%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT198^1 : 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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:06 AM UTC 2026
% Result : Theorem 9.08s 2.77s
% Output : Refutation 9.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT198^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n012.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 06:10:15 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.38 ---- Original DTF file ---
% 0.15/0.38 thf(spec,logic,$$dhol).
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 % File : DAT198^1 : TPTP v9.2.1. Released v7.0.0.
% 0.15/0.38 % Domain : Data Structures
% 0.15/0.38 % Problem : Lazy list mirror 164
% 0.15/0.38 % Version : [Bla16] axioms : Especial.
% 0.15/0.38 % English :
% 0.15/0.38
% 0.15/0.38 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.15/0.38 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.15/0.38 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.15/0.38 % Source : [Bla16]
% 0.15/0.38 % Names : lmirror__164.p [Bla16]
% 0.15/0.38
% 0.15/0.38 % Status : Theorem
% 0.15/0.38 % Rating : 0.67 v8.1.0, 1.00 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.15/0.38 % Syntax : Number of formulae : 306 ( 108 unt; 46 typ; 0 def)
% 0.15/0.38 % Number of atoms : 932 ( 306 equ; 12 cnn)
% 0.15/0.38 % Maximal formula atoms : 15 ( 3 avg)
% 0.15/0.38 % Number of connectives : 5128 ( 19 ~; 2 |; 30 &;4807 @)
% 0.15/0.38 % ( 0 <=>; 270 =>; 0 <=; 0 <~>)
% 0.15/0.38 % Maximal formula depth : 26 ( 11 avg)
% 0.15/0.38 % Number of types : 3 ( 2 usr)
% 0.15/0.38 % Number of type conns : 1562 (1562 >; 0 *; 0 +; 0 <<)
% 0.15/0.38 % Number of symbols : 49 ( 44 usr; 4 con; 0-8 aty)
% 0.15/0.38 % Number of variables : 1739 ( 262 ^;1391 !; 18 ?;1739 :)
% 0.15/0.38 % ( 68 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.38 % SPC : TH1_THM_EQU_NAR
% 0.15/0.38
% 0.15/0.38 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.15/0.38 % 2016-07-13 14:42:04.265
% 0.15/0.38 %------------------------------------------------------------------------------
% 0.15/0.38 %----Could-be-implicit typings (4)
% 0.15/0.38 thf(ty_t_Coinductive__List_Ollist,type,
% 0.15/0.38 coinductive_llist: $tType > $tType ).
% 0.15/0.38
% 0.15/0.38 thf(ty_t_itself,type,
% 0.15/0.38 itself: $tType > $tType ).
% 0.15/0.38
% 0.15/0.38 thf(ty_tf_b,type,
% 0.15/0.38 b: $tType ).
% 0.15/0.38
% 0.15/0.38 thf(ty_tf_a,type,
% 0.15/0.38 a: $tType ).
% 0.15/0.38
% 0.15/0.38 %----Explicit typings (42)
% 0.15/0.38 thf(sy_c_BNF__Def_Orel__fun,type,
% 0.15/0.38 bNF_rel_fun:
% 0.15/0.38 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Oiterates,type,
% 0.15/0.38 coinductive_iterates:
% 0.15/0.38 !>[A: $tType] : ( ( A > A ) > A > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_OldropWhile,type,
% 0.15/0.38 coindu218763757pWhile:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Olfilter,type,
% 0.15/0.38 coinductive_lfilter:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.15/0.38 coinductive_LCons:
% 0.15/0.38 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_Ocase__llist,type,
% 0.15/0.38 coindu1381640503_llist:
% 0.15/0.38 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_Ocorec__llist,type,
% 0.15/0.38 coindu1259883913_llist:
% 0.15/0.38 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 0.15/0.38 coinductive_lhd:
% 0.15/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_Ollist__all2,type,
% 0.15/0.38 coindu1486289336t_all2:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_Olmap,type,
% 0.15/0.38 coinductive_lmap:
% 0.15/0.38 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coinductive_llist @ A ) > ( coinductive_llist @ Aa ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ollist_Opred__llist,type,
% 0.15/0.38 coindu543516966_llist:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Olmember,type,
% 0.15/0.38 coinductive_lmember:
% 0.15/0.38 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_OltakeWhile,type,
% 0.15/0.38 coindu501562517eWhile:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Coinductive__List_Ounfold__llist,type,
% 0.15/0.38 coindu1441602521_llist:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coinductive_llist @ B ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Complete__Partial__Order_Omonotone,type,
% 0.15/0.38 comple1396247847notone:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( B > B > $o ) > ( A > B ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Fun_Ocomp,type,
% 0.15/0.38 comp:
% 0.15/0.38 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Fun_Ofun__upd,type,
% 0.15/0.38 fun_upd:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Fun_Oid,type,
% 0.15/0.38 id:
% 0.15/0.38 !>[A: $tType] : ( A > A ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Fun_Omap__fun,type,
% 0.15/0.38 map_fun:
% 0.15/0.38 !>[C: $tType,A: $tType,B: $tType,D: $tType] : ( ( C > A ) > ( B > D ) > ( A > B ) > C > D ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Fun_Oswap,type,
% 0.15/0.38 swap:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( A > A > ( A > B ) > A > B ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_HOL_OEx1,type,
% 0.15/0.38 ex1:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_If,type,
% 0.15/0.38 if:
% 0.15/0.38 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror,type,
% 0.15/0.38 lMirro427583474mirror:
% 0.15/0.38 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.15/0.38 ord_less_eq:
% 0.15/0.38 !>[A: $tType] : ( A > A > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Partial__Function_Ofun__ord,type,
% 0.15/0.38 partial_fun_ord:
% 0.15/0.38 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( C > A ) > ( C > B ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Pure_Otype,type,
% 0.15/0.38 type:
% 0.15/0.38 !>[A: $tType] : ( itself @ A ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Quotient_OBex1__rel,type,
% 0.15/0.38 bex1_rel:
% 0.15/0.38 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Quotient_OQuotient3,type,
% 0.15/0.38 quotient3:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > ( B > A ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Relation_ODomainp,type,
% 0.15/0.38 domainp:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > A > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Relation_Oreflp,type,
% 0.15/0.38 reflp:
% 0.15/0.38 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Relation_Orelcompp,type,
% 0.15/0.38 relcompp:
% 0.15/0.38 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > A > C > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Obi__total,type,
% 0.15/0.38 bi_total:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Obi__unique,type,
% 0.15/0.38 bi_unique:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Oleft__total,type,
% 0.15/0.38 left_total:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Oleft__unique,type,
% 0.15/0.38 left_unique:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Orev__implies,type,
% 0.15/0.38 rev_implies: $o > $o > $o ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Oright__total,type,
% 0.15/0.38 right_total:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Oright__unique,type,
% 0.15/0.38 right_unique:
% 0.15/0.38 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Otransfer__bforall,type,
% 0.15/0.38 transfer_bforall:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transfer_Otransfer__forall,type,
% 0.15/0.38 transfer_forall:
% 0.15/0.38 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_c_Transitive__Closure_Ortranclp,type,
% 0.15/0.38 transitive_rtranclp:
% 0.15/0.38 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 0.15/0.38
% 0.15/0.38 thf(sy_v_A,type,
% 0.15/0.38 a2: a > b > $o ).
% 0.15/0.38
% 0.15/0.38 %----Relevant facts (256)
% 0.15/0.38 thf(fact_0_llist__all2__lmirror,axiom,
% 0.15/0.38 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.38 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( lMirro427583474mirror @ A @ Xs ) @ ( lMirro427583474mirror @ B @ Ys ) )
% 0.15/0.38 = ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys ) ) ).
% 0.15/0.38
% 0.15/0.38 % llist_all2_lmirror
% 0.15/0.38 thf(fact_1_llist__all2__lmirrorD,axiom,
% 0.15/0.38 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.38 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( lMirro427583474mirror @ A @ Xs ) @ ( lMirro427583474mirror @ B @ Ys ) )
% 0.15/0.38 => ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys ) ) ).
% 0.15/0.38
% 0.15/0.38 % llist_all2_lmirrorD
% 0.15/0.38 thf(fact_2_llist__all2__lmirrorI,axiom,
% 0.15/0.38 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.38 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.38 => ( coindu1486289336t_all2 @ A @ B @ P @ ( lMirro427583474mirror @ A @ Xs ) @ ( lMirro427583474mirror @ B @ Ys ) ) ) ).
% 0.15/0.38
% 0.15/0.38 % llist_all2_lmirrorI
% 0.15/0.38 thf(fact_3_rel__funI,axiom,
% 0.15/0.38 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 0.15/0.38 ( ! [X: A,Y: B] :
% 0.15/0.38 ( ( A2 @ X @ Y )
% 0.15/0.38 => ( B2 @ ( F @ X ) @ ( G @ Y ) ) )
% 0.15/0.38 => ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 @ F @ G ) ) ).
% 0.15/0.38
% 0.15/0.38 % rel_funI
% 0.15/0.38 thf(fact_4_llist__all2__rsp,axiom,
% 0.15/0.38 ! [A: $tType,B: $tType,R: A > B > $o,S: A > A > $o,T: B > B > $o,X2: coinductive_llist @ A,Y2: coinductive_llist @ B,A3: coinductive_llist @ A,B3: coinductive_llist @ B] :
% 0.15/0.38 ( ! [X: A,Y: B] :
% 0.15/0.38 ( ( R @ X @ Y )
% 0.15/0.38 => ! [A4: A,B4: B] :
% 0.15/0.38 ( ( R @ A4 @ B4 )
% 0.15/0.38 => ( ( S @ X @ A4 )
% 0.15/0.38 = ( T @ Y @ B4 ) ) ) )
% 0.15/0.38 => ( ( coindu1486289336t_all2 @ A @ B @ R @ X2 @ Y2 )
% 0.15/0.38 => ( ( coindu1486289336t_all2 @ A @ B @ R @ A3 @ B3 )
% 0.15/0.39 => ( ( coindu1486289336t_all2 @ A @ A @ S @ X2 @ A3 )
% 0.15/0.39 = ( coindu1486289336t_all2 @ B @ B @ T @ Y2 @ B3 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_rsp
% 0.15/0.39 thf(fact_5_llist__all2__mono,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,P2: A > B > $o] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.39 => ( ! [X: A,Y: B] :
% 0.15/0.39 ( ( P @ X @ Y )
% 0.15/0.39 => ( P2 @ X @ Y ) )
% 0.15/0.39 => ( coindu1486289336t_all2 @ A @ B @ P2 @ Xs @ Ys ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_mono
% 0.15/0.39 thf(fact_6_llist_Orel__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.15/0.39 = ( ^ [Y3: coinductive_llist @ A,Z: coinductive_llist @ A] : ( Y3 = Z ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.rel_eq
% 0.15/0.39 thf(fact_7_llist_Orel__refl,axiom,
% 0.15/0.39 ! [B: $tType,Ra: B > B > $o,X2: coinductive_llist @ B] :
% 0.15/0.39 ( ! [X: B] : ( Ra @ X @ X )
% 0.15/0.39 => ( coindu1486289336t_all2 @ B @ B @ Ra @ X2 @ X2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.rel_refl
% 0.15/0.39 thf(fact_8_rel__funD,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y2: B] :
% 0.15/0.39 ( ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 @ F @ G )
% 0.15/0.39 => ( ( A2 @ X2 @ Y2 )
% 0.15/0.39 => ( B2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rel_funD
% 0.15/0.39 thf(fact_9_let__rsp,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o] :
% 0.15/0.39 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 ) @ R2 )
% 0.15/0.39 @ ^ [S2: A,F2: A > C] : ( F2 @ S2 )
% 0.15/0.39 @ ^ [S2: B,F2: B > D] : ( F2 @ S2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % let_rsp
% 0.15/0.39 thf(fact_10_rel__funE,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y2: B] :
% 0.15/0.39 ( ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 @ F @ G )
% 0.15/0.39 => ( ( A2 @ X2 @ Y2 )
% 0.15/0.39 => ( B2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rel_funE
% 0.15/0.39 thf(fact_11_apply__rsp_H,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o,F: A > C,G: B > D,X2: A,Y2: B] :
% 0.15/0.39 ( ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 @ F @ G )
% 0.15/0.39 => ( ( R1 @ X2 @ Y2 )
% 0.15/0.39 => ( R2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % apply_rsp'
% 0.15/0.39 thf(fact_12_rel__funD2,axiom,
% 0.15/0.39 ! [B: $tType,C: $tType,A: $tType,A2: A > A > $o,B2: B > C > $o,F: A > B,G: A > C,X2: A] :
% 0.15/0.39 ( ( bNF_rel_fun @ A @ A @ B @ C @ A2 @ B2 @ F @ G )
% 0.15/0.39 => ( ( A2 @ X2 @ X2 )
% 0.15/0.39 => ( B2 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rel_funD2
% 0.15/0.39 thf(fact_13_rel__fun__mono,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,X3: A > B > $o,A2: C > D > $o,F: A > C,G: B > D,Y4: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bNF_rel_fun @ A @ B @ C @ D @ X3 @ A2 @ F @ G )
% 0.15/0.39 => ( ! [X: A,Y: B] :
% 0.15/0.39 ( ( Y4 @ X @ Y )
% 0.15/0.39 => ( X3 @ X @ Y ) )
% 0.15/0.39 => ( ! [X: C,Y: D] :
% 0.15/0.39 ( ( A2 @ X @ Y )
% 0.15/0.39 => ( B2 @ X @ Y ) )
% 0.15/0.39 => ( bNF_rel_fun @ A @ B @ C @ D @ Y4 @ B2 @ F @ G ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rel_fun_mono
% 0.15/0.39 thf(fact_14_rel__fun__mono_H,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,Y4: A > B > $o,X3: A > B > $o,A2: C > D > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 0.15/0.39 ( ! [X: A,Y: B] :
% 0.15/0.39 ( ( Y4 @ X @ Y )
% 0.15/0.39 => ( X3 @ X @ Y ) )
% 0.15/0.39 => ( ! [X: C,Y: D] :
% 0.15/0.39 ( ( A2 @ X @ Y )
% 0.15/0.39 => ( B2 @ X @ Y ) )
% 0.15/0.39 => ( ( bNF_rel_fun @ A @ B @ C @ D @ X3 @ A2 @ F @ G )
% 0.15/0.39 => ( bNF_rel_fun @ A @ B @ C @ D @ Y4 @ B2 @ F @ G ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rel_fun_mono'
% 0.15/0.39 thf(fact_15_llist__all2__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ R
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > $o ) @ ( coindu1486289336t_all2 @ A @ B @ R )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ $o @ $o @ ( coindu1486289336t_all2 @ A @ B @ R )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( coindu1486289336t_all2 @ A @ A )
% 0.15/0.39 @ ( coindu1486289336t_all2 @ B @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_transfer
% 0.15/0.39 thf(fact_16_llist_Orel__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > $o ) @ ( ( coinductive_llist @ C ) > ( coinductive_llist @ D ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 0.15/0.39 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ C ) @ ( ( coinductive_llist @ B ) > $o ) @ ( ( coinductive_llist @ D ) > $o ) @ ( coindu1486289336t_all2 @ A @ C @ Sa )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ B ) @ ( coinductive_llist @ D ) @ $o @ $o @ ( coindu1486289336t_all2 @ B @ D @ Sc )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( coindu1486289336t_all2 @ A @ B )
% 0.15/0.39 @ ( coindu1486289336t_all2 @ C @ D ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.rel_transfer
% 0.15/0.39 thf(fact_17_Let__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ A2 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) @ B2 )
% 0.15/0.39 @ ^ [S2: A,F2: A > C] : ( F2 @ S2 )
% 0.15/0.39 @ ^ [S2: B,F2: B > D] : ( F2 @ S2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % Let_transfer
% 0.15/0.39 thf(fact_18_rel__fun__def__butlast,axiom,
% 0.15/0.39 ! [B: $tType,D: $tType,C: $tType,E: $tType,F3: $tType,A: $tType,R: A > B > $o,S: C > E > $o,T: D > F3 > $o,F: A > C > D,G: B > E > F3] :
% 0.15/0.39 ( ( bNF_rel_fun @ A @ B @ ( C > D ) @ ( E > F3 ) @ R @ ( bNF_rel_fun @ C @ E @ D @ F3 @ S @ T ) @ F @ G )
% 0.15/0.39 = ( ! [X4: A,Y5: B] :
% 0.15/0.39 ( ( R @ X4 @ Y5 )
% 0.15/0.39 => ( bNF_rel_fun @ C @ E @ D @ F3 @ S @ T @ ( F @ X4 ) @ ( G @ Y5 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rel_fun_def_butlast
% 0.15/0.39 thf(fact_19_If__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ $o @ $o @ ( A > A > A ) @ ( B > B > B )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > A ) @ ( B > B ) @ A2 @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) )
% 0.15/0.39 @ ( if @ A )
% 0.15/0.39 @ ( if @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % If_transfer
% 0.15/0.39 thf(fact_20_llist__corec__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( A > C ) > ( A > $o ) > ( A > ( coinductive_llist @ C ) ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > D ) > ( B > $o ) > ( B > ( coinductive_llist @ D ) ) > ( B > B ) > B > ( coinductive_llist @ D ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ ( ( A > $o ) > ( A > ( coinductive_llist @ C ) ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > $o ) > ( B > ( coinductive_llist @ D ) ) > ( B > B ) > B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( A > ( coinductive_llist @ C ) ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > ( coinductive_llist @ D ) ) > ( B > B ) > B > ( coinductive_llist @ D ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > ( coinductive_llist @ C ) ) @ ( B > ( coinductive_llist @ D ) ) @ ( ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > B ) > B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A2 @ ( coindu1486289336t_all2 @ C @ D @ B2 ) ) @ ( bNF_rel_fun @ ( A > A ) @ ( B > B ) @ ( A > ( coinductive_llist @ C ) ) @ ( B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A2 @ ( coindu1486289336t_all2 @ C @ D @ B2 ) ) ) ) ) )
% 0.15/0.39 @ ( coindu1259883913_llist @ A @ C )
% 0.15/0.39 @ ( coindu1259883913_llist @ B @ D ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_corec_transfer
% 0.15/0.39 thf(fact_21_llist_Ocorec__transfer,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( coinductive_llist @ B ) ) > ( D > D ) > D > ( coinductive_llist @ B ) )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > $o ) > ( D > ( coinductive_llist @ B ) ) > ( D > D ) > D > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
% 0.15/0.39 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > ( coinductive_llist @ B ) ) > ( D > D ) > D > ( coinductive_llist @ B ) )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( C > ( coinductive_llist @ A ) ) @ ( D > ( coinductive_llist @ B ) ) @ ( ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > D ) > D > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ S @ ( coindu1486289336t_all2 @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( coinductive_llist @ A ) ) @ ( D > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ S @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ) ) )
% 0.15/0.39 @ ( coindu1259883913_llist @ C @ A )
% 0.15/0.39 @ ( coindu1259883913_llist @ D @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.corec_transfer
% 0.15/0.39 thf(fact_22_unfold__llist__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( A > C ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > D ) > ( B > B ) > B > ( coinductive_llist @ D ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ ( ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > B ) > B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ ( A > A ) @ ( B > B ) @ ( A > ( coinductive_llist @ C ) ) @ ( B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A2 @ ( coindu1486289336t_all2 @ C @ D @ B2 ) ) ) )
% 0.15/0.39 @ ( coindu1441602521_llist @ A @ C )
% 0.15/0.39 @ ( coindu1441602521_llist @ B @ D ) ) ).
% 0.15/0.39
% 0.15/0.39 % unfold_llist_transfer
% 0.15/0.39 thf(fact_23_iterates__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] : ( bNF_rel_fun @ ( A > A ) @ ( B > B ) @ ( A > ( coinductive_llist @ A ) ) @ ( B > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ A2 @ ( coindu1486289336t_all2 @ A @ B @ A2 ) ) @ ( coinductive_iterates @ A ) @ ( coinductive_iterates @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % iterates_transfer
% 0.15/0.39 thf(fact_24_fun_Orel__transfer,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Sa: A > C > $o,Sc: B > E > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > E > $o ) @ ( ( D > A ) > ( D > B ) > $o ) @ ( ( D > C ) > ( D > E ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( E > $o ) @ Sa
% 0.15/0.39 @ ( bNF_rel_fun @ B @ E @ $o @ $o @ Sc
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( D > A ) @ ( D > C ) @ ( ( D > B ) > $o ) @ ( ( D > E ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ A @ C
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ Sa )
% 0.15/0.39 @ ( bNF_rel_fun @ ( D > B ) @ ( D > E ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ B @ E
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ Sc )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ C @ E
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.rel_transfer
% 0.15/0.39 thf(fact_25_fun_Orel__refl,axiom,
% 0.15/0.39 ! [B: $tType,D: $tType,Ra: B > B > $o,X2: D > B] :
% 0.15/0.39 ( ! [X: B] : ( Ra @ X @ X )
% 0.15/0.39 => ( bNF_rel_fun @ D @ D @ B @ B
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ Ra
% 0.15/0.39 @ X2
% 0.15/0.39 @ X2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.rel_refl
% 0.15/0.39 thf(fact_26_fun_Orel__eq,axiom,
% 0.15/0.39 ! [A: $tType,D: $tType] :
% 0.15/0.39 ( ( bNF_rel_fun @ D @ D @ A @ A
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.15/0.39 = ( ^ [Y3: D > A,Z: D > A] : ( Y3 = Z ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.rel_eq
% 0.15/0.39 thf(fact_27_case__llist__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,B2: A > B > $o,A2: C > D > $o] : ( bNF_rel_fun @ A @ B @ ( ( C > ( coinductive_llist @ C ) > A ) > ( coinductive_llist @ C ) > A ) @ ( ( D > ( coinductive_llist @ D ) > B ) > ( coinductive_llist @ D ) > B ) @ B2 @ ( bNF_rel_fun @ ( C > ( coinductive_llist @ C ) > A ) @ ( D > ( coinductive_llist @ D ) > B ) @ ( ( coinductive_llist @ C ) > A ) @ ( ( coinductive_llist @ D ) > B ) @ ( bNF_rel_fun @ C @ D @ ( ( coinductive_llist @ C ) > A ) @ ( ( coinductive_llist @ D ) > B ) @ A2 @ ( bNF_rel_fun @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A @ B @ ( coindu1486289336t_all2 @ C @ D @ A2 ) @ B2 ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A @ B @ ( coindu1486289336t_all2 @ C @ D @ A2 ) @ B2 ) ) @ ( coindu1381640503_llist @ A @ C ) @ ( coindu1381640503_llist @ B @ D ) ) ).
