 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X4 : X0,X5 : list @ X0] : ~(sorted1061247458sorted @ X0 @ (cons @ X0 @ X4 @ X5) @ nil @ X0))),
% 2.90/1.61 file('/export/starexec/sandbox2/tmp/tmp.Nyhxfz4wKg/DTF2THF_2830.p',fact_2_subset__sorted_Osimps_I2_J)).
% 2.90/1.61 % SZS output end Proof for DTF2THF_2830
% 2.90/1.61 % (2936)------------------------------
% 2.90/1.61 % (2936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (2936)Termination reason: Refutation
% 2.90/1.61
% 2.90/1.61 % (2936)Memory used [KB]: 7164
% 2.90/1.61 % (2936)Time elapsed: 0.054 s
% 2.90/1.61 % (2936)Instructions burned: 105 (million)
% 2.90/1.61 % (2936)------------------------------
% 2.90/1.61 % (2936)------------------------------
% 2.90/1.61 % (2930)Success in time 0.075 s
%------------------------------------------------------------------------------