% 0.15/0.39
% 0.15/0.39 % case_llist_transfer
% 0.15/0.39 thf(fact_28_llist_Ocase__transfer,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] : ( bNF_rel_fun @ C @ D @ ( ( A > ( coinductive_llist @ A ) > C ) > ( coinductive_llist @ A ) > C ) @ ( ( B > ( coinductive_llist @ B ) > D ) > ( coinductive_llist @ B ) > D ) @ S @ ( bNF_rel_fun @ ( A > ( coinductive_llist @ A ) > C ) @ ( B > ( coinductive_llist @ B ) > D ) @ ( ( coinductive_llist @ A ) > C ) @ ( ( coinductive_llist @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( coinductive_llist @ A ) > C ) @ ( ( coinductive_llist @ B ) > D ) @ R @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ D @ ( coindu1486289336t_all2 @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ D @ ( coindu1486289336t_all2 @ A @ B @ R ) @ S ) ) @ ( coindu1381640503_llist @ C @ A ) @ ( coindu1381640503_llist @ D @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.case_transfer
% 0.15/0.39 thf(fact_29_map__fun__parametric,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,E: $tType,F3: $tType,H: $tType,G2: $tType,D: $tType,C: $tType,A2: A > C > $o,B2: B > D > $o,C2: E > G2 > $o,D2: F3 > H > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > F3 ) > ( B > E ) > A > F3 ) @ ( ( G2 > H ) > ( D > G2 ) > C > H ) @ ( bNF_rel_fun @ A @ C @ B @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ ( E > F3 ) @ ( G2 > H ) @ ( ( B > E ) > A > F3 ) @ ( ( D > G2 ) > C > H ) @ ( bNF_rel_fun @ E @ G2 @ F3 @ H @ C2 @ D2 ) @ ( bNF_rel_fun @ ( B > E ) @ ( D > G2 ) @ ( A > F3 ) @ ( C > H ) @ ( bNF_rel_fun @ B @ D @ E @ G2 @ B2 @ C2 ) @ ( bNF_rel_fun @ A @ C @ F3 @ H @ A2 @ D2 ) ) ) @ ( map_fun @ A @ B @ E @ F3 ) @ ( map_fun @ C @ D @ G2 @ H ) ) ).
% 0.15/0.39
% 0.15/0.39 % map_fun_parametric
% 0.15/0.39 thf(fact_30_llist_Opred__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ $o @ $o @ ( coindu1486289336t_all2 @ A @ B @ R )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( coindu543516966_llist @ A )
% 0.15/0.39 @ ( coindu543516966_llist @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.pred_transfer
% 0.15/0.39 thf(fact_31_llist__all__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ $o @ $o @ ( coindu1486289336t_all2 @ A @ B @ A2 )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( coindu543516966_llist @ A )
% 0.15/0.39 @ ( coindu543516966_llist @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all_transfer
% 0.15/0.39 thf(fact_32_if__rsp,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( bNF_rel_fun @ $o @ $o @ ( A > A > A ) @ ( A > A > A )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ A @ ( A > A ) @ ( A > A ) @ R @ ( bNF_rel_fun @ A @ A @ A @ A @ R @ R ) )
% 0.15/0.39 @ ( if @ A )
% 0.15/0.39 @ ( if @ A ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % if_rsp
% 0.15/0.39 thf(fact_33_ldropWhile__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) )
% 0.15/0.39 @ ( coindu218763757pWhile @ A )
% 0.15/0.39 @ ( coindu218763757pWhile @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % ldropWhile_transfer
% 0.15/0.39 thf(fact_34_ltakeWhile__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) )
% 0.15/0.39 @ ( coindu501562517eWhile @ A )
% 0.15/0.39 @ ( coindu501562517eWhile @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % ltakeWhile_transfer
% 0.15/0.39 thf(fact_35_lfilter__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) )
% 0.15/0.39 @ ( coinductive_lfilter @ A )
% 0.15/0.39 @ ( coinductive_lfilter @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_transfer
% 0.15/0.39 thf(fact_36_fun_Omap__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,G2: $tType,F3: $tType,Rb: A > F3 > $o,Sd: B > G2 > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( A > B ) @ ( F3 > G2 ) @ ( ( D > A ) > D > B ) @ ( ( D > F3 ) > D > G2 ) @ ( bNF_rel_fun @ A @ F3 @ B @ G2 @ Rb @ Sd )
% 0.15/0.39 @ ( bNF_rel_fun @ ( D > A ) @ ( D > F3 ) @ ( D > B ) @ ( D > G2 )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ A @ F3
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ Rb )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ B @ G2
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ Sd ) )
% 0.15/0.39 @ ( comp @ A @ B @ D )
% 0.15/0.39 @ ( comp @ F3 @ G2 @ D ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.map_transfer
% 0.15/0.39 thf(fact_37_comp__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,E: $tType,F3: $tType,D: $tType,C: $tType,B2: A > C > $o,C2: B > D > $o,A2: E > F3 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > A ) > E > B ) @ ( ( F3 > C ) > F3 > D ) @ ( bNF_rel_fun @ A @ C @ B @ D @ B2 @ C2 ) @ ( bNF_rel_fun @ ( E > A ) @ ( F3 > C ) @ ( E > B ) @ ( F3 > D ) @ ( bNF_rel_fun @ E @ F3 @ A @ C @ A2 @ B2 ) @ ( bNF_rel_fun @ E @ F3 @ B @ D @ A2 @ C2 ) ) @ ( comp @ A @ B @ E ) @ ( comp @ C @ D @ F3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_transfer
% 0.15/0.39 thf(fact_38_lfilter__idem,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.15/0.39 = ( coinductive_lfilter @ A @ P @ Xs ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_idem
% 0.15/0.39 thf(fact_39_fun__quotient3,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > A > $o,Abs1: A > B,Rep1: B > A,R2: C > C > $o,Abs2: C > D,Rep2: D > C] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs1 @ Rep1 )
% 0.15/0.39 => ( ( quotient3 @ C @ D @ R2 @ Abs2 @ Rep2 )
% 0.15/0.39 => ( quotient3 @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ A @ C @ C @ R1 @ R2 ) @ ( map_fun @ B @ A @ C @ D @ Rep1 @ Abs2 ) @ ( map_fun @ A @ B @ D @ C @ Abs1 @ Rep2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_quotient3
% 0.15/0.39 thf(fact_40_unfold__llist__ltl__unroll,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B] :
% 0.15/0.39 ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) )
% 0.15/0.39 = ( coindu1441602521_llist @ B @ A @ ( comp @ B @ $o @ B @ IS_LNIL @ LTL ) @ ( comp @ B @ A @ B @ LHD @ LTL ) @ LTL @ B3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % unfold_llist_ltl_unroll
% 0.15/0.39 thf(fact_41_rewriteR__comp__comp2,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H2: A > C,R12: D > B,R22: A > D,F: B > E,L: D > E] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 0.15/0.39 = ( comp @ D @ B @ A @ R12 @ R22 ) )
% 0.15/0.39 => ( ( ( comp @ B @ E @ D @ F @ R12 )
% 0.15/0.39 = L )
% 0.15/0.39 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H2 )
% 0.15/0.39 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rewriteR_comp_comp2
% 0.15/0.39 thf(fact_42_rewriteL__comp__comp2,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H2: E > A,R3: E > D] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.15/0.39 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.15/0.39 => ( ( ( comp @ A @ D @ E @ L2 @ H2 )
% 0.15/0.39 = R3 )
% 0.15/0.39 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H2 ) )
% 0.15/0.39 = ( comp @ D @ B @ E @ L1 @ R3 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rewriteL_comp_comp2
% 0.15/0.39 thf(fact_43_rewriteR__comp__comp,axiom,
% 0.15/0.39 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H2: A > C,R3: A > B,F: B > D] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 0.15/0.39 = R3 )
% 0.15/0.39 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H2 )
% 0.15/0.39 = ( comp @ B @ D @ A @ F @ R3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rewriteR_comp_comp
% 0.15/0.39 thf(fact_44_rewriteL__comp__comp,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H2: D > A] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ F @ G )
% 0.15/0.39 = L )
% 0.15/0.39 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H2 ) )
% 0.15/0.39 = ( comp @ A @ B @ D @ L @ H2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rewriteL_comp_comp
% 0.15/0.39 thf(fact_45_ext,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.15/0.39 ( ! [X: A] :
% 0.15/0.39 ( ( F @ X )
% 0.15/0.39 = ( G @ X ) )
% 0.15/0.39 => ( F = G ) ) ).
% 0.15/0.39
% 0.15/0.39 % ext
% 0.15/0.39 thf(fact_46_fun_Omap__comp,axiom,
% 0.15/0.39 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 0.15/0.39 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 0.15/0.39 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.map_comp
% 0.15/0.39 thf(fact_47_Quotient3__rep__reflp,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,A3: B] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( R @ ( Rep @ A3 ) @ ( Rep @ A3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_rep_reflp
% 0.15/0.39 thf(fact_48_Quotient3__rep__abs,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ R3 @ R3 )
% 0.15/0.39 => ( R @ ( Rep @ ( Abs @ R3 ) ) @ R3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_rep_abs
% 0.15/0.39 thf(fact_49_Quotient3__rel__rep,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,A3: B,B3: B] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ ( Rep @ A3 ) @ ( Rep @ B3 ) )
% 0.15/0.39 = ( A3 = B3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_rel_rep
% 0.15/0.39 thf(fact_50_Quotient3__rel__abs,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ R3 @ S3 )
% 0.15/0.39 => ( ( Abs @ R3 )
% 0.15/0.39 = ( Abs @ S3 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_rel_abs
% 0.15/0.39 thf(fact_51_Quotient3__abs__rep,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,A3: B] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( Abs @ ( Rep @ A3 ) )
% 0.15/0.39 = A3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_abs_rep
% 0.15/0.39 thf(fact_52_rep__abs__rsp__left,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,X1: A,X22: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ X1 @ X22 )
% 0.15/0.39 => ( R @ ( Rep @ ( Abs @ X1 ) ) @ X22 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rep_abs_rsp_left
% 0.15/0.39 thf(fact_53_Quotient3__refl2,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ R3 @ S3 )
% 0.15/0.39 => ( R @ S3 @ S3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_refl2
% 0.15/0.39 thf(fact_54_Quotient3__refl1,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ R3 @ S3 )
% 0.15/0.39 => ( R @ R3 @ R3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_refl1
% 0.15/0.39 thf(fact_55_Quotient3__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( ( R @ R3 @ R3 )
% 0.15/0.39 & ( R @ S3 @ S3 )
% 0.15/0.39 & ( ( Abs @ R3 )
% 0.15/0.39 = ( Abs @ S3 ) ) )
% 0.15/0.39 = ( R @ R3 @ S3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_rel
% 0.15/0.39 thf(fact_56_Quotient3__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( quotient3 @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > A > $o,Abs3: A > B,Rep3: B > A] :
% 0.15/0.39 ( ! [A5: B] :
% 0.15/0.39 ( ( Abs3 @ ( Rep3 @ A5 ) )
% 0.15/0.39 = A5 )
% 0.15/0.39 & ! [A5: B] : ( R4 @ ( Rep3 @ A5 ) @ ( Rep3 @ A5 ) )
% 0.15/0.39 & ! [R5: A,S2: A] :
% 0.15/0.39 ( ( R4 @ R5 @ S2 )
% 0.15/0.39 = ( ( R4 @ R5 @ R5 )
% 0.15/0.39 & ( R4 @ S2 @ S2 )
% 0.15/0.39 & ( ( Abs3 @ R5 )
% 0.15/0.39 = ( Abs3 @ S2 ) ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3_def
% 0.15/0.39 thf(fact_57_comp__apply__eq,axiom,
% 0.15/0.39 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X2: C,H2: D > A,K: C > D] :
% 0.15/0.39 ( ( ( F @ ( G @ X2 ) )
% 0.15/0.39 = ( H2 @ ( K @ X2 ) ) )
% 0.15/0.39 => ( ( comp @ B @ A @ C @ F @ G @ X2 )
% 0.15/0.39 = ( comp @ D @ A @ C @ H2 @ K @ X2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_apply_eq
% 0.15/0.39 thf(fact_58_rep__abs__rsp,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,X1: A,X22: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ X1 @ X22 )
% 0.15/0.39 => ( R @ X1 @ ( Rep @ ( Abs @ X22 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rep_abs_rsp
% 0.15/0.39 thf(fact_59_equals__rsp,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,Xa: A,Xb: A,Ya: A,Yb: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( R @ Xa @ Xb )
% 0.15/0.39 => ( ( R @ Ya @ Yb )
% 0.15/0.39 => ( ( R @ Xa @ Ya )
% 0.15/0.39 = ( R @ Xb @ Yb ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % equals_rsp
% 0.15/0.39 thf(fact_60_Quotient3I,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,Abs: B > A,Rep: A > B,R: B > B > $o] :
% 0.15/0.39 ( ! [A4: A] :
% 0.15/0.39 ( ( Abs @ ( Rep @ A4 ) )
% 0.15/0.39 = A4 )
% 0.15/0.39 => ( ! [A4: A] : ( R @ ( Rep @ A4 ) @ ( Rep @ A4 ) )
% 0.15/0.39 => ( ! [R6: B,S4: B] :
% 0.15/0.39 ( ( R @ R6 @ S4 )
% 0.15/0.39 = ( ( R @ R6 @ R6 )
% 0.15/0.39 & ( R @ S4 @ S4 )
% 0.15/0.39 & ( ( Abs @ R6 )
% 0.15/0.39 = ( Abs @ S4 ) ) ) )
% 0.15/0.39 => ( quotient3 @ B @ A @ R @ Abs @ Rep ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Quotient3I
% 0.15/0.39 thf(fact_61_cond__prs,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Absf: A > B,Repf: B > A,A3: $o,B3: B,C3: B] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Absf @ Repf )
% 0.15/0.39 => ( ( A3
% 0.15/0.39 => ( ( Absf @ ( if @ A @ A3 @ ( Repf @ B3 ) @ ( Repf @ C3 ) ) )
% 0.15/0.39 = B3 ) )
% 0.15/0.39 & ( ~ A3
% 0.15/0.39 => ( ( Absf @ ( if @ A @ A3 @ ( Repf @ B3 ) @ ( Repf @ C3 ) ) )
% 0.15/0.39 = C3 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % cond_prs
% 0.15/0.39 thf(fact_62_let__prs,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,B: $tType,D: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,Abs22: C > D,Rep22: D > C] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 0.15/0.39 => ( ( quotient3 @ C @ D @ R2 @ Abs22 @ Rep22 )
% 0.15/0.39 => ( ( map_fun @ D @ C @ ( ( C > A ) > A ) @ ( ( D > B ) > B ) @ Rep22 @ ( map_fun @ ( D > B ) @ ( C > A ) @ A @ B @ ( map_fun @ C @ D @ B @ A @ Abs22 @ Rep12 ) @ Abs12 )
% 0.15/0.39 @ ^ [S2: C,F2: C > A] : ( F2 @ S2 ) )
% 0.15/0.39 = ( ^ [S2: D,F2: D > B] : ( F2 @ S2 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % let_prs
% 0.15/0.39 thf(fact_63_o__prs_I1_J,axiom,
% 0.15/0.39 ! [C: $tType,E: $tType,A: $tType,B: $tType,F3: $tType,D: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,Abs22: C > D,Rep22: D > C,R32: E > E > $o,Abs32: E > F3,Rep32: F3 > E] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 0.15/0.39 => ( ( quotient3 @ C @ D @ R2 @ Abs22 @ Rep22 )
% 0.15/0.39 => ( ( quotient3 @ E @ F3 @ R32 @ Abs32 @ Rep32 )
% 0.15/0.39 => ( ( map_fun @ ( D > F3 ) @ ( C > E ) @ ( ( A > C ) > A > E ) @ ( ( B > D ) > B > F3 ) @ ( map_fun @ C @ D @ F3 @ E @ Abs22 @ Rep32 ) @ ( map_fun @ ( B > D ) @ ( A > C ) @ ( A > E ) @ ( B > F3 ) @ ( map_fun @ A @ B @ D @ C @ Abs12 @ Rep22 ) @ ( map_fun @ B @ A @ E @ F3 @ Rep12 @ Abs32 ) ) @ ( comp @ C @ E @ A ) )
% 0.15/0.39 = ( comp @ D @ F3 @ B ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % o_prs(1)
% 0.15/0.39 thf(fact_64_llist__all2__lfilterI,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Q1: A > $o,Q2: B > $o] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.39 => ( ! [X: A,Y: B] :
% 0.15/0.39 ( ( P @ X @ Y )
% 0.15/0.39 => ( ( Q1 @ X )
% 0.15/0.39 = ( Q2 @ Y ) ) )
% 0.15/0.39 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_lfilter @ A @ Q1 @ Xs ) @ ( coinductive_lfilter @ B @ Q2 @ Ys ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_lfilterI
% 0.15/0.39 thf(fact_65_apply__rspQ3_H_H,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,S: C > C > $o,F: A > C,X2: B] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( bNF_rel_fun @ A @ A @ C @ C @ R @ S @ F @ F )
% 0.15/0.39 => ( S @ ( F @ ( Rep @ X2 ) ) @ ( F @ ( Rep @ X2 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % apply_rspQ3''
% 0.15/0.39 thf(fact_66_apply__rspQ3,axiom,
% 0.15/0.39 ! [B: $tType,C: $tType,A: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,F: A > C,G: A > C,X2: A,Y2: A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 0.15/0.39 => ( ( bNF_rel_fun @ A @ A @ C @ C @ R1 @ R2 @ F @ G )
% 0.15/0.39 => ( ( R1 @ X2 @ Y2 )
% 0.15/0.39 => ( R2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % apply_rspQ3
% 0.15/0.39 thf(fact_67_llist__all2__ldropWhileI,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Q1: A > $o,Q2: B > $o] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.39 => ( ! [X: A,Y: B] :
% 0.15/0.39 ( ( P @ X @ Y )
% 0.15/0.39 => ( ( Q1 @ X )
% 0.15/0.39 = ( Q2 @ Y ) ) )
% 0.15/0.39 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coindu218763757pWhile @ A @ Q1 @ Xs ) @ ( coindu218763757pWhile @ B @ Q2 @ Ys ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_ldropWhileI
% 0.15/0.39 thf(fact_68_quot__rel__rsp,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( bNF_rel_fun @ A @ A @ ( A > $o ) @ ( A > $o ) @ R
% 0.15/0.39 @ ( bNF_rel_fun @ A @ A @ $o @ $o @ R
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ R
% 0.15/0.39 @ R ) ) ).
% 0.15/0.39
% 0.15/0.39 % quot_rel_rsp
% 0.15/0.39 thf(fact_69_o__rsp_I1_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,E: $tType,F3: $tType,D: $tType,C: $tType,R2: A > C > $o,R32: B > D > $o,R1: E > F3 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > A ) > E > B ) @ ( ( F3 > C ) > F3 > D ) @ ( bNF_rel_fun @ A @ C @ B @ D @ R2 @ R32 ) @ ( bNF_rel_fun @ ( E > A ) @ ( F3 > C ) @ ( E > B ) @ ( F3 > D ) @ ( bNF_rel_fun @ E @ F3 @ A @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ E @ F3 @ B @ D @ R1 @ R32 ) ) @ ( comp @ A @ B @ E ) @ ( comp @ C @ D @ F3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % o_rsp(1)
% 0.15/0.39 thf(fact_70_o__rsp_I2_J,axiom,
% 0.15/0.39 ! [E: $tType,F3: $tType,H: $tType,G2: $tType,R1: E > F3 > $o] :
% 0.15/0.39 ( bNF_rel_fun @ ( G2 > H ) @ ( G2 > H ) @ ( ( E > G2 ) > E > H ) @ ( ( F3 > G2 ) > F3 > H )
% 0.15/0.39 @ ^ [Y3: G2 > H,Z: G2 > H] : ( Y3 = Z )
% 0.15/0.39 @ ( bNF_rel_fun @ ( E > G2 ) @ ( F3 > G2 ) @ ( E > H ) @ ( F3 > H )
% 0.15/0.39 @ ( bNF_rel_fun @ E @ F3 @ G2 @ G2 @ R1
% 0.15/0.39 @ ^ [Y3: G2,Z: G2] : ( Y3 = Z ) )
% 0.15/0.39 @ ( bNF_rel_fun @ E @ F3 @ H @ H @ R1
% 0.15/0.39 @ ^ [Y3: H,Z: H] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( comp @ G2 @ H @ E )
% 0.15/0.39 @ ( comp @ G2 @ H @ F3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % o_rsp(2)
% 0.15/0.39 thf(fact_71_map__fun__apply,axiom,
% 0.15/0.39 ! [D: $tType,A: $tType,C: $tType,B: $tType] :
% 0.15/0.39 ( ( map_fun @ B @ C @ D @ A )
% 0.15/0.39 = ( ^ [F2: B > C,G3: D > A,H3: C > D,X4: B] : ( G3 @ ( H3 @ ( F2 @ X4 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % map_fun_apply
% 0.15/0.39 thf(fact_72_comp__apply,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,B: $tType] :
% 0.15/0.39 ( ( comp @ B @ A @ C )
% 0.15/0.39 = ( ^ [F2: B > A,G3: C > B,X4: C] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_apply
% 0.15/0.39 thf(fact_73_map__fun__def,axiom,
% 0.15/0.39 ! [B: $tType,D: $tType,A: $tType,C: $tType] :
% 0.15/0.39 ( ( map_fun @ C @ A @ B @ D )
% 0.15/0.39 = ( ^ [F2: C > A,G3: B > D,H3: A > B] : ( comp @ A @ D @ C @ ( comp @ B @ D @ A @ G3 @ H3 ) @ F2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % map_fun_def
% 0.15/0.39 thf(fact_74_map__fun_Ocomp,axiom,
% 0.15/0.39 ! [E: $tType,C: $tType,A: $tType,F3: $tType,D: $tType,B: $tType,F: E > C,G: D > F3,H2: C > A,I: B > D] :
% 0.15/0.39 ( ( comp @ ( C > D ) @ ( E > F3 ) @ ( A > B ) @ ( map_fun @ E @ C @ D @ F3 @ F @ G ) @ ( map_fun @ C @ A @ B @ D @ H2 @ I ) )
% 0.15/0.39 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H2 @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % map_fun.comp
% 0.15/0.39 thf(fact_75_map__fun_Ocompositionality,axiom,
% 0.15/0.39 ! [D: $tType,F3: $tType,C: $tType,E: $tType,B: $tType,A: $tType,F: E > C,G: D > F3,H2: C > A,I: B > D,Fun: A > B] :
% 0.15/0.39 ( ( map_fun @ E @ C @ D @ F3 @ F @ G @ ( map_fun @ C @ A @ B @ D @ H2 @ I @ Fun ) )
% 0.15/0.39 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H2 @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Fun ) ) ).
% 0.15/0.39
% 0.15/0.39 % map_fun.compositionality
% 0.15/0.39 thf(fact_76_llist_Omap__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F3: $tType,E: $tType,Rb: A > E > $o,Sd: B > F3 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F3 ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) ) @ ( ( coinductive_llist @ E ) > ( coinductive_llist @ F3 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F3 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ E ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ F3 ) @ ( coindu1486289336t_all2 @ A @ E @ Rb ) @ ( coindu1486289336t_all2 @ B @ F3 @ Sd ) ) @ ( coinductive_lmap @ A @ B ) @ ( coinductive_lmap @ E @ F3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.map_transfer
% 0.15/0.39 thf(fact_77_lmap__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > C > $o,B2: B > D > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) ) @ ( ( coinductive_llist @ C ) > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ C @ B @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ C ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ D ) @ ( coindu1486289336t_all2 @ A @ C @ A2 ) @ ( coindu1486289336t_all2 @ B @ D @ B2 ) ) @ ( coinductive_lmap @ A @ B ) @ ( coinductive_lmap @ C @ D ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmap_transfer
% 0.15/0.39 thf(fact_78_bex1__rel__rsp,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > A > $o,Absf: A > B,Repf: B > A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Absf @ Repf )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( A > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ A @ $o @ $o @ R
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( bex1_rel @ A @ R )
% 0.15/0.39 @ ( bex1_rel @ A @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bex1_rel_rsp
% 0.15/0.39 thf(fact_79_LCons__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) ) @ A2 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) ) @ ( coinductive_LCons @ A ) @ ( coinductive_LCons @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % LCons_transfer
% 0.15/0.39 thf(fact_80_llist_Oinject,axiom,
% 0.15/0.39 ! [A: $tType,X21: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.15/0.39 ( ( ( coinductive_LCons @ A @ X21 @ X222 )
% 0.15/0.39 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.15/0.39 = ( ( X21 = Y21 )
% 0.15/0.39 & ( X222 = Y22 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.inject
% 0.15/0.39 thf(fact_81_llist__all2__LCons__LCons,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X222: coinductive_llist @ A,Y21: B,Y22: coinductive_llist @ B] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ B @ R @ ( coinductive_LCons @ A @ X21 @ X222 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) )
% 0.15/0.39 = ( ( R @ X21 @ Y21 )
% 0.15/0.39 & ( coindu1486289336t_all2 @ A @ B @ R @ X222 @ Y22 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_LCons_LCons
% 0.15/0.39 thf(fact_82_lfilter__LCons,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,X2: A,Xs: coinductive_llist @ A] :
% 0.15/0.39 ( ( ( P @ X2 )
% 0.15/0.39 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 0.15/0.39 = ( coinductive_LCons @ A @ X2 @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) )
% 0.15/0.39 & ( ~ ( P @ X2 )
% 0.15/0.39 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 0.15/0.39 = ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_LCons
% 0.15/0.39 thf(fact_83_ldropWhile__LCons,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,X2: A,Xs: coinductive_llist @ A] :
% 0.15/0.39 ( ( ( P @ X2 )
% 0.15/0.39 => ( ( coindu218763757pWhile @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 0.15/0.39 = ( coindu218763757pWhile @ A @ P @ Xs ) ) )
% 0.15/0.39 & ( ~ ( P @ X2 )
% 0.15/0.39 => ( ( coindu218763757pWhile @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 0.15/0.39 = ( coinductive_LCons @ A @ X2 @ Xs ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % ldropWhile_LCons
% 0.15/0.39 thf(fact_84_unfold__llist__eq__LCons,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B,X2: A,Xs: coinductive_llist @ A] :
% 0.15/0.39 ( ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B3 )
% 0.15/0.39 = ( coinductive_LCons @ A @ X2 @ Xs ) )
% 0.15/0.39 = ( ~ ( IS_LNIL @ B3 )
% 0.15/0.39 & ( X2
% 0.15/0.39 = ( LHD @ B3 ) )
% 0.15/0.39 & ( Xs
% 0.15/0.39 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % unfold_llist_eq_LCons
% 0.15/0.39 thf(fact_85_llist_Opred__inject_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,A3: A,Aa2: coinductive_llist @ A] :
% 0.15/0.39 ( ( coindu543516966_llist @ A @ P @ ( coinductive_LCons @ A @ A3 @ Aa2 ) )
% 0.15/0.39 = ( ( P @ A3 )
% 0.15/0.39 & ( coindu543516966_llist @ A @ P @ Aa2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.pred_inject(2)
% 0.15/0.39 thf(fact_86_llist_Osimps_I13_J,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F: A > B,X21: A,X222: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lmap @ A @ B @ F @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.15/0.39 = ( coinductive_LCons @ B @ ( F @ X21 ) @ ( coinductive_lmap @ A @ B @ F @ X222 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.simps(13)
% 0.15/0.39 thf(fact_87_bex1__rel__aux,axiom,
% 0.15/0.39 ! [A: $tType,R: A > A > $o,X2: A > $o,Y2: A > $o] :
% 0.15/0.39 ( ! [Xa2: A,Ya2: A] :
% 0.15/0.39 ( ( R @ Xa2 @ Ya2 )
% 0.15/0.39 => ( ( X2 @ Xa2 )
% 0.15/0.39 = ( Y2 @ Ya2 ) ) )
% 0.15/0.39 => ( ( bex1_rel @ A @ R @ X2 )
% 0.15/0.39 => ( bex1_rel @ A @ R @ Y2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bex1_rel_aux
% 0.15/0.39 thf(fact_88_bex1__rel__aux2,axiom,
% 0.15/0.39 ! [A: $tType,R: A > A > $o,X2: A > $o,Y2: A > $o] :
% 0.15/0.39 ( ! [Xa2: A,Ya2: A] :
% 0.15/0.39 ( ( R @ Xa2 @ Ya2 )
% 0.15/0.39 => ( ( X2 @ Xa2 )
% 0.15/0.39 = ( Y2 @ Ya2 ) ) )
% 0.15/0.39 => ( ( bex1_rel @ A @ R @ Y2 )
% 0.15/0.39 => ( bex1_rel @ A @ R @ X2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bex1_rel_aux2
% 0.15/0.39 thf(fact_89_lmap__eq__LCons__conv,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B,Y2: A,Ys: coinductive_llist @ A] :
% 0.15/0.39 ( ( ( coinductive_lmap @ B @ A @ F @ Xs )
% 0.15/0.39 = ( coinductive_LCons @ A @ Y2 @ Ys ) )
% 0.15/0.39 = ( ? [X4: B,Xs2: coinductive_llist @ B] :
% 0.15/0.39 ( ( Xs
% 0.15/0.39 = ( coinductive_LCons @ B @ X4 @ Xs2 ) )
% 0.15/0.39 & ( Y2
% 0.15/0.39 = ( F @ X4 ) )
% 0.15/0.39 & ( Ys
% 0.15/0.39 = ( coinductive_lmap @ B @ A @ F @ Xs2 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmap_eq_LCons_conv
% 0.15/0.39 thf(fact_90_iterates__equality,axiom,
% 0.15/0.39 ! [A: $tType,H2: A > ( coinductive_llist @ A ),F: A > A] :
% 0.15/0.39 ( ! [X: A] :
% 0.15/0.39 ( ( H2 @ X )
% 0.15/0.39 = ( coinductive_LCons @ A @ X @ ( coinductive_lmap @ A @ A @ F @ ( H2 @ X ) ) ) )
% 0.15/0.39 => ( H2
% 0.15/0.39 = ( coinductive_iterates @ A @ F ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % iterates_equality
% 0.15/0.39 thf(fact_91_iterates__lmap,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( ( coinductive_iterates @ A )
% 0.15/0.39 = ( ^ [F2: A > A,X4: A] : ( coinductive_LCons @ A @ X4 @ ( coinductive_lmap @ A @ A @ F2 @ ( coinductive_iterates @ A @ F2 @ X4 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % iterates_lmap
% 0.15/0.39 thf(fact_92_llist_Omap__comp,axiom,
% 0.15/0.39 ! [B: $tType,C: $tType,A: $tType,G: B > C,F: A > B,V: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lmap @ B @ C @ G @ ( coinductive_lmap @ A @ B @ F @ V ) )
% 0.15/0.39 = ( coinductive_lmap @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.map_comp
% 0.15/0.39 thf(fact_93_lfilter__lmap,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > $o,F: B > A,Xs: coinductive_llist @ B] :
% 0.15/0.39 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.15/0.39 = ( coinductive_lmap @ B @ A @ F @ ( coinductive_lfilter @ B @ ( comp @ A @ $o @ B @ P @ F ) @ Xs ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_lmap
% 0.15/0.39 thf(fact_94_ltakeWhile__lmap,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > $o,F: B > A,Xs: coinductive_llist @ B] :
% 0.15/0.39 ( ( coindu501562517eWhile @ A @ P @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.15/0.39 = ( coinductive_lmap @ B @ A @ F @ ( coindu501562517eWhile @ B @ ( comp @ A @ $o @ B @ P @ F ) @ Xs ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % ltakeWhile_lmap
% 0.15/0.39 thf(fact_95_ldropWhile__lmap,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > $o,F: B > A,Xs: coinductive_llist @ B] :
% 0.15/0.39 ( ( coindu218763757pWhile @ A @ P @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.15/0.39 = ( coinductive_lmap @ B @ A @ F @ ( coindu218763757pWhile @ B @ ( comp @ A @ $o @ B @ P @ F ) @ Xs ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % ldropWhile_lmap
% 0.15/0.39 thf(fact_96_lmap__iterates,axiom,
% 0.15/0.39 ! [A: $tType,F: A > A,X2: A] :
% 0.15/0.39 ( ( coinductive_lmap @ A @ A @ F @ ( coinductive_iterates @ A @ F @ X2 ) )
% 0.15/0.39 = ( coinductive_iterates @ A @ F @ ( F @ X2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmap_iterates
% 0.15/0.39 thf(fact_97_llist_Orel__intros_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X222: coinductive_llist @ A,Y22: coinductive_llist @ B] :
% 0.15/0.39 ( ( R @ X21 @ Y21 )
% 0.15/0.39 => ( ( coindu1486289336t_all2 @ A @ B @ R @ X222 @ Y22 )
% 0.15/0.39 => ( coindu1486289336t_all2 @ A @ B @ R @ ( coinductive_LCons @ A @ X21 @ X222 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.rel_intros(2)
% 0.15/0.39 thf(fact_98_llist__all2__LCons1,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,P: A > B > $o,X2: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) @ Ys )
% 0.15/0.39 = ( ? [Y5: B,Ys2: coinductive_llist @ B] :
% 0.15/0.39 ( ( Ys
% 0.15/0.39 = ( coinductive_LCons @ B @ Y5 @ Ys2 ) )
% 0.15/0.39 & ( P @ X2 @ Y5 )
% 0.15/0.39 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_LCons1
% 0.15/0.39 thf(fact_99_llist__all2__LCons2,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Y2: B,Ys: coinductive_llist @ B] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ ( coinductive_LCons @ B @ Y2 @ Ys ) )
% 0.15/0.39 = ( ? [X4: A,Xs2: coinductive_llist @ A] :
% 0.15/0.39 ( ( Xs
% 0.15/0.39 = ( coinductive_LCons @ A @ X4 @ Xs2 ) )
% 0.15/0.39 & ( P @ X4 @ Y2 )
% 0.15/0.39 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs2 @ Ys ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist_all2_LCons2
% 0.15/0.39 thf(fact_100_lmap__lmirror,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.15/0.39 ( ( coinductive_lmap @ B @ A @ F @ ( lMirro427583474mirror @ B @ Xs ) )
% 0.15/0.39 = ( lMirro427583474mirror @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmap_lmirror
% 0.15/0.39 thf(fact_101_llist_Opred__map,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,Q: B > $o,F: A > B,X2: coinductive_llist @ A] :
% 0.15/0.39 ( ( coindu543516966_llist @ B @ Q @ ( coinductive_lmap @ A @ B @ F @ X2 ) )
% 0.15/0.39 = ( coindu543516966_llist @ A @ ( comp @ B @ $o @ A @ Q @ F ) @ X2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.pred_map
% 0.15/0.39 thf(fact_102_llist_Osimps_I5_J,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F1: B,F22: A > ( coinductive_llist @ A ) > B,X21: A,X222: coinductive_llist @ A] :
% 0.15/0.39 ( ( coindu1381640503_llist @ B @ A @ F1 @ F22 @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.15/0.39 = ( F22 @ X21 @ X222 ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.simps(5)
% 0.15/0.39 thf(fact_103_lfilter__LCons__seek,axiom,
% 0.15/0.39 ! [A: $tType,P3: A > $o,X2: A,L: coinductive_llist @ A] :
% 0.15/0.39 ( ~ ( P3 @ X2 )
% 0.15/0.39 => ( ( coinductive_lfilter @ A @ P3 @ ( coinductive_LCons @ A @ X2 @ L ) )
% 0.15/0.39 = ( coinductive_lfilter @ A @ P3 @ L ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_LCons_seek
% 0.15/0.39 thf(fact_104_lfilter__LCons__found,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,X2: A,Xs: coinductive_llist @ A] :
% 0.15/0.39 ( ( P @ X2 )
% 0.15/0.39 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 0.15/0.39 = ( coinductive_LCons @ A @ X2 @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_LCons_found
% 0.15/0.39 thf(fact_105_iterates_Ocode,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( ( coinductive_iterates @ A )
% 0.15/0.39 = ( ^ [F2: A > A,X4: A] : ( coinductive_LCons @ A @ X4 @ ( coinductive_iterates @ A @ F2 @ ( F2 @ X4 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % iterates.code
% 0.15/0.39 thf(fact_106_unfold__llist_Octr_I2_J,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,P3: A > $o,A3: A,G21: A > B,G22: A > A] :
% 0.15/0.39 ( ~ ( P3 @ A3 )
% 0.15/0.39 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A3 )
% 0.15/0.39 = ( coinductive_LCons @ B @ ( G21 @ A3 ) @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % unfold_llist.ctr(2)
% 0.15/0.39 thf(fact_107_llist_Ocorec_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,P3: C > $o,A3: C,G21: C > A,Q22: C > $o,G221: C > ( coinductive_llist @ A ),G222: C > C] :
% 0.15/0.39 ( ~ ( P3 @ A3 )
% 0.15/0.39 => ( ( coindu1259883913_llist @ C @ A @ P3 @ G21 @ Q22 @ G221 @ G222 @ A3 )
% 0.15/0.39 = ( coinductive_LCons @ A @ ( G21 @ A3 ) @ ( if @ ( coinductive_llist @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( coindu1259883913_llist @ C @ A @ P3 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.corec(2)
% 0.15/0.39 thf(fact_108_lmap__unfold__llist,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,F: B > A,IS_LNIL: C > $o,LHD: C > B,LTL: C > C,B3: C] :
% 0.15/0.39 ( ( coinductive_lmap @ B @ A @ F @ ( coindu1441602521_llist @ C @ B @ IS_LNIL @ LHD @ LTL @ B3 ) )
% 0.15/0.39 = ( coindu1441602521_llist @ C @ A @ IS_LNIL @ ( comp @ B @ A @ C @ F @ LHD ) @ LTL @ B3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmap_unfold_llist
% 0.15/0.39 thf(fact_109_llist_Omap__o__corec,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: C > $o,Ga: C > A,Gb: C > $o,Gc: C > ( coinductive_llist @ A ),Gd: C > C] :
% 0.15/0.39 ( ( comp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ ( coinductive_lmap @ A @ B @ F ) @ ( coindu1259883913_llist @ C @ A @ G @ Ga @ Gb @ Gc @ Gd ) )
% 0.15/0.39 = ( coindu1259883913_llist @ C @ B @ G @ ( comp @ A @ B @ C @ F @ Ga ) @ Gb @ ( comp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ ( coinductive_lmap @ A @ B @ F ) @ Gc ) @ Gd ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.map_o_corec
% 0.15/0.39 thf(fact_110_lmap__corec__llist,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,F: B > A,IS_LNIL: C > $o,LHD: C > B,EndORmore: C > $o,TTL_end: C > ( coinductive_llist @ B ),TTL_more: C > C,B3: C] :
% 0.15/0.39 ( ( coinductive_lmap @ B @ A @ F @ ( coindu1259883913_llist @ C @ B @ IS_LNIL @ LHD @ EndORmore @ TTL_end @ TTL_more @ B3 ) )
% 0.15/0.39 = ( coindu1259883913_llist @ C @ A @ IS_LNIL @ ( comp @ B @ A @ C @ F @ LHD ) @ EndORmore @ ( comp @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ C @ ( coinductive_lmap @ B @ A @ F ) @ TTL_end ) @ TTL_more @ B3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmap_corec_llist
% 0.15/0.39 thf(fact_111_lfilter__eq__LCons,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A,X2: A,Xs3: coinductive_llist @ A] :
% 0.15/0.39 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.15/0.39 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 0.15/0.39 => ? [Xs4: coinductive_llist @ A] :
% 0.15/0.39 ( ( Xs3
% 0.15/0.39 = ( coinductive_lfilter @ A @ P @ Xs4 ) )
% 0.15/0.39 & ( ( coindu218763757pWhile @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ Xs )
% 0.15/0.39 = ( coinductive_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lfilter_eq_LCons
% 0.15/0.39 thf(fact_112_comp__eq__dest__lhs,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B3: A > C,C3: A > B,V: A] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.15/0.39 = C3 )
% 0.15/0.39 => ( ( A3 @ ( B3 @ V ) )
% 0.15/0.39 = ( C3 @ V ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_eq_dest_lhs
% 0.15/0.39 thf(fact_113_comp__eq__elim,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C3: D > B,D3: A > D] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.15/0.39 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 0.15/0.39 => ! [V2: A] :
% 0.15/0.39 ( ( A3 @ ( B3 @ V2 ) )
% 0.15/0.39 = ( C3 @ ( D3 @ V2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_eq_elim
% 0.15/0.39 thf(fact_114_comp__eq__dest,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C3: D > B,D3: A > D,V: A] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.15/0.39 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 0.15/0.39 => ( ( A3 @ ( B3 @ V ) )
% 0.15/0.39 = ( C3 @ ( D3 @ V ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_eq_dest
% 0.15/0.39 thf(fact_115_comp__assoc,axiom,
% 0.15/0.39 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H2: A > C] :
% 0.15/0.39 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H2 )
% 0.15/0.39 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_assoc
% 0.15/0.39 thf(fact_116_comp__def,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType] :
% 0.15/0.39 ( ( comp @ B @ C @ A )
% 0.15/0.39 = ( ^ [F2: B > C,G3: A > B,X4: A] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_def
% 0.15/0.39 thf(fact_117_llist_Octr__transfer_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) ) @ R @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) @ ( coinductive_LCons @ A ) @ ( coinductive_LCons @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.ctr_transfer(2)
% 0.15/0.39 thf(fact_118_lmember__code_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,X2: A,Y2: A,Ys: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lmember @ A @ X2 @ ( coinductive_LCons @ A @ Y2 @ Ys ) )
% 0.15/0.39 = ( ( X2 = Y2 )
% 0.15/0.39 | ( coinductive_lmember @ A @ X2 @ Ys ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lmember_code(2)
% 0.15/0.39 thf(fact_119_type__copy__map__cong0,axiom,
% 0.15/0.39 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X2: C,N: D > A,H2: C > D,F: A > E] :
% 0.15/0.39 ( ( ( M @ ( G @ X2 ) )
% 0.15/0.39 = ( N @ ( H2 @ X2 ) ) )
% 0.15/0.39 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X2 )
% 0.15/0.39 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N ) @ H2 @ X2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % type_copy_map_cong0
% 0.15/0.39 thf(fact_120_comp__cong,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F: B > A,G: C > B,X2: C,F4: D > A,G4: E > D,X5: E] :
% 0.15/0.39 ( ( ( F @ ( G @ X2 ) )
% 0.15/0.39 = ( F4 @ ( G4 @ X5 ) ) )
% 0.15/0.39 => ( ( comp @ B @ A @ C @ F @ G @ X2 )
% 0.15/0.39 = ( comp @ D @ A @ E @ F4 @ G4 @ X5 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_cong
% 0.15/0.39 thf(fact_121_if__prs,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( map_fun @ $o @ $o @ ( A > A > A ) @ ( B > B > B ) @ ( id @ $o ) @ ( map_fun @ B @ A @ ( A > A ) @ ( B > B ) @ Rep @ ( map_fun @ B @ A @ A @ B @ Rep @ Abs ) ) @ ( if @ A ) )
% 0.15/0.39 = ( if @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % if_prs
% 0.15/0.39 thf(fact_122_o__prs_I2_J,axiom,
% 0.15/0.39 ! [F3: $tType,E: $tType,C: $tType,D: $tType,A: $tType,B: $tType,H: $tType,G2: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,Abs22: C > D,Rep22: D > C,R32: E > E > $o,Abs32: E > F3,Rep32: F3 > E] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 0.15/0.39 => ( ( quotient3 @ C @ D @ R2 @ Abs22 @ Rep22 )
% 0.15/0.39 => ( ( quotient3 @ E @ F3 @ R32 @ Abs32 @ Rep32 )
% 0.15/0.39 => ( ( map_fun @ ( G2 > H ) @ ( G2 > H ) @ ( ( A > G2 ) > A > H ) @ ( ( B > G2 ) > B > H ) @ ( id @ ( G2 > H ) ) @ ( map_fun @ ( B > G2 ) @ ( A > G2 ) @ ( A > H ) @ ( B > H ) @ ( map_fun @ A @ B @ G2 @ G2 @ Abs12 @ ( id @ G2 ) ) @ ( map_fun @ B @ A @ H @ H @ Rep12 @ ( id @ H ) ) ) @ ( comp @ G2 @ H @ A ) )
% 0.15/0.39 = ( comp @ G2 @ H @ B ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % o_prs(2)
% 0.15/0.39 thf(fact_123_fun__ord__parametric,axiom,
% 0.15/0.39 ! [C: $tType,D: $tType,A: $tType,B: $tType,F3: $tType,E: $tType,C2: A > B > $o,A2: C > E > $o,B2: D > F3 > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ C2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( C > D > $o ) @ ( E > F3 > $o ) @ ( ( A > C ) > ( A > D ) > $o ) @ ( ( B > E ) > ( B > F3 ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ E @ ( D > $o ) @ ( F3 > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ D @ F3 @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > C ) @ ( B > E ) @ ( ( A > D ) > $o ) @ ( ( B > F3 ) > $o ) @ ( bNF_rel_fun @ A @ B @ C @ E @ C2 @ A2 )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > D ) @ ( B > F3 ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ D @ F3 @ C2 @ B2 )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( partial_fun_ord @ C @ D @ A )
% 0.15/0.39 @ ( partial_fun_ord @ E @ F3 @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_ord_parametric
% 0.15/0.39 thf(fact_124_id__apply,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( ( id @ A )
% 0.15/0.39 = ( ^ [X4: A] : X4 ) ) ).
% 0.15/0.39
% 0.15/0.39 % id_apply
% 0.15/0.39 thf(fact_125_fun_Omap__id,axiom,
% 0.15/0.39 ! [A: $tType,D: $tType,T2: D > A] :
% 0.15/0.39 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 0.15/0.39 = T2 ) ).
% 0.15/0.39
% 0.15/0.39 % fun.map_id
% 0.15/0.39 thf(fact_126_comp__id,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F: A > B] :
% 0.15/0.39 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 0.15/0.39 = F ) ).
% 0.15/0.39
% 0.15/0.39 % comp_id
% 0.15/0.39 thf(fact_127_id__comp,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,G: A > B] :
% 0.15/0.39 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 0.15/0.39 = G ) ).
% 0.15/0.39
% 0.15/0.39 % id_comp
% 0.15/0.39 thf(fact_128_fun_Omap__id0,axiom,
% 0.15/0.39 ! [A: $tType,D: $tType] :
% 0.15/0.39 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 0.15/0.39 = ( id @ ( D > A ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.map_id0
% 0.15/0.39 thf(fact_129_map__fun__id,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( map_fun @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 0.15/0.39 = ( id @ ( A > B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % map_fun_id
% 0.15/0.39 thf(fact_130_llist_Omap__id0,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( ( coinductive_lmap @ A @ A @ ( id @ A ) )
% 0.15/0.39 = ( id @ ( coinductive_llist @ A ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.map_id0
% 0.15/0.39 thf(fact_131_eq__id__iff,axiom,
% 0.15/0.39 ! [A: $tType,F: A > A] :
% 0.15/0.39 ( ( ! [X4: A] :
% 0.15/0.39 ( ( F @ X4 )
% 0.15/0.39 = X4 ) )
% 0.15/0.39 = ( F
% 0.15/0.39 = ( id @ A ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % eq_id_iff
% 0.15/0.39 thf(fact_132_id__def,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( ( id @ A )
% 0.15/0.39 = ( ^ [X4: A] : X4 ) ) ).
% 0.15/0.39
% 0.15/0.39 % id_def
% 0.15/0.39 thf(fact_133_llist_Obi__total__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ R )
% 0.15/0.39 => ( bi_total @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.bi_total_rel
% 0.15/0.39 thf(fact_134_bi__total__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( bi_total @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ( ! [X4: A] :
% 0.15/0.39 ( ^ [P4: B > $o] :
% 0.15/0.39 ? [X6: B] : ( P4 @ X6 )
% 0.15/0.39 @ ( R4 @ X4 ) )
% 0.15/0.39 & ! [Y5: B] :
% 0.15/0.39 ? [X4: A] : ( R4 @ X4 @ Y5 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_total_def
% 0.15/0.39 thf(fact_135_bi__total__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( bi_total @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_total_eq
% 0.15/0.39 thf(fact_136_id__rsp,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ A @ B @ R @ R @ ( id @ A ) @ ( id @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % id_rsp
% 0.15/0.39 thf(fact_137_id__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] : ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 @ ( id @ A ) @ ( id @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % id_transfer
% 0.15/0.39 thf(fact_138_pointfree__idE,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F: B > A,G: A > B,X2: A] :
% 0.15/0.39 ( ( ( comp @ B @ A @ A @ F @ G )
% 0.15/0.39 = ( id @ A ) )
% 0.15/0.39 => ( ( F @ ( G @ X2 ) )
% 0.15/0.39 = X2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % pointfree_idE
% 0.15/0.39 thf(fact_139_comp__eq__id__dest,axiom,
% 0.15/0.39 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B3: A > C,C3: A > B,V: A] :
% 0.15/0.39 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.15/0.39 = ( comp @ B @ B @ A @ ( id @ B ) @ C3 ) )
% 0.15/0.39 => ( ( A3 @ ( B3 @ V ) )
% 0.15/0.39 = ( C3 @ V ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_eq_id_dest
% 0.15/0.39 thf(fact_140_llist_Omap__id,axiom,
% 0.15/0.39 ! [A: $tType,T2: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lmap @ A @ A @ ( id @ A ) @ T2 )
% 0.15/0.39 = T2 ) ).
% 0.15/0.39
% 0.15/0.39 % llist.map_id
% 0.15/0.39 thf(fact_141_identity__quotient3,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( quotient3 @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ ( id @ A )
% 0.15/0.39 @ ( id @ A ) ) ).
% 0.15/0.39
% 0.15/0.39 % identity_quotient3
% 0.15/0.39 thf(fact_142_abs__o__rep,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( comp @ A @ B @ B @ Abs @ Rep )
% 0.15/0.39 = ( id @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % abs_o_rep
% 0.15/0.39 thf(fact_143_id__prs,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 0.15/0.39 => ( ( map_fun @ B @ A @ A @ B @ Rep @ Abs @ ( id @ A ) )
% 0.15/0.39 = ( id @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % id_prs
% 0.15/0.39 thf(fact_144_transfer__forall__transfer_I1_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( transfer_forall @ A )
% 0.15/0.39 @ ( transfer_forall @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % transfer_forall_transfer(1)
% 0.15/0.39 thf(fact_145_monotone__parametric,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ ( ( C > C > $o ) > ( A > C ) > $o ) @ ( ( D > D > $o ) > ( B > D ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( C > C > $o ) @ ( D > D > $o ) @ ( ( A > C ) > $o ) @ ( ( B > D ) > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ ( C > $o ) @ ( D > $o ) @ B2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( comple1396247847notone @ A @ C )
% 0.15/0.39 @ ( comple1396247847notone @ B @ D ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % monotone_parametric
% 0.15/0.39 thf(fact_146_swap__comp__involutory,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A3: A,B3: A] :
% 0.15/0.39 ( ( comp @ ( A > B ) @ ( A > B ) @ ( A > B ) @ ( swap @ A @ B @ A3 @ B3 ) @ ( swap @ A @ B @ A3 @ B3 ) )
% 0.15/0.39 = ( id @ ( A > B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_comp_involutory
% 0.15/0.39 thf(fact_147_ex1__prs,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > A > $o,Absf: A > B,Repf: B > A,F: B > $o] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R @ Absf @ Repf )
% 0.15/0.39 => ( ( map_fun @ ( B > $o ) @ ( A > $o ) @ $o @ $o @ ( map_fun @ A @ B @ $o @ $o @ Absf @ ( id @ $o ) ) @ ( id @ $o ) @ ( bex1_rel @ A @ R ) @ F )
% 0.15/0.39 = ( ? [X4: B] :
% 0.15/0.39 ( ( F @ X4 )
% 0.15/0.39 & ! [Y5: B] :
% 0.15/0.39 ( ( F @ Y5 )
% 0.15/0.39 => ( Y5 = X4 ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % ex1_prs
% 0.15/0.39 thf(fact_148_swap__apply_I3_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C3: B,A3: B,B3: B,F: B > A] :
% 0.15/0.39 ( ( C3 != A3 )
% 0.15/0.39 => ( ( C3 != B3 )
% 0.15/0.39 => ( ( swap @ B @ A @ A3 @ B3 @ F @ C3 )
% 0.15/0.39 = ( F @ C3 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_apply(3)
% 0.15/0.39 thf(fact_149_swap__apply_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A3: B,B3: B,F: B > A] :
% 0.15/0.39 ( ( swap @ B @ A @ A3 @ B3 @ F @ B3 )
% 0.15/0.39 = ( F @ A3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_apply(2)
% 0.15/0.39 thf(fact_150_swap__apply_I1_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A3: B,B3: B,F: B > A] :
% 0.15/0.39 ( ( swap @ B @ A @ A3 @ B3 @ F @ A3 )
% 0.15/0.39 = ( F @ B3 ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_apply(1)
% 0.15/0.39 thf(fact_151_swap__self,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A3: A,F: A > B] :
% 0.15/0.39 ( ( swap @ A @ B @ A3 @ A3 @ F )
% 0.15/0.39 = F ) ).
% 0.15/0.39
% 0.15/0.39 % swap_self
% 0.15/0.39 thf(fact_152_swap__nilpotent,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A3: A,B3: A,F: A > B] :
% 0.15/0.39 ( ( swap @ A @ B @ A3 @ B3 @ ( swap @ A @ B @ A3 @ B3 @ F ) )
% 0.15/0.39 = F ) ).
% 0.15/0.39
% 0.15/0.39 % swap_nilpotent
% 0.15/0.39 thf(fact_153_swap__triple,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A3: A,C3: A,B3: A,F: A > B] :
% 0.15/0.39 ( ( A3 != C3 )
% 0.15/0.39 => ( ( B3 != C3 )
% 0.15/0.39 => ( ( swap @ A @ B @ A3 @ B3 @ ( swap @ A @ B @ B3 @ C3 @ ( swap @ A @ B @ A3 @ B3 @ F ) ) )
% 0.15/0.39 = ( swap @ A @ B @ A3 @ C3 @ F ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_triple
% 0.15/0.39 thf(fact_154_swap__commute,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( swap @ A @ B )
% 0.15/0.39 = ( ^ [A5: A,B5: A] : ( swap @ A @ B @ B5 @ A5 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_commute
% 0.15/0.39 thf(fact_155_comp__swap,axiom,
% 0.15/0.39 ! [B: $tType,C: $tType,A: $tType,F: C > B,A3: A,B3: A,G: A > C] :
% 0.15/0.39 ( ( comp @ C @ B @ A @ F @ ( swap @ A @ C @ A3 @ B3 @ G ) )
% 0.15/0.39 = ( swap @ A @ B @ A3 @ B3 @ ( comp @ C @ B @ A @ F @ G ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % comp_swap
% 0.15/0.39 thf(fact_156_transfer__forall__transfer_I4_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ rev_implies
% 0.15/0.39 @ ( transfer_forall @ A )
% 0.15/0.39 @ ( transfer_forall @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % transfer_forall_transfer(4)
% 0.15/0.39 thf(fact_157_transfer__forall__transfer_I5_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ rev_implies ) @ rev_implies @ ( transfer_forall @ A ) @ ( transfer_forall @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % transfer_forall_transfer(5)
% 0.15/0.39 thf(fact_158_Domainp__transfer,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,B: $tType,D: $tType,B2: A > B > $o,A2: C > D > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( C > A > $o ) @ ( D > B > $o ) @ ( C > $o ) @ ( D > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ( domainp @ C @ A )
% 0.15/0.39 @ ( domainp @ D @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Domainp_transfer
% 0.15/0.39 thf(fact_159_rev__implies__def,axiom,
% 0.15/0.39 ( rev_implies
% 0.15/0.39 = ( ^ [X4: $o,Y5: $o] :
% 0.15/0.39 ( Y5
% 0.15/0.39 => X4 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rev_implies_def
% 0.15/0.39 thf(fact_160_Domainp__refl,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( domainp @ A @ B )
% 0.15/0.39 = ( domainp @ A @ B ) ) ).
% 0.15/0.39
% 0.15/0.39 % Domainp_refl
% 0.15/0.39 thf(fact_161_Domainp__iff,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( domainp @ A @ B )
% 0.15/0.39 = ( ^ [T3: A > B > $o,X4: A] :
% 0.15/0.39 ( ^ [P4: B > $o] :
% 0.15/0.39 ? [X6: B] : ( P4 @ X6 )
% 0.15/0.39 @ ( T3 @ X4 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Domainp_iff
% 0.15/0.39 thf(fact_162_llist_ODomainp__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( domainp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) )
% 0.15/0.39 = ( coindu543516966_llist @ A @ ( domainp @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.Domainp_rel
% 0.15/0.39 thf(fact_163_reflp__transfer_I5_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ rev_implies
% 0.15/0.39 @ ( reflp @ A )
% 0.15/0.39 @ ( reflp @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % reflp_transfer(5)
% 0.15/0.39 thf(fact_164_reflp__transfer_I4_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ rev_implies ) ) @ rev_implies @ ( reflp @ A ) @ ( reflp @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % reflp_transfer(4)
% 0.15/0.39 thf(fact_165_Ex1__parametric,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( ex1 @ A )
% 0.15/0.39 @ ( ex1 @ B ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Ex1_parametric
% 0.15/0.39 thf(fact_166_bi__unique__fun,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_unique @ C @ D @ B2 )
% 0.15/0.39 => ( bi_unique @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_unique_fun
% 0.15/0.39 thf(fact_167_fun_Orel__reflp,axiom,
% 0.15/0.39 ! [D: $tType,A: $tType,R: A > A > $o] :
% 0.15/0.39 ( ( reflp @ A @ R )
% 0.15/0.39 => ( reflp @ ( D > A )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ A @ A
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.rel_reflp
% 0.15/0.39 thf(fact_168_DEADID_Orel__reflp,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( reflp @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % DEADID.rel_reflp
% 0.15/0.39 thf(fact_169_bi__uniqueDl,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A2: A > B > $o,X2: A,Y2: B,Z2: A] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( A2 @ X2 @ Y2 )
% 0.15/0.39 => ( ( A2 @ Z2 @ Y2 )
% 0.15/0.39 => ( X2 = Z2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_uniqueDl
% 0.15/0.39 thf(fact_170_bi__uniqueDr,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o,X2: A,Y2: B,Z2: B] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( A2 @ X2 @ Y2 )
% 0.15/0.39 => ( ( A2 @ X2 @ Z2 )
% 0.15/0.39 => ( Y2 = Z2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_uniqueDr
% 0.15/0.39 thf(fact_171_bi__unique__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( bi_unique @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_unique_eq
% 0.15/0.39 thf(fact_172_bi__unique__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( bi_unique @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ( ! [X4: A,Y5: B,Z3: B] :
% 0.15/0.39 ( ( R4 @ X4 @ Y5 )
% 0.15/0.39 => ( ( R4 @ X4 @ Z3 )
% 0.15/0.39 => ( Y5 = Z3 ) ) )
% 0.15/0.39 & ! [X4: A,Y5: A,Z3: B] :
% 0.15/0.39 ( ( R4 @ X4 @ Z3 )
% 0.15/0.39 => ( ( R4 @ Y5 @ Z3 )
% 0.15/0.39 => ( X4 = Y5 ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_unique_def
% 0.15/0.39 thf(fact_173_llist_Orel__reflp,axiom,
% 0.15/0.39 ! [A: $tType,R: A > A > $o] :
% 0.15/0.39 ( ( reflp @ A @ R )
% 0.15/0.39 => ( reflp @ ( coinductive_llist @ A ) @ ( coindu1486289336t_all2 @ A @ A @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.rel_reflp
% 0.15/0.39 thf(fact_174_llist_Obi__unique__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ R )
% 0.15/0.39 => ( bi_unique @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.bi_unique_rel
% 0.15/0.39 thf(fact_175_bi__total__fun,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ C @ D @ B2 )
% 0.15/0.39 => ( bi_total @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_total_fun
% 0.15/0.39 thf(fact_176_eq__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % eq_transfer
% 0.15/0.39 thf(fact_177_bi__unique__alt__def2,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( bi_unique @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ R4
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R4
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_unique_alt_def2
% 0.15/0.39 thf(fact_178_reflp__transfer_I1_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( reflp @ A )
% 0.15/0.39 @ ( reflp @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % reflp_transfer(1)
% 0.15/0.39 thf(fact_179_fun__upd__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ ( A > C > A > C ) @ ( B > D > B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ A @ B @ ( C > A > C ) @ ( D > B > D ) @ A2 @ ( bNF_rel_fun @ C @ D @ ( A > C ) @ ( B > D ) @ B2 @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) @ ( fun_upd @ A @ C ) @ ( fun_upd @ B @ D ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_transfer
% 0.15/0.39 thf(fact_180_right__unique__parametric,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_unique @ C @ D @ B2 )
% 0.15/0.39 => ( ( bi_total @ C @ D @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( right_unique @ A @ C )
% 0.15/0.39 @ ( right_unique @ B @ D ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_parametric
% 0.15/0.39 thf(fact_181_left__unique__parametric,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ C @ D @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( left_unique @ A @ C )
% 0.15/0.39 @ ( left_unique @ B @ D ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_unique_parametric
% 0.15/0.39 thf(fact_182_fun__upd__apply,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType] :
% 0.15/0.39 ( ( fun_upd @ B @ A )
% 0.15/0.39 = ( ^ [F2: B > A,X4: B,Y5: A,Z3: B] : ( if @ A @ ( Z3 = X4 ) @ Y5 @ ( F2 @ Z3 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_apply
% 0.15/0.39 thf(fact_183_fun__upd__triv,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F: A > B,X2: A] :
% 0.15/0.39 ( ( fun_upd @ A @ B @ F @ X2 @ ( F @ X2 ) )
% 0.15/0.39 = F ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_triv
% 0.15/0.39 thf(fact_184_fun__upd__upd,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F: A > B,X2: A,Y2: B,Z2: B] :
% 0.15/0.39 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X2 @ Y2 ) @ X2 @ Z2 )
% 0.15/0.39 = ( fun_upd @ A @ B @ F @ X2 @ Z2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_upd
% 0.15/0.39 thf(fact_185_bi__uniqueI,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( left_unique @ A @ B @ R )
% 0.15/0.39 => ( ( right_unique @ A @ B @ R )
% 0.15/0.39 => ( bi_unique @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_uniqueI
% 0.15/0.39 thf(fact_186_bi__unique__alt__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( bi_unique @ A @ B )
% 0.15/0.39 = ( ^ [A6: A > B > $o] :
% 0.15/0.39 ( ( left_unique @ A @ B @ A6 )
% 0.15/0.39 & ( right_unique @ A @ B @ A6 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_unique_alt_def
% 0.15/0.39 thf(fact_187_fun__upd__comp,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: A > C,X2: A,Y2: C] :
% 0.15/0.39 ( ( comp @ C @ B @ A @ F @ ( fun_upd @ A @ C @ G @ X2 @ Y2 ) )
% 0.15/0.39 = ( fun_upd @ A @ B @ ( comp @ C @ B @ A @ F @ G ) @ X2 @ ( F @ Y2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_comp
% 0.15/0.39 thf(fact_188_fun__upd__idem__iff,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F: A > B,X2: A,Y2: B] :
% 0.15/0.39 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y2 )
% 0.15/0.39 = F )
% 0.15/0.39 = ( ( F @ X2 )
% 0.15/0.39 = Y2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_idem_iff
% 0.15/0.39 thf(fact_189_fun__upd__twist,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A3: A,C3: A,M2: A > B,B3: B,D3: B] :
% 0.15/0.39 ( ( A3 != C3 )
% 0.15/0.39 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ A3 @ B3 ) @ C3 @ D3 )
% 0.15/0.39 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ C3 @ D3 ) @ A3 @ B3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_twist
% 0.15/0.39 thf(fact_190_fun__upd__other,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,Z2: A,X2: A,F: A > B,Y2: B] :
% 0.15/0.39 ( ( Z2 != X2 )
% 0.15/0.39 => ( ( fun_upd @ A @ B @ F @ X2 @ Y2 @ Z2 )
% 0.15/0.39 = ( F @ Z2 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_other
% 0.15/0.39 thf(fact_191_fun__upd__same,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,F: B > A,X2: B,Y2: A] :
% 0.15/0.39 ( ( fun_upd @ B @ A @ F @ X2 @ Y2 @ X2 )
% 0.15/0.39 = Y2 ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_same
% 0.15/0.39 thf(fact_192_fun__upd__idem,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F: B > A,X2: B,Y2: A] :
% 0.15/0.39 ( ( ( F @ X2 )
% 0.15/0.39 = Y2 )
% 0.15/0.39 => ( ( fun_upd @ B @ A @ F @ X2 @ Y2 )
% 0.15/0.39 = F ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_idem
% 0.15/0.39 thf(fact_193_fun__upd__eqD,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,F: A > B,X2: A,Y2: B,G: A > B,Z2: B] :
% 0.15/0.39 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y2 )
% 0.15/0.39 = ( fun_upd @ A @ B @ G @ X2 @ Z2 ) )
% 0.15/0.39 => ( Y2 = Z2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_eqD
% 0.15/0.39 thf(fact_194_fun__upd__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( fun_upd @ A @ B )
% 0.15/0.39 = ( ^ [F2: A > B,A5: A,B5: B,X4: A] : ( if @ B @ ( X4 = A5 ) @ B5 @ ( F2 @ X4 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun_upd_def
% 0.15/0.39 thf(fact_195_right__unique__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( right_unique @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ! [X4: A,Y5: B,Z3: B] :
% 0.15/0.39 ( ( R4 @ X4 @ Y5 )
% 0.15/0.39 => ( ( R4 @ X4 @ Z3 )
% 0.15/0.39 => ( Y5 = Z3 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_def
% 0.15/0.39 thf(fact_196_right__unique__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( right_unique @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_eq
% 0.15/0.39 thf(fact_197_left__unique__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( left_unique @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ! [X4: A,Y5: A,Z3: B] :
% 0.15/0.39 ( ( R4 @ X4 @ Z3 )
% 0.15/0.39 => ( ( R4 @ Y5 @ Z3 )
% 0.15/0.39 => ( X4 = Y5 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_unique_def
% 0.15/0.39 thf(fact_198_left__unique__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( left_unique @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_unique_eq
% 0.15/0.39 thf(fact_199_right__uniqueI,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ! [X: A,Y: B,Z4: B] :
% 0.15/0.39 ( ( A2 @ X @ Y )
% 0.15/0.39 => ( ( A2 @ X @ Z4 )
% 0.15/0.39 => ( Y = Z4 ) ) )
% 0.15/0.39 => ( right_unique @ A @ B @ A2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_uniqueI
% 0.15/0.39 thf(fact_200_right__uniqueD,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o,X2: A,Y2: B,Z2: B] :
% 0.15/0.39 ( ( right_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( A2 @ X2 @ Y2 )
% 0.15/0.39 => ( ( A2 @ X2 @ Z2 )
% 0.15/0.39 => ( Y2 = Z2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_uniqueD
% 0.15/0.39 thf(fact_201_left__uniqueI,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ! [X: A,Y: A,Z4: B] :
% 0.15/0.39 ( ( A2 @ X @ Z4 )
% 0.15/0.39 => ( ( A2 @ Y @ Z4 )
% 0.15/0.39 => ( X = Y ) ) )
% 0.15/0.39 => ( left_unique @ A @ B @ A2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_uniqueI
% 0.15/0.39 thf(fact_202_left__uniqueD,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,A2: A > B > $o,X2: A,Z2: B,Y2: A] :
% 0.15/0.39 ( ( left_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( A2 @ X2 @ Z2 )
% 0.15/0.39 => ( ( A2 @ Y2 @ Z2 )
% 0.15/0.39 => ( X2 = Y2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_uniqueD
% 0.15/0.39 thf(fact_203_llist_Oright__unique__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( right_unique @ A @ B @ R )
% 0.15/0.39 => ( right_unique @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.right_unique_rel
% 0.15/0.39 thf(fact_204_llist_Oleft__unique__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( left_unique @ A @ B @ R )
% 0.15/0.39 => ( left_unique @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.left_unique_rel
% 0.15/0.39 thf(fact_205_swap__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( swap @ A @ B )
% 0.15/0.39 = ( ^ [A5: A,B5: A,F2: A > B] : ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F2 @ A5 @ ( F2 @ B5 ) ) @ B5 @ ( F2 @ A5 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % swap_def
% 0.15/0.39 thf(fact_206_right__unique__alt__def2,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( right_unique @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ R4 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R4 @ (=>) )
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_alt_def2
% 0.15/0.39 thf(fact_207_eq__imp__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( right_unique @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ (=>) )
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % eq_imp_transfer
% 0.15/0.39 thf(fact_208_left__unique__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( right_total @ C @ D @ B2 )
% 0.15/0.39 => ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ (=>)
% 0.15/0.39 @ ( left_unique @ A @ C )
% 0.15/0.39 @ ( left_unique @ B @ D ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_unique_transfer
% 0.15/0.39 thf(fact_209_right__unique__transfer,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( right_total @ C @ D @ B2 )
% 0.15/0.39 => ( ( bi_unique @ C @ D @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ (=>)
% 0.15/0.39 @ ( right_unique @ A @ C )
% 0.15/0.39 @ ( right_unique @ B @ D ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_transfer
% 0.15/0.39 thf(fact_210_rtranclp__parametric,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ ( A > A > $o ) @ ( B > B > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( transitive_rtranclp @ A )
% 0.15/0.39 @ ( transitive_rtranclp @ B ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % rtranclp_parametric
% 0.15/0.39 thf(fact_211_right__total__fun,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( right_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( right_total @ C @ D @ B2 )
% 0.15/0.39 => ( right_total @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_total_fun
% 0.15/0.39 thf(fact_212_functional__converse__relation,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( left_unique @ A @ B @ R )
% 0.15/0.39 => ( ( right_total @ A @ B @ R )
% 0.15/0.39 => ! [Y6: B] :
% 0.15/0.39 ? [X: A] :
% 0.15/0.39 ( ( R @ X @ Y6 )
% 0.15/0.39 & ! [Ya3: A] :
% 0.15/0.39 ( ( R @ Ya3 @ Y6 )
% 0.15/0.39 => ( Ya3 = X ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % functional_converse_relation
% 0.15/0.39 thf(fact_213_right__totalE,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o,Y2: B] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ~ ! [X: A] :
% 0.15/0.39 ~ ( A2 @ X @ Y2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_totalE
% 0.15/0.39 thf(fact_214_right__totalI,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: B > A > $o] :
% 0.15/0.39 ( ! [Y: A] :
% 0.15/0.39 ? [X7: B] : ( A2 @ X7 @ Y )
% 0.15/0.39 => ( right_total @ B @ A @ A2 ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_totalI
% 0.15/0.39 thf(fact_215_right__total__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( right_total @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_total_eq
% 0.15/0.39 thf(fact_216_right__total__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( right_total @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ! [Y5: B] :
% 0.15/0.39 ? [X4: A] : ( R4 @ X4 @ Y5 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_total_def
% 0.15/0.39 thf(fact_217_llist_Oright__total__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ R )
% 0.15/0.39 => ( right_total @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.right_total_rel
% 0.15/0.39 thf(fact_218_right__unique__fun,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( right_unique @ C @ D @ B2 )
% 0.15/0.39 => ( right_unique @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_fun
% 0.15/0.39 thf(fact_219_transfer__forall__transfer_I3_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ (=>) ) @ (=>) @ ( transfer_forall @ A ) @ ( transfer_forall @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % transfer_forall_transfer(3)
% 0.15/0.39 thf(fact_220_transfer__forall__transfer_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ (=>)
% 0.15/0.39 @ ( transfer_forall @ A )
% 0.15/0.39 @ ( transfer_forall @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % transfer_forall_transfer(2)
% 0.15/0.39 thf(fact_221_right__total__parametric,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ C @ D @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( right_total @ A @ C )
% 0.15/0.39 @ ( right_total @ B @ D ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_total_parametric
% 0.15/0.39 thf(fact_222_reflp__transfer_I2_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ (=>) ) ) @ (=>) @ ( reflp @ A ) @ ( reflp @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % reflp_transfer(2)
% 0.15/0.39 thf(fact_223_reflp__transfer_I3_J,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ (=>)
% 0.15/0.39 @ ( reflp @ A )
% 0.15/0.39 @ ( reflp @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % reflp_transfer(3)
% 0.15/0.39 thf(fact_224_Domainp__forall__transfer,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( transfer_bforall @ A @ ( domainp @ A @ B @ A2 ) )
% 0.15/0.39 @ ( transfer_forall @ B ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % Domainp_forall_transfer
% 0.15/0.39 thf(fact_225_left__total__parametric,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ C @ D @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ ( left_total @ A @ C )
% 0.15/0.39 @ ( left_total @ B @ D ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_total_parametric
% 0.15/0.39 thf(fact_226_left__total__fun,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( left_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( left_total @ C @ D @ B2 )
% 0.15/0.39 => ( left_total @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_total_fun
% 0.15/0.39 thf(fact_227_functional__relation,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( right_unique @ A @ B @ R )
% 0.15/0.39 => ( ( left_total @ A @ B @ R )
% 0.15/0.39 => ! [X7: A] :
% 0.15/0.39 ? [Xa2: B] :
% 0.15/0.39 ( ( R @ X7 @ Xa2 )
% 0.15/0.39 & ! [Y6: B] :
% 0.15/0.39 ( ( R @ X7 @ Y6 )
% 0.15/0.39 => ( Y6 = Xa2 ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % functional_relation
% 0.15/0.39 thf(fact_228_left__unique__fun,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( left_unique @ C @ D @ B2 )
% 0.15/0.39 => ( left_unique @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_unique_fun
% 0.15/0.39 thf(fact_229_left__total__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( left_total @ A @ B )
% 0.15/0.39 = ( ^ [R4: A > B > $o] :
% 0.15/0.39 ! [X4: A] :
% 0.15/0.39 ( ^ [P4: B > $o] :
% 0.15/0.39 ? [X6: B] : ( P4 @ X6 )
% 0.15/0.39 @ ( R4 @ X4 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_total_def
% 0.15/0.39 thf(fact_230_left__total__eq,axiom,
% 0.15/0.39 ! [A: $tType] :
% 0.15/0.39 ( left_total @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_total_eq
% 0.15/0.39 thf(fact_231_left__totalI,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ! [X: A] :
% 0.15/0.39 ? [X12: B] : ( R @ X @ X12 )
% 0.15/0.39 => ( left_total @ A @ B @ R ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_totalI
% 0.15/0.39 thf(fact_232_left__totalE,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ R )
% 0.15/0.39 => ! [X7: A] :
% 0.15/0.39 ? [X13: B] : ( R @ X7 @ X13 ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_totalE
% 0.15/0.39 thf(fact_233_llist_Oleft__total__rel,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ R )
% 0.15/0.39 => ( left_total @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.left_total_rel
% 0.15/0.39 thf(fact_234_bi__totalI,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,R: A > B > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ R )
% 0.15/0.39 => ( ( right_total @ A @ B @ R )
% 0.15/0.39 => ( bi_total @ A @ B @ R ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_totalI
% 0.15/0.39 thf(fact_235_bi__total__alt__def,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType] :
% 0.15/0.39 ( ( bi_total @ A @ B )
% 0.15/0.39 = ( ^ [A6: A > B > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ A6 )
% 0.15/0.39 & ( right_total @ A @ B @ A6 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_total_alt_def
% 0.15/0.39 thf(fact_236_lhd__lfilter,axiom,
% 0.15/0.39 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lhd @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.15/0.39 = ( coinductive_lhd @ A @ ( coindu218763757pWhile @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ Xs ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % lhd_lfilter
% 0.15/0.39 thf(fact_237_relcompp__transfer,axiom,
% 0.15/0.39 ! [C: $tType,A: $tType,E: $tType,F3: $tType,B: $tType,D: $tType,B2: A > B > $o,A2: C > D > $o,C2: E > F3 > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ B2 )
% 0.15/0.39 => ( bNF_rel_fun @ ( C > A > $o ) @ ( D > B > $o ) @ ( ( A > E > $o ) > C > E > $o ) @ ( ( B > F3 > $o ) > D > F3 > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ ( A > $o ) @ ( B > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ B2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ ( A > E > $o ) @ ( B > F3 > $o ) @ ( C > E > $o ) @ ( D > F3 > $o )
% 0.15/0.39 @ ( bNF_rel_fun @ A @ B @ ( E > $o ) @ ( F3 > $o ) @ B2
% 0.15/0.39 @ ( bNF_rel_fun @ E @ F3 @ $o @ $o @ C2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 0.15/0.39 @ ( bNF_rel_fun @ C @ D @ ( E > $o ) @ ( F3 > $o ) @ A2
% 0.15/0.39 @ ( bNF_rel_fun @ E @ F3 @ $o @ $o @ C2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) ) )
% 0.15/0.39 @ ( relcompp @ C @ A @ E )
% 0.15/0.39 @ ( relcompp @ D @ B @ F3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % relcompp_transfer
% 0.15/0.39 thf(fact_238_pcr__Domainp__par__left__total,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,B2: A > B > $o,P: A > $o,A2: C > A > $o,P2: C > $o] :
% 0.15/0.39 ( ( ( domainp @ A @ B @ B2 )
% 0.15/0.39 = P )
% 0.15/0.39 => ( ( left_total @ C @ A @ A2 )
% 0.15/0.39 => ( ( bNF_rel_fun @ C @ A @ $o @ $o @ A2
% 0.15/0.39 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 0.15/0.39 @ P2
% 0.15/0.39 @ P )
% 0.15/0.39 => ( ( domainp @ C @ B @ ( relcompp @ C @ A @ B @ A2 @ B2 ) )
% 0.15/0.39 = P2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % pcr_Domainp_par_left_total
% 0.15/0.39 thf(fact_239_right__unique__OO,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 0.15/0.39 ( ( right_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( right_unique @ B @ C @ B2 )
% 0.15/0.39 => ( right_unique @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_unique_OO
% 0.15/0.39 thf(fact_240_right__total__OO,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 0.15/0.39 ( ( right_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( right_total @ B @ C @ B2 )
% 0.15/0.39 => ( right_total @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % right_total_OO
% 0.15/0.39 thf(fact_241_pcr__Domainp__total,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,B2: A > B > $o,A2: C > A > $o,P: C > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ B2 )
% 0.15/0.39 => ( ( ( domainp @ C @ A @ A2 )
% 0.15/0.39 = P )
% 0.15/0.39 => ( ( domainp @ C @ B @ ( relcompp @ C @ A @ B @ A2 @ B2 ) )
% 0.15/0.39 = P ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % pcr_Domainp_total
% 0.15/0.39 thf(fact_242_left__total__OO,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 0.15/0.39 ( ( left_total @ A @ B @ R )
% 0.15/0.39 => ( ( left_total @ B @ C @ S )
% 0.15/0.39 => ( left_total @ A @ C @ ( relcompp @ A @ B @ C @ R @ S ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_total_OO
% 0.15/0.39 thf(fact_243_bi__unique__OO,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 0.15/0.39 ( ( bi_unique @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_unique @ B @ C @ B2 )
% 0.15/0.39 => ( bi_unique @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_unique_OO
% 0.15/0.39 thf(fact_244_bi__total__OO,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 0.15/0.39 ( ( bi_total @ A @ B @ A2 )
% 0.15/0.39 => ( ( bi_total @ B @ C @ B2 )
% 0.15/0.39 => ( bi_total @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % bi_total_OO
% 0.15/0.39 thf(fact_245_lhd__LCons,axiom,
% 0.15/0.39 ! [A: $tType,X21: A,X222: coinductive_llist @ A] :
% 0.15/0.39 ( ( coinductive_lhd @ A @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.15/0.39 = X21 ) ).
% 0.15/0.39
% 0.15/0.39 % lhd_LCons
% 0.15/0.39 thf(fact_246_lhd__iterates,axiom,
% 0.15/0.39 ! [A: $tType,F: A > A,X2: A] :
% 0.15/0.39 ( ( coinductive_lhd @ A @ ( coinductive_iterates @ A @ F @ X2 ) )
% 0.15/0.39 = X2 ) ).
% 0.15/0.39
% 0.15/0.39 % lhd_iterates
% 0.15/0.39 thf(fact_247_unfold__llist_Osimps_I3_J,axiom,
% 0.15/0.39 ! [B: $tType,A: $tType,P3: A > $o,A3: A,G21: A > B,G22: A > A] :
% 0.15/0.39 ( ~ ( P3 @ A3 )
% 0.15/0.39 => ( ( coinductive_lhd @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A3 ) )
% 0.15/0.39 = ( G21 @ A3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % unfold_llist.simps(3)
% 0.15/0.39 thf(fact_248_llist_Ocorec__sel_I1_J,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,P3: C > $o,A3: C,G21: C > A,Q22: C > $o,G221: C > ( coinductive_llist @ A ),G222: C > C] :
% 0.15/0.39 ( ~ ( P3 @ A3 )
% 0.15/0.39 => ( ( coinductive_lhd @ A @ ( coindu1259883913_llist @ C @ A @ P3 @ G21 @ Q22 @ G221 @ G222 @ A3 ) )
% 0.15/0.39 = ( G21 @ A3 ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.corec_sel(1)
% 0.15/0.39 thf(fact_249_eq__comp__r,axiom,
% 0.15/0.39 ! [A: $tType,R: A > A > $o] :
% 0.15/0.39 ( ( relcompp @ A @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ ( relcompp @ A @ A @ A @ R
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) )
% 0.15/0.39 = R ) ).
% 0.15/0.39
% 0.15/0.39 % eq_comp_r
% 0.15/0.39 thf(fact_250_llist_Orel__compp,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 0.15/0.39 ( ( coindu1486289336t_all2 @ A @ C @ ( relcompp @ A @ B @ C @ R @ S ) )
% 0.15/0.39 = ( relcompp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ C ) @ ( coindu1486289336t_all2 @ A @ B @ R ) @ ( coindu1486289336t_all2 @ B @ C @ S ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % llist.rel_compp
% 0.15/0.39 thf(fact_251_OOO__eq__quotient3,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,Abs22: B > C,Rep22: C > B] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 0.15/0.39 => ( ( quotient3 @ B @ C
% 0.15/0.39 @ ^ [Y3: B,Z: B] : ( Y3 = Z )
% 0.15/0.39 @ Abs22
% 0.15/0.39 @ Rep22 )
% 0.15/0.39 => ( quotient3 @ A @ C
% 0.15/0.39 @ ( relcompp @ A @ A @ A @ R1
% 0.15/0.39 @ ( relcompp @ A @ A @ A
% 0.15/0.39 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.15/0.39 @ R1 ) )
% 0.15/0.39 @ ( comp @ B @ C @ A @ Abs22 @ Abs12 )
% 0.15/0.39 @ ( comp @ B @ A @ C @ Rep12 @ Rep22 ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % OOO_eq_quotient3
% 0.15/0.39 thf(fact_252_OOO__quotient3,axiom,
% 0.15/0.39 ! [A: $tType,B: $tType,C: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: B > B > $o,Abs22: B > C,Rep22: C > B,R23: A > A > $o] :
% 0.15/0.39 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 0.15/0.39 => ( ( quotient3 @ B @ C @ R2 @ Abs22 @ Rep22 )
% 0.15/0.39 => ( ! [X: A,Y: A] :
% 0.15/0.39 ( ( R23 @ X @ Y )
% 0.15/0.39 => ( ( R1 @ X @ X )
% 0.15/0.39 => ( ( R1 @ Y @ Y )
% 0.15/0.39 => ( R2 @ ( Abs12 @ X ) @ ( Abs12 @ Y ) ) ) ) )
% 0.15/0.39 => ( ! [X: B,Y: B] :
% 0.15/0.39 ( ( R2 @ X @ Y )
% 0.15/0.39 => ( R23 @ ( Rep12 @ X ) @ ( Rep12 @ Y ) ) )
% 0.15/0.39 => ( quotient3 @ A @ C @ ( relcompp @ A @ A @ A @ R1 @ ( relcompp @ A @ A @ A @ R23 @ R1 ) ) @ ( comp @ B @ C @ A @ Abs22 @ Abs12 ) @ ( comp @ B @ A @ C @ Rep12 @ Rep22 ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % OOO_quotient3
% 0.15/0.39 thf(fact_253_left__unique__OO,axiom,
% 0.15/0.39 ! [A: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 0.15/0.39 ( ( left_unique @ A @ B @ R )
% 0.15/0.39 => ( ( left_unique @ B @ C @ S )
% 0.15/0.39 => ( left_unique @ A @ C @ ( relcompp @ A @ B @ C @ R @ S ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % left_unique_OO
% 0.15/0.39 thf(fact_254_fun_Orel__compp,axiom,
% 0.15/0.39 ! [A: $tType,D: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 0.15/0.39 ( ( bNF_rel_fun @ D @ D @ A @ C
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ ( relcompp @ A @ B @ C @ R @ S ) )
% 0.15/0.39 = ( relcompp @ ( D > A ) @ ( D > B ) @ ( D > C )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ A @ B
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ R )
% 0.15/0.39 @ ( bNF_rel_fun @ D @ D @ B @ C
% 0.15/0.39 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 0.15/0.39 @ S ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % fun.rel_compp
% 0.15/0.39 thf(fact_255_neg__fun__distr2,axiom,
% 0.15/0.39 ! [F3: $tType,E: $tType,A: $tType,B: $tType,D: $tType,C: $tType,R7: A > B > $o,S5: C > D > $o,R: E > A > $o,S: F3 > C > $o] :
% 0.15/0.39 ( ( right_unique @ A @ B @ R7 )
% 0.15/0.39 => ( ( left_total @ A @ B @ R7 )
% 0.15/0.39 => ( ( left_unique @ C @ D @ S5 )
% 0.15/0.39 => ( ( right_total @ C @ D @ S5 )
% 0.15/0.39 => ( ord_less_eq @ ( ( E > F3 ) > ( B > D ) > $o ) @ ( bNF_rel_fun @ E @ B @ F3 @ D @ ( relcompp @ E @ A @ B @ R @ R7 ) @ ( relcompp @ F3 @ C @ D @ S @ S5 ) ) @ ( relcompp @ ( E > F3 ) @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ E @ A @ F3 @ C @ R @ S ) @ ( bNF_rel_fun @ A @ B @ C @ D @ R7 @ S5 ) ) ) ) ) ) ) ).
% 0.15/0.39
% 0.15/0.39 % neg_fun_distr2
% 0.15/0.39
% 0.15/0.39 %----Helper facts (3)
% 0.15/0.39 thf(help_If_3_1_T,axiom,
% 0.15/0.39 ! [P: $o] :
% 0.15/0.39 ( ( P = $true )
% 0.15/0.39 | ( P = $false ) ) ).
% 0.15/0.39
% 0.15/0.39 thf(help_If_2_1_T,axiom,
% 0.15/0.39 ! [A: $tType,X2: A,Y2: A] :
% 0.15/0.39 ( ( if @ A @ $false @ X2 @ Y2 )
% 0.15/0.39 = Y2 ) ).
% 0.15/0.39
% 0.15/0.39 thf(help_If_1_1_T,axiom,
% 0.15/0.39 ! [A: $tType,X2: A,Y2: A] :
% 0.15/0.39 ( ( if @ A @ $true @ X2 @ Y2 )
% 0.15/0.39 = X2 ) ).
% 0.15/0.39
% 0.15/0.39 %----Conjectures (1)
% 0.15/0.39 thf(conj_0,conjecture,
% 0.15/0.39 bNF_rel_fun @ ( coinductive_llist @ a ) @ ( coinductive_llist @ b ) @ ( coinductive_llist @ a ) @ ( coinductive_llist @ b ) @ ( coindu1486289336t_all2 @ a @ b @ a2 ) @ ( coindu1486289336t_all2 @ a @ b @ a2 ) @ ( lMirro427583474mirror @ a ) @ ( lMirro427583474mirror @ b ) ).
% 0.15/0.39
% 0.15/0.39 %------------------------------------------------------------------------------
% 0.15/0.39 ------------------------
% 3.19/1.63 ---- Embedded in THF ---
% 3.19/1.64 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.19/1.64 %%% Generated on Tue Feb 24 06:10:17 EST 2026
% 3.19/1.64 %%% using '$$dhol' embedding, version 1.3.0.
% 3.19/1.64 %%% Logic specification used:
% 3.19/1.64 %%% thf(spec, logic, $$dhol).
% 3.19/1.64
% 3.19/1.64 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7OvFDdixfL/DTF2DTF25247.p
% 3.19/1.64 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 3.19/1.64 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.19/1.64 thf(ty_tf_b, type, b: $tType).
% 3.19/1.64 thf(ty_tf_a, type, a: $tType).
% 3.19/1.64 thf(sy_c_BNF__Def_Orel__fun, type, bNF_rel_fun: (!> [A:$tType,C:$tType,B:$tType,D:$tType]: (((A > (C > $o)) > ((B > (D > $o)) > ((A > B) > ((C > D) > $o))))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Oiterates, type, coinductive_iterates: (!> [A:$tType]: (((A > A) > (A > (coinductive_llist @ A)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_OldropWhile, type, coindu218763757pWhile: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Olfilter, type, coinductive_lfilter: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_Ocase__llist, type, coindu1381640503_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coinductive_llist @ A) > B)) > ((coinductive_llist @ A) > B)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_Ocorec__llist, type, coindu1259883913_llist: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (coinductive_llist @ A)) > ((C > C) > (C > (coinductive_llist @ A)))))))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_Olhd, type, coinductive_lhd: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_Ollist__all2, type, coindu1486289336t_all2: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((coinductive_llist @ A) > ((coinductive_llist @ B) > $o)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_Olmap, type, coinductive_lmap: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((coinductive_llist @ A) > (coinductive_llist @ Aa)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ollist_Opred__llist, type, coindu543516966_llist: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Olmember, type, coinductive_lmember: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > $o))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_OltakeWhile, type, coindu501562517eWhile: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 3.19/1.64 thf(sy_c_Coinductive__List_Ounfold__llist, type, coindu1441602521_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coinductive_llist @ B)))))))).
% 3.19/1.64 thf(sy_c_Complete__Partial__Order_Omonotone, type, comple1396247847notone: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((B > (B > $o)) > ((A > B) > $o)))))).
% 3.19/1.64 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 3.19/1.64 thf(sy_c_Fun_Ofun__upd, type, fun_upd: (!> [A:$tType,B:$tType]: (((A > B) > (A > (B > (A > B))))))).
% 3.19/1.64 thf(sy_c_Fun_Oid, type, id: (!> [A:$tType]: ((A > A)))).
% 3.19/1.64 thf(sy_c_Fun_Omap__fun, type, map_fun: (!> [C:$tType,A:$tType,B:$tType,D:$tType]: (((C > A) > ((B > D) > ((A > B) > (C > D))))))).
% 3.19/1.64 thf(sy_c_Fun_Oswap, type, swap: (!> [A:$tType,B:$tType]: ((A > (A > ((A > B) > (A > B))))))).
% 3.19/1.64 thf(sy_c_HOL_OEx1, type, ex1: (!> [A:$tType]: (((A > $o) > $o)))).
% 3.19/1.64 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.19/1.64 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror, type, lMirro427583474mirror: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 3.19/1.64 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.19/1.64 thf(sy_c_Partial__Function_Ofun__ord, type, partial_fun_ord: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > $o)) > ((C > A) > ((C > B) > $o)))))).
% 3.19/1.64 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 3.19/1.64 thf(sy_c_Quotient_OBex1__rel, type, bex1_rel: (!> [A:$tType]: (((A > (A > $o)) > ((A > $o) > $o))))).
% 3.19/1.64 thf(sy_c_Quotient_OQuotient3, type, quotient3: (!> [A:$tType,B:$tType]: (((A > (A > $o)) > ((A > B) > ((B > A) > $o)))))).
% 3.19/1.64 thf(sy_c_Relation_ODomainp, type, domainp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > (A > $o))))).
% 3.19/1.64 thf(sy_c_Relation_Oreflp, type, reflp: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Relation_Orelcompp, type, relcompp: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > $o)) > ((B > (C > $o)) > (A > (C > $o))))))).
% 3.19/1.64 thf(sy_c_Transfer_Obi__total, type, bi_total: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Transfer_Obi__unique, type, bi_unique: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Transfer_Oleft__total, type, left_total: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Transfer_Oleft__unique, type, left_unique: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Transfer_Orev__implies, type, rev_implies: ($o > ($o > $o))).
% 3.19/1.64 thf(sy_c_Transfer_Oright__total, type, right_total: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Transfer_Oright__unique, type, right_unique: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > $o)))).
% 3.19/1.64 thf(sy_c_Transfer_Otransfer__bforall, type, transfer_bforall: (!> [A:$tType]: (((A > $o) > ((A > $o) > $o))))).
% 3.19/1.64 thf(sy_c_Transfer_Otransfer__forall, type, transfer_forall: (!> [A:$tType]: (((A > $o) > $o)))).
% 3.19/1.64 thf(sy_c_Transitive__Closure_Ortranclp, type, transitive_rtranclp: (!> [A:$tType]: (((A > (A > $o)) > (A > (A > $o)))))).
% 3.19/1.64 thf(sy_v_A, type, a2: (a > (b > $o))).
% 3.19/1.64 thf(fact_0_llist__all2__lmirror, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ ((lMirro427583474mirror @ A) @ Xs)) @ ((lMirro427583474mirror @ B) @ Ys)) = (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys))))).
% 3.19/1.64 thf(fact_1_llist__all2__lmirrorD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ ((lMirro427583474mirror @ A) @ Xs)) @ ((lMirro427583474mirror @ B) @ Ys)) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys))))).
% 3.19/1.64 thf(fact_2_llist__all2__lmirrorI, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ ((lMirro427583474mirror @ A) @ Xs)) @ ((lMirro427583474mirror @ B) @ Ys)))))).
% 3.19/1.64 thf(fact_3_rel__funI, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D)]: (((! [X:A,Y:B]: ((((A2 @ X) @ Y) => ((B2 @ (F @ X)) @ (G @ Y))))) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2) @ F) @ G))))).
% 3.19/1.64 thf(fact_4_llist__all2__rsp, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),S:(A > (A > $o)),T:(B > (B > $o)),X2:(coinductive_llist @ A),Y2:(coinductive_llist @ B),A3:(coinductive_llist @ A),B3:(coinductive_llist @ B)]: (((! [X:A,Y:B]: ((((R @ X) @ Y) => (! [A4:A,B4:B]: ((((R @ A4) @ B4) => (((S @ X) @ A4) = ((T @ Y) @ B4)))))))) => ((((((coindu1486289336t_all2 @ A) @ B) @ R) @ X2) @ Y2) => ((((((coindu1486289336t_all2 @ A) @ B) @ R) @ A3) @ B3) => ((((((coindu1486289336t_all2 @ A) @ A) @ S) @ X2) @ A3) = (((((coindu1486289336t_all2 @ B) @ B) @ T) @ Y2) @ B3)))))))).
% 3.19/1.64 thf(fact_5_llist__all2__mono, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),P2:(A > (B > $o))]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((! [X:A,Y:B]: ((((P @ X) @ Y) => ((P2 @ X) @ Y)))) => (((((coindu1486289336t_all2 @ A) @ B) @ P2) @ Xs) @ Ys)))))).
% 3.19/1.64 thf(fact_6_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu1486289336t_all2 @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) = (^ [Y3:(coinductive_llist @ A),Z:(coinductive_llist @ A)]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_7_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X2:(coinductive_llist @ B)]: (((! [X:B]: (((Ra @ X) @ X))) => (((((coindu1486289336t_all2 @ B) @ B) @ Ra) @ X2) @ X2))))).
% 3.19/1.64 thf(fact_8_rel__funD, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D),X2:A,Y2:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2) @ F) @ G) => (((A2 @ X2) @ Y2) => ((B2 @ (F @ X2)) @ (G @ Y2))))))).
% 3.19/1.64 thf(fact_9_let__rsp, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (B > $o)),R2:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((A > C) > C)) @ ((B > D) > D)) @ R1) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ C) @ D) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ R1) @ R2)) @ R2)) @ (^ [S2:A,F2:(A > C)]: ((F2 @ S2)))) @ (^ [S2:B,F2:(B > D)]: ((F2 @ S2))))))).
% 3.19/1.64 thf(fact_10_rel__funE, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D),X2:A,Y2:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2) @ F) @ G) => (((A2 @ X2) @ Y2) => ((B2 @ (F @ X2)) @ (G @ Y2))))))).
% 3.19/1.64 thf(fact_11_apply__rsp_H, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,R1:(A > (B > $o)),R2:(C > (D > $o)),F:(A > C),G:(B > D),X2:A,Y2:B]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ R1) @ R2) @ F) @ G) => (((R1 @ X2) @ Y2) => ((R2 @ (F @ X2)) @ (G @ Y2))))))).
% 3.19/1.64 thf(fact_12_rel__funD2, axiom, (! [B:$tType,C:$tType,A:$tType,A2:(A > (A > $o)),B2:(B > (C > $o)),F:(A > B),G:(A > C),X2:A]: ((((((((((bNF_rel_fun @ A) @ A) @ B) @ C) @ A2) @ B2) @ F) @ G) => (((A2 @ X2) @ X2) => ((B2 @ (F @ X2)) @ (G @ X2))))))).
% 3.19/1.64 thf(fact_13_rel__fun__mono, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,X3:(A > (B > $o)),A2:(C > (D > $o)),F:(A > C),G:(B > D),Y4:(A > (B > $o)),B2:(C > (D > $o))]: ((((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ X3) @ A2) @ F) @ G) => ((! [X:A,Y:B]: ((((Y4 @ X) @ Y) => ((X3 @ X) @ Y)))) => ((! [X:C,Y:D]: ((((A2 @ X) @ Y) => ((B2 @ X) @ Y)))) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ Y4) @ B2) @ F) @ G))))))).
% 3.19/1.64 thf(fact_14_rel__fun__mono_H, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,Y4:(A > (B > $o)),X3:(A > (B > $o)),A2:(C > (D > $o)),B2:(C > (D > $o)),F:(A > C),G:(B > D)]: (((! [X:A,Y:B]: ((((Y4 @ X) @ Y) => ((X3 @ X) @ Y)))) => ((! [X:C,Y:D]: ((((A2 @ X) @ Y) => ((B2 @ X) @ Y)))) => (((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ X3) @ A2) @ F) @ G) => ((((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ Y4) @ B2) @ F) @ G))))))).
% 3.19/1.64 thf(fact_15_llist__all2__transfer, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ ((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))) @ ((coinductive_llist @ B) > ((coinductive_llist @ B) > $o))) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ R) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ ((coinductive_llist @ A) > $o)) @ ((coinductive_llist @ B) > $o)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ $o) @ $o) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((coindu1486289336t_all2 @ A) @ A)) @ ((coindu1486289336t_all2 @ B) @ B))))).
% 3.19/1.64 thf(fact_16_llist_Orel__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,Sa:(A > (C > $o)),Sc:(B > (D > $o))]: (((((((((bNF_rel_fun @ (A > (B > $o))) @ (C > (D > $o))) @ ((coinductive_llist @ A) > ((coinductive_llist @ B) > $o))) @ ((coinductive_llist @ C) > ((coinductive_llist @ D) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ (B > $o)) @ (D > $o)) @ Sa) @ ((((((bNF_rel_fun @ B) @ D) @ $o) @ $o) @ Sc) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ C)) @ ((coinductive_llist @ B) > $o)) @ ((coinductive_llist @ D) > $o)) @ (((coindu1486289336t_all2 @ A) @ C) @ Sa)) @ ((((((bNF_rel_fun @ (coinductive_llist @ B)) @ (coinductive_llist @ D)) @ $o) @ $o) @ (((coindu1486289336t_all2 @ B) @ D) @ Sc)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((coindu1486289336t_all2 @ A) @ B)) @ ((coindu1486289336t_all2 @ C) @ D))))).
% 3.19/1.64 thf(fact_17_Let__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((A > C) > C)) @ ((B > D) > D)) @ A2) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ C) @ D) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2)) @ B2)) @ (^ [S2:A,F2:(A > C)]: ((F2 @ S2)))) @ (^ [S2:B,F2:(B > D)]: ((F2 @ S2))))))).
% 3.19/1.64 thf(fact_18_rel__fun__def__butlast, axiom, (! [B:$tType,D:$tType,C:$tType,E:$tType,F3:$tType,A:$tType,R:(A > (B > $o)),S:(C > (E > $o)),T:(D > (F3 > $o)),F:(A > (C > D)),G:(B > (E > F3))]: ((((((((((bNF_rel_fun @ A) @ B) @ (C > D)) @ (E > F3)) @ R) @ ((((((bNF_rel_fun @ C) @ E) @ D) @ F3) @ S) @ T)) @ F) @ G) = (! [X4:A,Y5:B]: ((((R @ X4) @ Y5) => ((((((((bNF_rel_fun @ C) @ E) @ D) @ F3) @ S) @ T) @ (F @ X4)) @ (G @ Y5))))))))).
% 3.19/1.64 thf(fact_19_If__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ $o) @ $o) @ (A > (A > A))) @ (B > (B > B))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((((((bNF_rel_fun @ A) @ B) @ (A > A)) @ (B > B)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ A2) @ A2))) @ (if @ A)) @ (if @ B))))).
% 3.19/1.64 thf(fact_20_llist__corec__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((A > C) > ((A > $o) > ((A > (coinductive_llist @ C)) > ((A > A) > (A > (coinductive_llist @ C))))))) @ ((B > D) > ((B > $o) > ((B > (coinductive_llist @ D)) > ((B > B) > (B > (coinductive_llist @ D))))))) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ ((A > $o) > ((A > (coinductive_llist @ C)) > ((A > A) > (A > (coinductive_llist @ C)))))) @ ((B > $o) > ((B > (coinductive_llist @ D)) > ((B > B) > (B > (coinductive_llist @ D)))))) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2)) @ ((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((A > (coinductive_llist @ C)) > ((A > A) > (A > (coinductive_llist @ C))))) @ ((B > (coinductive_llist @ D)) > ((B > B) > (B > (coinductive_llist @ D))))) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (A > (coinductive_llist @ C))) @ (B > (coinductive_llist @ D))) @ ((A > A) > (A > (coinductive_llist @ C)))) @ ((B > B) > (B > (coinductive_llist @ D)))) @ ((((((bNF_rel_fun @ A) @ B) @ (coinductive_llist @ C)) @ (coinductive_llist @ D)) @ A2) @ (((coindu1486289336t_all2 @ C) @ D) @ B2))) @ ((((((bNF_rel_fun @ (A > A)) @ (B > B)) @ (A > (coinductive_llist @ C))) @ (B > (coinductive_llist @ D))) @ ((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ A2) @ A2)) @ ((((((bNF_rel_fun @ A) @ B) @ (coinductive_llist @ C)) @ (coinductive_llist @ D)) @ A2) @ (((coindu1486289336t_all2 @ C) @ D) @ B2))))))) @ ((coindu1259883913_llist @ A) @ C)) @ ((coindu1259883913_llist @ B) @ D))))).
% 3.19/1.64 thf(fact_21_llist_Ocorec__transfer, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,S:(C > (D > $o)),R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > A) > ((C > $o) > ((C > (coinductive_llist @ A)) > ((C > C) > (C > (coinductive_llist @ A))))))) @ ((D > B) > ((D > $o) > ((D > (coinductive_llist @ B)) > ((D > D) > (D > (coinductive_llist @ B))))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (C > A)) @ (D > B)) @ ((C > $o) > ((C > (coinductive_llist @ A)) > ((C > C) > (C > (coinductive_llist @ A)))))) @ ((D > $o) > ((D > (coinductive_llist @ B)) > ((D > D) > (D > (coinductive_llist @ B)))))) @ ((((((bNF_rel_fun @ C) @ D) @ A) @ B) @ S) @ R)) @ ((((((bNF_rel_fun @ (C > $o)) @ (D > $o)) @ ((C > (coinductive_llist @ A)) > ((C > C) > (C > (coinductive_llist @ A))))) @ ((D > (coinductive_llist @ B)) > ((D > D) > (D > (coinductive_llist @ B))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ S) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (C > (coinductive_llist @ A))) @ (D > (coinductive_llist @ B))) @ ((C > C) > (C > (coinductive_llist @ A)))) @ ((D > D) > (D > (coinductive_llist @ B)))) @ ((((((bNF_rel_fun @ C) @ D) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ S) @ (((coindu1486289336t_all2 @ A) @ B) @ R))) @ ((((((bNF_rel_fun @ (C > C)) @ (D > D)) @ (C > (coinductive_llist @ A))) @ (D > (coinductive_llist @ B))) @ ((((((bNF_rel_fun @ C) @ D) @ C) @ D) @ S) @ S)) @ ((((((bNF_rel_fun @ C) @ D) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ S) @ (((coindu1486289336t_all2 @ A) @ B) @ R))))))) @ ((coindu1259883913_llist @ C) @ A)) @ ((coindu1259883913_llist @ D) @ B))))).
% 3.19/1.64 thf(fact_22_unfold__llist__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((A > C) > ((A > A) > (A > (coinductive_llist @ C))))) @ ((B > D) > ((B > B) > (B > (coinductive_llist @ D))))) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ ((A > A) > (A > (coinductive_llist @ C)))) @ ((B > B) > (B > (coinductive_llist @ D)))) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2)) @ ((((((bNF_rel_fun @ (A > A)) @ (B > B)) @ (A > (coinductive_llist @ C))) @ (B > (coinductive_llist @ D))) @ ((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ A2) @ A2)) @ ((((((bNF_rel_fun @ A) @ B) @ (coinductive_llist @ C)) @ (coinductive_llist @ D)) @ A2) @ (((coindu1486289336t_all2 @ C) @ D) @ B2))))) @ ((coindu1441602521_llist @ A) @ C)) @ ((coindu1441602521_llist @ B) @ D))))).
% 3.19/1.64 thf(fact_23_iterates__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > A)) @ (B > B)) @ (A > (coinductive_llist @ A))) @ (B > (coinductive_llist @ B))) @ ((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ A2) @ A2)) @ ((((((bNF_rel_fun @ A) @ B) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ A2) @ (((coindu1486289336t_all2 @ A) @ B) @ A2))) @ (coinductive_iterates @ A)) @ (coinductive_iterates @ B))))).
% 3.19/1.64 thf(fact_24_fun_Orel__transfer, axiom, (! [B:$tType,A:$tType,C:$tType,E:$tType,D:$tType,Sa:(A > (C > $o)),Sc:(B > (E > $o))]: (((((((((bNF_rel_fun @ (A > (B > $o))) @ (C > (E > $o))) @ ((D > A) > ((D > B) > $o))) @ ((D > C) > ((D > E) > $o))) @ ((((((bNF_rel_fun @ A) @ C) @ (B > $o)) @ (E > $o)) @ Sa) @ ((((((bNF_rel_fun @ B) @ E) @ $o) @ $o) @ Sc) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (D > A)) @ (D > C)) @ ((D > B) > $o)) @ ((D > E) > $o)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ C) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ Sa)) @ ((((((bNF_rel_fun @ (D > B)) @ (D > E)) @ $o) @ $o) @ ((((((bNF_rel_fun @ D) @ D) @ B) @ E) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ Sc)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y3:D,Z:D]: ((Y3 = Z))))) @ (((((bNF_rel_fun @ D) @ D) @ C) @ E) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))))))).
% 3.19/1.64 thf(fact_25_fun_Orel__refl, axiom, (! [B:$tType,D:$tType,Ra:(B > (B > $o)),X2:(D > B)]: (((! [X:B]: (((Ra @ X) @ X))) => ((((((((bNF_rel_fun @ D) @ D) @ B) @ B) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ Ra) @ X2) @ X2))))).
% 3.19/1.64 thf(fact_26_fun_Orel__eq, axiom, (! [A:$tType,D:$tType]: ((((((((bNF_rel_fun @ D) @ D) @ A) @ A) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) = (^ [Y3:(D > A),Z:(D > A)]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_27_case__llist__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,B2:(A > (B > $o)),A2:(C > (D > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((C > ((coinductive_llist @ C) > A)) > ((coinductive_llist @ C) > A))) @ ((D > ((coinductive_llist @ D) > B)) > ((coinductive_llist @ D) > B))) @ B2) @ ((((((bNF_rel_fun @ (C > ((coinductive_llist @ C) > A))) @ (D > ((coinductive_llist @ D) > B))) @ ((coinductive_llist @ C) > A)) @ ((coinductive_llist @ D) > B)) @ ((((((bNF_rel_fun @ C) @ D) @ ((coinductive_llist @ C) > A)) @ ((coinductive_llist @ D) > B)) @ A2) @ ((((((bNF_rel_fun @ (coinductive_llist @ C)) @ (coinductive_llist @ D)) @ A) @ B) @ (((coindu1486289336t_all2 @ C) @ D) @ A2)) @ B2))) @ ((((((bNF_rel_fun @ (coinductive_llist @ C)) @ (coinductive_llist @ D)) @ A) @ B) @ (((coindu1486289336t_all2 @ C) @ D) @ A2)) @ B2))) @ ((coindu1381640503_llist @ A) @ C)) @ ((coindu1381640503_llist @ B) @ D))))).
% 3.19/1.64 thf(fact_28_llist_Ocase__transfer, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,S:(C > (D > $o)),R:(A > (B > $o))]: (((((((((bNF_rel_fun @ C) @ D) @ ((A > ((coinductive_llist @ A) > C)) > ((coinductive_llist @ A) > C))) @ ((B > ((coinductive_llist @ B) > D)) > ((coinductive_llist @ B) > D))) @ S) @ ((((((bNF_rel_fun @ (A > ((coinductive_llist @ A) > C))) @ (B > ((coinductive_llist @ B) > D))) @ ((coinductive_llist @ A) > C)) @ ((coinductive_llist @ B) > D)) @ ((((((bNF_rel_fun @ A) @ B) @ ((coinductive_llist @ A) > C)) @ ((coinductive_llist @ B) > D)) @ R) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ C) @ D) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ S))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ C) @ D) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ S))) @ ((coindu1381640503_llist @ C) @ A)) @ ((coindu1381640503_llist @ D) @ B))))).
% 3.19/1.64 thf(fact_29_map__fun__parametric, axiom, (! [A:$tType,B:$tType,E:$tType,F3:$tType,H:$tType,G2:$tType,D:$tType,C:$tType,A2:(A > (C > $o)),B2:(B > (D > $o)),C2:(E > (G2 > $o)),D2:(F3 > (H > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (C > D)) @ ((E > F3) > ((B > E) > (A > F3)))) @ ((G2 > H) > ((D > G2) > (C > H)))) @ ((((((bNF_rel_fun @ A) @ C) @ B) @ D) @ A2) @ B2)) @ ((((((bNF_rel_fun @ (E > F3)) @ (G2 > H)) @ ((B > E) > (A > F3))) @ ((D > G2) > (C > H))) @ ((((((bNF_rel_fun @ E) @ G2) @ F3) @ H) @ C2) @ D2)) @ ((((((bNF_rel_fun @ (B > E)) @ (D > G2)) @ (A > F3)) @ (C > H)) @ ((((((bNF_rel_fun @ B) @ D) @ E) @ G2) @ B2) @ C2)) @ ((((((bNF_rel_fun @ A) @ C) @ F3) @ H) @ A2) @ D2)))) @ ((((map_fun @ A) @ B) @ E) @ F3)) @ ((((map_fun @ C) @ D) @ G2) @ H))))).
% 3.19/1.64 thf(fact_30_llist_Opred__transfer, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((coinductive_llist @ A) > $o)) @ ((coinductive_llist @ B) > $o)) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ $o) @ $o) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (coindu543516966_llist @ A)) @ (coindu543516966_llist @ B))))).
% 3.19/1.64 thf(fact_31_llist__all__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((coinductive_llist @ A) > $o)) @ ((coinductive_llist @ B) > $o)) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ $o) @ $o) @ (((coindu1486289336t_all2 @ A) @ B) @ A2)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (coindu543516966_llist @ A)) @ (coindu543516966_llist @ B))))).
% 3.19/1.64 thf(fact_32_if__rsp, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A)]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((((((((bNF_rel_fun @ $o) @ $o) @ (A > (A > A))) @ (A > (A > A))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((((((bNF_rel_fun @ A) @ A) @ (A > A)) @ (A > A)) @ R) @ ((((((bNF_rel_fun @ A) @ A) @ A) @ A) @ R) @ R))) @ (if @ A)) @ (if @ A)))))).
% 3.19/1.64 thf(fact_33_ldropWhile__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((coinductive_llist @ A) > (coinductive_llist @ A))) @ ((coinductive_llist @ B) > (coinductive_llist @ B))) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2))) @ (coindu218763757pWhile @ A)) @ (coindu218763757pWhile @ B))))).
% 3.19/1.64 thf(fact_34_ltakeWhile__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((coinductive_llist @ A) > (coinductive_llist @ A))) @ ((coinductive_llist @ B) > (coinductive_llist @ B))) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2))) @ (coindu501562517eWhile @ A)) @ (coindu501562517eWhile @ B))))).
% 3.19/1.64 thf(fact_35_lfilter__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ ((coinductive_llist @ A) > (coinductive_llist @ A))) @ ((coinductive_llist @ B) > (coinductive_llist @ B))) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2))) @ (coinductive_lfilter @ A)) @ (coinductive_lfilter @ B))))).
% 3.19/1.64 thf(fact_36_fun_Omap__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,G2:$tType,F3:$tType,Rb:(A > (F3 > $o)),Sd:(B > (G2 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (F3 > G2)) @ ((D > A) > (D > B))) @ ((D > F3) > (D > G2))) @ ((((((bNF_rel_fun @ A) @ F3) @ B) @ G2) @ Rb) @ Sd)) @ ((((((bNF_rel_fun @ (D > A)) @ (D > F3)) @ (D > B)) @ (D > G2)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ F3) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ Rb)) @ ((((((bNF_rel_fun @ D) @ D) @ B) @ G2) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ Sd))) @ (((comp @ A) @ B) @ D)) @ (((comp @ F3) @ G2) @ D))))).
% 3.19/1.64 thf(fact_37_comp__transfer, axiom, (! [A:$tType,B:$tType,E:$tType,F3:$tType,D:$tType,C:$tType,B2:(A > (C > $o)),C2:(B > (D > $o)),A2:(E > (F3 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (C > D)) @ ((E > A) > (E > B))) @ ((F3 > C) > (F3 > D))) @ ((((((bNF_rel_fun @ A) @ C) @ B) @ D) @ B2) @ C2)) @ ((((((bNF_rel_fun @ (E > A)) @ (F3 > C)) @ (E > B)) @ (F3 > D)) @ ((((((bNF_rel_fun @ E) @ F3) @ A) @ C) @ A2) @ B2)) @ ((((((bNF_rel_fun @ E) @ F3) @ B) @ D) @ A2) @ C2))) @ (((comp @ A) @ B) @ E)) @ (((comp @ C) @ D) @ F3))))).
% 3.19/1.64 thf(fact_38_lfilter__idem, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ P) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = (((coinductive_lfilter @ A) @ P) @ Xs))))).
% 3.19/1.64 thf(fact_39_fun__quotient3, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,R1:(A > (A > $o)),Abs1:(A > B),Rep1:(B > A),R2:(C > (C > $o)),Abs2:(C > D),Rep2:(D > C)]: (((((((quotient3 @ A) @ B) @ R1) @ Abs1) @ Rep1) => ((((((quotient3 @ C) @ D) @ R2) @ Abs2) @ Rep2) => (((((quotient3 @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ A) @ C) @ C) @ R1) @ R2)) @ ((((((map_fun @ B) @ A) @ C) @ D) @ Rep1) @ Abs2)) @ ((((((map_fun @ A) @ B) @ D) @ C) @ Abs1) @ Rep2))))))).
% 3.19/1.64 thf(fact_40_unfold__llist__ltl__unroll, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B3:B]: ((((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B3)) = ((((((coindu1441602521_llist @ B) @ A) @ (((((comp @ B) @ $o) @ B) @ IS_LNIL) @ LTL)) @ (((((comp @ B) @ A) @ B) @ LHD) @ LTL)) @ LTL) @ B3))))).
% 3.19/1.64 thf(fact_41_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E:$tType,D:$tType,A:$tType,G:(C > B),H2:(A > C),R12:(D > B),R22:(A > D),F:(B > E),L:(D > E)]: ((((((((comp @ C) @ B) @ A) @ G) @ H2) = (((((comp @ D) @ B) @ A) @ R12) @ R22)) => (((((((comp @ B) @ E) @ D) @ F) @ R12) = L) => ((((((comp @ C) @ E) @ A) @ (((((comp @ B) @ E) @ C) @ F) @ G)) @ H2) = (((((comp @ D) @ E) @ A) @ L) @ R22))))))).
% 3.19/1.64 thf(fact_42_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E:$tType,F:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H2:(E > A),R3:(E > D)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E) @ L2) @ H2) = R3) => ((((((comp @ C) @ B) @ E) @ F) @ (((((comp @ A) @ C) @ E) @ G) @ H2)) = (((((comp @ D) @ B) @ E) @ L1) @ R3))))))).
% 3.19/1.64 thf(fact_43_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H2:(A > C),R3:(A > B),F:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H2) = R3) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F) @ G)) @ H2) = (((((comp @ B) @ D) @ A) @ F) @ R3)))))).
% 3.19/1.64 thf(fact_44_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F:(C > B),G:(A > C),L:(A > B),H2:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F) @ (((((comp @ A) @ C) @ D) @ G) @ H2)) = (((((comp @ A) @ B) @ D) @ L) @ H2)))))).
% 3.19/1.64 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 3.19/1.64 thf(fact_46_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G:(B > C),F:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G) @ (((((comp @ A) @ B) @ D) @ F) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ V))))).
% 3.19/1.64 thf(fact_47_Quotient3__rep__reflp, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),A3:B]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((R @ (Rep @ A3)) @ (Rep @ A3)))))).
% 3.19/1.64 thf(fact_48_Quotient3__rep__abs, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),R3:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ R3) @ R3) => ((R @ (Rep @ (Abs @ R3))) @ R3)))))).
% 3.19/1.64 thf(fact_49_Quotient3__rel__rep, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),A3:B,B3:B]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ (Rep @ A3)) @ (Rep @ B3)) = (A3 = B3)))))).
% 3.19/1.64 thf(fact_50_Quotient3__rel__abs, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),R3:A,S3:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ R3) @ S3) => ((Abs @ R3) = (Abs @ S3))))))).
% 3.19/1.64 thf(fact_51_Quotient3__abs__rep, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),A3:B]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((Abs @ (Rep @ A3)) = A3))))).
% 3.19/1.64 thf(fact_52_rep__abs__rsp__left, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),X1:A,X22:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ X1) @ X22) => ((R @ (Rep @ (Abs @ X1))) @ X22)))))).
% 3.19/1.64 thf(fact_53_Quotient3__refl2, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),R3:A,S3:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ R3) @ S3) => ((R @ S3) @ S3)))))).
% 3.19/1.64 thf(fact_54_Quotient3__refl1, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),R3:A,S3:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ R3) @ S3) => ((R @ R3) @ R3)))))).
% 3.19/1.64 thf(fact_55_Quotient3__rel, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),R3:A,S3:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((((R @ R3) @ R3) & (((R @ S3) @ S3) & ((Abs @ R3) = (Abs @ S3)))) = ((R @ R3) @ S3)))))).
% 3.19/1.64 thf(fact_56_Quotient3__def, axiom, (! [B:$tType,A:$tType]: ((((quotient3 @ A) @ B) = (^ [R4:(A > (A > $o)),Abs3:(A > B),Rep3:(B > A)]: (((! [A5:B]: (((Abs3 @ (Rep3 @ A5)) = A5))) & ((! [A5:B]: (((R4 @ (Rep3 @ A5)) @ (Rep3 @ A5)))) & (! [R5:A,S2:A]: ((((R4 @ R5) @ S2) = (((R4 @ R5) @ R5) & (((R4 @ S2) @ S2) & ((Abs3 @ R5) = (Abs3 @ S2))))))))))))))).
% 3.19/1.64 thf(fact_57_comp__apply__eq, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,F:(B > A),G:(C > B),X2:C,H2:(D > A),K:(C > D)]: ((((F @ (G @ X2)) = (H2 @ (K @ X2))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X2) = ((((((comp @ D) @ A) @ C) @ H2) @ K) @ X2)))))).
% 3.19/1.64 thf(fact_58_rep__abs__rsp, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),X1:A,X22:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ X1) @ X22) => ((R @ X1) @ (Rep @ (Abs @ X22)))))))).
% 3.19/1.64 thf(fact_59_equals__rsp, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),Xa:A,Xb:A,Ya:A,Yb:A]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((R @ Xa) @ Xb) => (((R @ Ya) @ Yb) => (((R @ Xa) @ Ya) = ((R @ Xb) @ Yb)))))))).
% 3.19/1.64 thf(fact_60_Quotient3I, axiom, (! [B:$tType,A:$tType,Abs:(B > A),Rep:(A > B),R:(B > (B > $o))]: (((! [A4:A]: (((Abs @ (Rep @ A4)) = A4))) => ((! [A4:A]: (((R @ (Rep @ A4)) @ (Rep @ A4)))) => ((! [R6:B,S4:B]: ((((R @ R6) @ S4) = (((R @ R6) @ R6) & (((R @ S4) @ S4) & ((Abs @ R6) = (Abs @ S4))))))) => (((((quotient3 @ B) @ A) @ R) @ Abs) @ Rep))))))).
% 3.19/1.64 thf(fact_61_cond__prs, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Absf:(A > B),Repf:(B > A),A3:$o,B3:B,C3:B]: (((((((quotient3 @ A) @ B) @ R) @ Absf) @ Repf) => ((A3 => ((Absf @ ((((if @ A) @ A3) @ (Repf @ B3)) @ (Repf @ C3))) = B3)) & ((~ (A3)) => ((Absf @ ((((if @ A) @ A3) @ (Repf @ B3)) @ (Repf @ C3))) = C3))))))).
% 3.19/1.64 thf(fact_62_let__prs, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,R1:(A > (A > $o)),Abs12:(A > B),Rep12:(B > A),R2:(C > (C > $o)),Abs22:(C > D),Rep22:(D > C)]: (((((((quotient3 @ A) @ B) @ R1) @ Abs12) @ Rep12) => ((((((quotient3 @ C) @ D) @ R2) @ Abs22) @ Rep22) => ((((((((map_fun @ D) @ C) @ ((C > A) > A)) @ ((D > B) > B)) @ Rep22) @ ((((((map_fun @ (D > B)) @ (C > A)) @ A) @ B) @ ((((((map_fun @ C) @ D) @ B) @ A) @ Abs22) @ Rep12)) @ Abs12)) @ (^ [S2:C,F2:(C > A)]: ((F2 @ S2)))) = (^ [S2:D,F2:(D > B)]: ((F2 @ S2))))))))).
% 3.19/1.64 thf(fact_63_o__prs_I1_J, axiom, (! [C:$tType,E:$tType,A:$tType,B:$tType,F3:$tType,D:$tType,R1:(A > (A > $o)),Abs12:(A > B),Rep12:(B > A),R2:(C > (C > $o)),Abs22:(C > D),Rep22:(D > C),R32:(E > (E > $o)),Abs32:(E > F3),Rep32:(F3 > E)]: (((((((quotient3 @ A) @ B) @ R1) @ Abs12) @ Rep12) => ((((((quotient3 @ C) @ D) @ R2) @ Abs22) @ Rep22) => ((((((quotient3 @ E) @ F3) @ R32) @ Abs32) @ Rep32) => ((((((((map_fun @ (D > F3)) @ (C > E)) @ ((A > C) > (A > E))) @ ((B > D) > (B > F3))) @ ((((((map_fun @ C) @ D) @ F3) @ E) @ Abs22) @ Rep32)) @ ((((((map_fun @ (B > D)) @ (A > C)) @ (A > E)) @ (B > F3)) @ ((((((map_fun @ A) @ B) @ D) @ C) @ Abs12) @ Rep22)) @ ((((((map_fun @ B) @ A) @ E) @ F3) @ Rep12) @ Abs32))) @ (((comp @ C) @ E) @ A)) = (((comp @ D) @ F3) @ B)))))))).
% 3.19/1.64 thf(fact_64_llist__all2__lfilterI, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),Q1:(A > $o),Q2:(B > $o)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((! [X:A,Y:B]: ((((P @ X) @ Y) => ((Q1 @ X) = (Q2 @ Y))))) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ (((coinductive_lfilter @ A) @ Q1) @ Xs)) @ (((coinductive_lfilter @ B) @ Q2) @ Ys))))))).
% 3.19/1.64 thf(fact_65_apply__rspQ3_H_H, axiom, (! [C:$tType,A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A),S:(C > (C > $o)),F:(A > C),X2:B]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => (((((((((bNF_rel_fun @ A) @ A) @ C) @ C) @ R) @ S) @ F) @ F) => ((S @ (F @ (Rep @ X2))) @ (F @ (Rep @ X2)))))))).
% 3.19/1.64 thf(fact_66_apply__rspQ3, axiom, (! [B:$tType,C:$tType,A:$tType,R1:(A > (A > $o)),Abs12:(A > B),Rep12:(B > A),R2:(C > (C > $o)),F:(A > C),G:(A > C),X2:A,Y2:A]: (((((((quotient3 @ A) @ B) @ R1) @ Abs12) @ Rep12) => (((((((((bNF_rel_fun @ A) @ A) @ C) @ C) @ R1) @ R2) @ F) @ G) => (((R1 @ X2) @ Y2) => ((R2 @ (F @ X2)) @ (G @ Y2)))))))).
% 3.19/1.64 thf(fact_67_llist__all2__ldropWhileI, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),Q1:(A > $o),Q2:(B > $o)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((! [X:A,Y:B]: ((((P @ X) @ Y) => ((Q1 @ X) = (Q2 @ Y))))) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ (((coindu218763757pWhile @ A) @ Q1) @ Xs)) @ (((coindu218763757pWhile @ B) @ Q2) @ Ys))))))).
% 3.19/1.64 thf(fact_68_quot__rel__rsp, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A)]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((((((((bNF_rel_fun @ A) @ A) @ (A > $o)) @ (A > $o)) @ R) @ ((((((bNF_rel_fun @ A) @ A) @ $o) @ $o) @ R) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ R) @ R))))).
% 3.19/1.64 thf(fact_69_o__rsp_I1_J, axiom, (! [A:$tType,B:$tType,E:$tType,F3:$tType,D:$tType,C:$tType,R2:(A > (C > $o)),R32:(B > (D > $o)),R1:(E > (F3 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (C > D)) @ ((E > A) > (E > B))) @ ((F3 > C) > (F3 > D))) @ ((((((bNF_rel_fun @ A) @ C) @ B) @ D) @ R2) @ R32)) @ ((((((bNF_rel_fun @ (E > A)) @ (F3 > C)) @ (E > B)) @ (F3 > D)) @ ((((((bNF_rel_fun @ E) @ F3) @ A) @ C) @ R1) @ R2)) @ ((((((bNF_rel_fun @ E) @ F3) @ B) @ D) @ R1) @ R32))) @ (((comp @ A) @ B) @ E)) @ (((comp @ C) @ D) @ F3))))).
% 3.19/1.64 thf(fact_70_o__rsp_I2_J, axiom, (! [E:$tType,F3:$tType,H:$tType,G2:$tType,R1:(E > (F3 > $o))]: (((((((((bNF_rel_fun @ (G2 > H)) @ (G2 > H)) @ ((E > G2) > (E > H))) @ ((F3 > G2) > (F3 > H))) @ (^ [Y3:(G2 > H),Z:(G2 > H)]: ((Y3 = Z)))) @ ((((((bNF_rel_fun @ (E > G2)) @ (F3 > G2)) @ (E > H)) @ (F3 > H)) @ ((((((bNF_rel_fun @ E) @ F3) @ G2) @ G2) @ R1) @ (^ [Y3:G2,Z:G2]: ((Y3 = Z))))) @ ((((((bNF_rel_fun @ E) @ F3) @ H) @ H) @ R1) @ (^ [Y3:H,Z:H]: ((Y3 = Z)))))) @ (((comp @ G2) @ H) @ E)) @ (((comp @ G2) @ H) @ F3))))).
% 3.19/1.64 thf(fact_71_map__fun__apply, axiom, (! [D:$tType,A:$tType,C:$tType,B:$tType]: ((((((map_fun @ B) @ C) @ D) @ A) = (^ [F2:(B > C),G3:(D > A),H3:(C > D),X4:B]: ((G3 @ (H3 @ (F2 @ X4))))))))).
% 3.19/1.64 thf(fact_72_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F2:(B > A),G3:(C > B),X4:C]: ((F2 @ (G3 @ X4)))))))).
% 3.19/1.64 thf(fact_73_map__fun__def, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType]: ((((((map_fun @ C) @ A) @ B) @ D) = (^ [F2:(C > A),G3:(B > D),H3:(A > B)]: ((((((comp @ A) @ D) @ C) @ (((((comp @ B) @ D) @ A) @ G3) @ H3)) @ F2))))))).
% 3.19/1.64 thf(fact_74_map__fun_Ocomp, axiom, (! [E:$tType,C:$tType,A:$tType,F3:$tType,D:$tType,B:$tType,F:(E > C),G:(D > F3),H2:(C > A),I:(B > D)]: (((((((comp @ (C > D)) @ (E > F3)) @ (A > B)) @ ((((((map_fun @ E) @ C) @ D) @ F3) @ F) @ G)) @ ((((((map_fun @ C) @ A) @ B) @ D) @ H2) @ I)) = ((((((map_fun @ E) @ A) @ B) @ F3) @ (((((comp @ C) @ A) @ E) @ H2) @ F)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)))))).
% 3.19/1.64 thf(fact_75_map__fun_Ocompositionality, axiom, (! [D:$tType,F3:$tType,C:$tType,E:$tType,B:$tType,A:$tType,F:(E > C),G:(D > F3),H2:(C > A),I:(B > D),Fun:(A > B)]: (((((((((map_fun @ E) @ C) @ D) @ F3) @ F) @ G) @ (((((((map_fun @ C) @ A) @ B) @ D) @ H2) @ I) @ Fun)) = (((((((map_fun @ E) @ A) @ B) @ F3) @ (((((comp @ C) @ A) @ E) @ H2) @ F)) @ (((((comp @ D) @ F3) @ B) @ G) @ I)) @ Fun))))).
% 3.19/1.64 thf(fact_76_llist_Omap__transfer, axiom, (! [A:$tType,B:$tType,F3:$tType,E:$tType,Rb:(A > (E > $o)),Sd:(B > (F3 > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (E > F3)) @ ((coinductive_llist @ A) > (coinductive_llist @ B))) @ ((coinductive_llist @ E) > (coinductive_llist @ F3))) @ ((((((bNF_rel_fun @ A) @ E) @ B) @ F3) @ Rb) @ Sd)) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ E)) @ (coinductive_llist @ B)) @ (coinductive_llist @ F3)) @ (((coindu1486289336t_all2 @ A) @ E) @ Rb)) @ (((coindu1486289336t_all2 @ B) @ F3) @ Sd))) @ ((coinductive_lmap @ A) @ B)) @ ((coinductive_lmap @ E) @ F3))))).
% 3.19/1.64 thf(fact_77_lmap__transfer, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (C > $o)),B2:(B > (D > $o))]: (((((((((bNF_rel_fun @ (A > B)) @ (C > D)) @ ((coinductive_llist @ A) > (coinductive_llist @ B))) @ ((coinductive_llist @ C) > (coinductive_llist @ D))) @ ((((((bNF_rel_fun @ A) @ C) @ B) @ D) @ A2) @ B2)) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ C)) @ (coinductive_llist @ B)) @ (coinductive_llist @ D)) @ (((coindu1486289336t_all2 @ A) @ C) @ A2)) @ (((coindu1486289336t_all2 @ B) @ D) @ B2))) @ ((coinductive_lmap @ A) @ B)) @ ((coinductive_lmap @ C) @ D))))).
% 3.19/1.64 thf(fact_78_bex1__rel__rsp, axiom, (! [B:$tType,A:$tType,R:(A > (A > $o)),Absf:(A > B),Repf:(B > A)]: (((((((quotient3 @ A) @ B) @ R) @ Absf) @ Repf) => ((((((((bNF_rel_fun @ (A > $o)) @ (A > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ A) @ $o) @ $o) @ R) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((bex1_rel @ A) @ R)) @ ((bex1_rel @ A) @ R)))))).
% 3.19/1.64 thf(fact_79_LCons__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((coinductive_llist @ A) > (coinductive_llist @ A))) @ ((coinductive_llist @ B) > (coinductive_llist @ B))) @ A2) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2)) @ (((coindu1486289336t_all2 @ A) @ B) @ A2))) @ (coinductive_LCons @ A)) @ (coinductive_LCons @ B))))).
% 3.19/1.64 thf(fact_80_llist_Oinject, axiom, (! [A:$tType,X21:A,X222:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X222) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.19/1.64 thf(fact_81_llist__all2__LCons__LCons, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,X222:(coinductive_llist @ A),Y21:B,Y22:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ R) @ (((coinductive_LCons @ A) @ X21) @ X222)) @ (((coinductive_LCons @ B) @ Y21) @ Y22)) = (((R @ X21) @ Y21) & (((((coindu1486289336t_all2 @ A) @ B) @ R) @ X222) @ Y22)))))).
% 3.19/1.64 thf(fact_82_lfilter__LCons, axiom, (! [A:$tType,P:(A > $o),X2:A,Xs:(coinductive_llist @ A)]: ((((P @ X2) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X2) @ Xs)) = (((coinductive_LCons @ A) @ X2) @ (((coinductive_lfilter @ A) @ P) @ Xs)))) & ((~ ((P @ X2))) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X2) @ Xs)) = (((coinductive_lfilter @ A) @ P) @ Xs))))))).
% 3.19/1.64 thf(fact_83_ldropWhile__LCons, axiom, (! [A:$tType,P:(A > $o),X2:A,Xs:(coinductive_llist @ A)]: ((((P @ X2) => ((((coindu218763757pWhile @ A) @ P) @ (((coinductive_LCons @ A) @ X2) @ Xs)) = (((coindu218763757pWhile @ A) @ P) @ Xs))) & ((~ ((P @ X2))) => ((((coindu218763757pWhile @ A) @ P) @ (((coinductive_LCons @ A) @ X2) @ Xs)) = (((coinductive_LCons @ A) @ X2) @ Xs))))))).
% 3.19/1.64 thf(fact_84_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B3:B,X2:A,Xs:(coinductive_llist @ A)]: (((((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B3) = (((coinductive_LCons @ A) @ X2) @ Xs)) = ((~ ((IS_LNIL @ B3))) & ((X2 = (LHD @ B3)) & (Xs = ((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B3))))))))).
% 3.19/1.64 thf(fact_85_llist_Opred__inject_I2_J, axiom, (! [A:$tType,P:(A > $o),A3:A,Aa2:(coinductive_llist @ A)]: (((((coindu543516966_llist @ A) @ P) @ (((coinductive_LCons @ A) @ A3) @ Aa2)) = ((P @ A3) & (((coindu543516966_llist @ A) @ P) @ Aa2)))))).
% 3.19/1.64 thf(fact_86_llist_Osimps_I13_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:A,X222:(coinductive_llist @ A)]: ((((((coinductive_lmap @ A) @ B) @ F) @ (((coinductive_LCons @ A) @ X21) @ X222)) = (((coinductive_LCons @ B) @ (F @ X21)) @ ((((coinductive_lmap @ A) @ B) @ F) @ X222)))))).
% 3.19/1.64 thf(fact_87_bex1__rel__aux, axiom, (! [A:$tType,R:(A > (A > $o)),X2:(A > $o),Y2:(A > $o)]: (((! [Xa2:A,Ya2:A]: ((((R @ Xa2) @ Ya2) => ((X2 @ Xa2) = (Y2 @ Ya2))))) => ((((bex1_rel @ A) @ R) @ X2) => (((bex1_rel @ A) @ R) @ Y2)))))).
% 3.19/1.64 thf(fact_88_bex1__rel__aux2, axiom, (! [A:$tType,R:(A > (A > $o)),X2:(A > $o),Y2:(A > $o)]: (((! [Xa2:A,Ya2:A]: ((((R @ Xa2) @ Ya2) => ((X2 @ Xa2) = (Y2 @ Ya2))))) => ((((bex1_rel @ A) @ R) @ Y2) => (((bex1_rel @ A) @ R) @ X2)))))).
% 3.19/1.64 thf(fact_89_lmap__eq__LCons__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coinductive_llist @ B),Y2:A,Ys:(coinductive_llist @ A)]: (((((((coinductive_lmap @ B) @ A) @ F) @ Xs) = (((coinductive_LCons @ A) @ Y2) @ Ys)) = (? [X4:B,Xs2:(coinductive_llist @ B)]: (((Xs = (((coinductive_LCons @ B) @ X4) @ Xs2)) & ((Y2 = (F @ X4)) & (Ys = ((((coinductive_lmap @ B) @ A) @ F) @ Xs2)))))))))).
% 3.19/1.64 thf(fact_90_iterates__equality, axiom, (! [A:$tType,H2:(A > (coinductive_llist @ A)),F:(A > A)]: (((! [X:A]: (((H2 @ X) = (((coinductive_LCons @ A) @ X) @ ((((coinductive_lmap @ A) @ A) @ F) @ (H2 @ X)))))) => (H2 = ((coinductive_iterates @ A) @ F)))))).
% 3.19/1.64 thf(fact_91_iterates__lmap, axiom, (! [A:$tType]: (((coinductive_iterates @ A) = (^ [F2:(A > A),X4:A]: ((((coinductive_LCons @ A) @ X4) @ ((((coinductive_lmap @ A) @ A) @ F2) @ (((coinductive_iterates @ A) @ F2) @ X4))))))))).
% 3.19/1.64 thf(fact_92_llist_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,G:(B > C),F:(A > B),V:(coinductive_llist @ A)]: ((((((coinductive_lmap @ B) @ C) @ G) @ ((((coinductive_lmap @ A) @ B) @ F) @ V)) = ((((coinductive_lmap @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F)) @ V))))).
% 3.19/1.64 thf(fact_93_lfilter__lmap, axiom, (! [A:$tType,B:$tType,P:(A > $o),F:(B > A),Xs:(coinductive_llist @ B)]: (((((coinductive_lfilter @ A) @ P) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)) = ((((coinductive_lmap @ B) @ A) @ F) @ (((coinductive_lfilter @ B) @ (((((comp @ A) @ $o) @ B) @ P) @ F)) @ Xs)))))).
% 3.19/1.64 thf(fact_94_ltakeWhile__lmap, axiom, (! [A:$tType,B:$tType,P:(A > $o),F:(B > A),Xs:(coinductive_llist @ B)]: (((((coindu501562517eWhile @ A) @ P) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)) = ((((coinductive_lmap @ B) @ A) @ F) @ (((coindu501562517eWhile @ B) @ (((((comp @ A) @ $o) @ B) @ P) @ F)) @ Xs)))))).
% 3.19/1.64 thf(fact_95_ldropWhile__lmap, axiom, (! [A:$tType,B:$tType,P:(A > $o),F:(B > A),Xs:(coinductive_llist @ B)]: (((((coindu218763757pWhile @ A) @ P) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)) = ((((coinductive_lmap @ B) @ A) @ F) @ (((coindu218763757pWhile @ B) @ (((((comp @ A) @ $o) @ B) @ P) @ F)) @ Xs)))))).
% 3.19/1.64 thf(fact_96_lmap__iterates, axiom, (! [A:$tType,F:(A > A),X2:A]: ((((((coinductive_lmap @ A) @ A) @ F) @ (((coinductive_iterates @ A) @ F) @ X2)) = (((coinductive_iterates @ A) @ F) @ (F @ X2)))))).
% 3.19/1.64 thf(fact_97_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,Y21:B,X222:(coinductive_llist @ A),Y22:(coinductive_llist @ B)]: ((((R @ X21) @ Y21) => ((((((coindu1486289336t_all2 @ A) @ B) @ R) @ X222) @ Y22) => (((((coindu1486289336t_all2 @ A) @ B) @ R) @ (((coinductive_LCons @ A) @ X21) @ X222)) @ (((coinductive_LCons @ B) @ Y21) @ Y22))))))).
% 3.19/1.64 thf(fact_98_llist__all2__LCons1, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X2:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ (((coinductive_LCons @ A) @ X2) @ Xs)) @ Ys) = (? [Y5:B,Ys2:(coinductive_llist @ B)]: (((Ys = (((coinductive_LCons @ B) @ Y5) @ Ys2)) & (((P @ X2) @ Y5) & (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys2))))))))).
% 3.19/1.64 thf(fact_99_llist__all2__LCons2, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Y2:B,Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ (((coinductive_LCons @ B) @ Y2) @ Ys)) = (? [X4:A,Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ X4) @ Xs2)) & (((P @ X4) @ Y2) & (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs2) @ Ys))))))))).
% 3.19/1.64 thf(fact_100_lmap__lmirror, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coinductive_llist @ B)]: ((((((coinductive_lmap @ B) @ A) @ F) @ ((lMirro427583474mirror @ B) @ Xs)) = ((lMirro427583474mirror @ A) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)))))).
% 3.19/1.64 thf(fact_101_llist_Opred__map, axiom, (! [B:$tType,A:$tType,Q:(B > $o),F:(A > B),X2:(coinductive_llist @ A)]: (((((coindu543516966_llist @ B) @ Q) @ ((((coinductive_lmap @ A) @ B) @ F) @ X2)) = (((coindu543516966_llist @ A) @ (((((comp @ B) @ $o) @ A) @ Q) @ F)) @ X2))))).
% 3.19/1.64 thf(fact_102_llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F22:(A > ((coinductive_llist @ A) > B)),X21:A,X222:(coinductive_llist @ A)]: (((((((coindu1381640503_llist @ B) @ A) @ F1) @ F22) @ (((coinductive_LCons @ A) @ X21) @ X222)) = ((F22 @ X21) @ X222))))).
% 3.19/1.64 thf(fact_103_lfilter__LCons__seek, axiom, (! [A:$tType,P3:(A > $o),X2:A,L:(coinductive_llist @ A)]: (((~ ((P3 @ X2))) => ((((coinductive_lfilter @ A) @ P3) @ (((coinductive_LCons @ A) @ X2) @ L)) = (((coinductive_lfilter @ A) @ P3) @ L)))))).
% 3.19/1.64 thf(fact_104_lfilter__LCons__found, axiom, (! [A:$tType,P:(A > $o),X2:A,Xs:(coinductive_llist @ A)]: (((P @ X2) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X2) @ Xs)) = (((coinductive_LCons @ A) @ X2) @ (((coinductive_lfilter @ A) @ P) @ Xs))))))).
% 3.19/1.64 thf(fact_105_iterates_Ocode, axiom, (! [A:$tType]: (((coinductive_iterates @ A) = (^ [F2:(A > A),X4:A]: ((((coinductive_LCons @ A) @ X4) @ (((coinductive_iterates @ A) @ F2) @ (F2 @ X4))))))))).
% 3.19/1.64 thf(fact_106_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A3:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A3))) => (((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A3) = (((coinductive_LCons @ B) @ (G21 @ A3)) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ (G22 @ A3)))))))).
% 3.19/1.64 thf(fact_107_llist_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A3:C,G21:(C > A),Q22:(C > $o),G221:(C > (coinductive_llist @ A)),G222:(C > C)]: (((~ ((P3 @ A3))) => (((((((((coindu1259883913_llist @ C) @ A) @ P3) @ G21) @ Q22) @ G221) @ G222) @ A3) = (((coinductive_LCons @ A) @ (G21 @ A3)) @ ((((if @ (coinductive_llist @ A)) @ (Q22 @ A3)) @ (G221 @ A3)) @ ((((((((coindu1259883913_llist @ C) @ A) @ P3) @ G21) @ Q22) @ G221) @ G222) @ (G222 @ A3))))))))).
% 3.19/1.64 thf(fact_108_lmap__unfold__llist, axiom, (! [A:$tType,B:$tType,C:$tType,F:(B > A),IS_LNIL:(C > $o),LHD:(C > B),LTL:(C > C),B3:C]: ((((((coinductive_lmap @ B) @ A) @ F) @ ((((((coindu1441602521_llist @ C) @ B) @ IS_LNIL) @ LHD) @ LTL) @ B3)) = ((((((coindu1441602521_llist @ C) @ A) @ IS_LNIL) @ (((((comp @ B) @ A) @ C) @ F) @ LHD)) @ LTL) @ B3))))).
% 3.19/1.64 thf(fact_109_llist_Omap__o__corec, axiom, (! [A:$tType,B:$tType,C:$tType,F:(A > B),G:(C > $o),Ga:(C > A),Gb:(C > $o),Gc:(C > (coinductive_llist @ A)),Gd:(C > C)]: (((((((comp @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ C) @ (((coinductive_lmap @ A) @ B) @ F)) @ (((((((coindu1259883913_llist @ C) @ A) @ G) @ Ga) @ Gb) @ Gc) @ Gd)) = (((((((coindu1259883913_llist @ C) @ B) @ G) @ (((((comp @ A) @ B) @ C) @ F) @ Ga)) @ Gb) @ (((((comp @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ C) @ (((coinductive_lmap @ A) @ B) @ F)) @ Gc)) @ Gd))))).
% 3.19/1.64 thf(fact_110_lmap__corec__llist, axiom, (! [A:$tType,B:$tType,C:$tType,F:(B > A),IS_LNIL:(C > $o),LHD:(C > B),EndORmore:(C > $o),TTL_end:(C > (coinductive_llist @ B)),TTL_more:(C > C),B3:C]: ((((((coinductive_lmap @ B) @ A) @ F) @ ((((((((coindu1259883913_llist @ C) @ B) @ IS_LNIL) @ LHD) @ EndORmore) @ TTL_end) @ TTL_more) @ B3)) = ((((((((coindu1259883913_llist @ C) @ A) @ IS_LNIL) @ (((((comp @ B) @ A) @ C) @ F) @ LHD)) @ EndORmore) @ (((((comp @ (coinductive_llist @ B)) @ (coinductive_llist @ A)) @ C) @ (((coinductive_lmap @ B) @ A) @ F)) @ TTL_end)) @ TTL_more) @ B3))))).
% 3.19/1.64 thf(fact_111_lfilter__eq__LCons, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A),X2:A,Xs3:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = (((coinductive_LCons @ A) @ X2) @ Xs3)) => (? [Xs4:(coinductive_llist @ A)]: (((Xs3 = (((coinductive_lfilter @ A) @ P) @ Xs4)) & ((((coindu218763757pWhile @ A) @ (((((comp @ $o) @ $o) @ A) @ (~)) @ P)) @ Xs) = (((coinductive_LCons @ A) @ X2) @ Xs4))))))))).
% 3.19/1.64 thf(fact_112_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A3:(C > B),B3:(A > C),C3:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = C3) => ((A3 @ (B3 @ V)) = (C3 @ V)))))).
% 3.19/1.64 thf(fact_113_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A3:(C > B),B3:(A > C),C3:(D > B),D3:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = (((((comp @ D) @ B) @ A) @ C3) @ D3)) => (! [V2:A]: (((A3 @ (B3 @ V2)) = (C3 @ (D3 @ V2))))))))).
% 3.19/1.64 thf(fact_114_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A3:(C > B),B3:(A > C),C3:(D > B),D3:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = (((((comp @ D) @ B) @ A) @ C3) @ D3)) => ((A3 @ (B3 @ V)) = (C3 @ (D3 @ V))))))).
% 3.19/1.64 thf(fact_115_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F:(D > B),G:(C > D),H2:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F) @ G)) @ H2) = (((((comp @ D) @ B) @ A) @ F) @ (((((comp @ C) @ D) @ A) @ G) @ H2)))))).
% 3.19/1.64 thf(fact_116_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F2:(B > C),G3:(A > B),X4:A]: ((F2 @ (G3 @ X4)))))))).
% 3.19/1.64 thf(fact_117_llist_Octr__transfer_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ ((coinductive_llist @ A) > (coinductive_llist @ A))) @ ((coinductive_llist @ B) > (coinductive_llist @ B))) @ R) @ ((((((bNF_rel_fun @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ (((coindu1486289336t_all2 @ A) @ B) @ R))) @ (coinductive_LCons @ A)) @ (coinductive_LCons @ B))))).
% 3.19/1.64 thf(fact_118_lmember__code_I2_J, axiom, (! [A:$tType,X2:A,Y2:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lmember @ A) @ X2) @ (((coinductive_LCons @ A) @ Y2) @ Ys)) = ((X2 = Y2) | (((coinductive_lmember @ A) @ X2) @ Ys)))))).
% 3.19/1.64 thf(fact_119_type__copy__map__cong0, axiom, (! [B:$tType,D:$tType,E:$tType,A:$tType,C:$tType,M:(B > A),G:(C > B),X2:C,N:(D > A),H2:(C > D),F:(A > E)]: ((((M @ (G @ X2)) = (N @ (H2 @ X2))) => (((((((comp @ B) @ E) @ C) @ (((((comp @ A) @ E) @ B) @ F) @ M)) @ G) @ X2) = ((((((comp @ D) @ E) @ C) @ (((((comp @ A) @ E) @ D) @ F) @ N)) @ H2) @ X2)))))).
% 3.19/1.64 thf(fact_120_comp__cong, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,E:$tType,F:(B > A),G:(C > B),X2:C,F4:(D > A),G4:(E > D),X5:E]: ((((F @ (G @ X2)) = (F4 @ (G4 @ X5))) => (((((((comp @ B) @ A) @ C) @ F) @ G) @ X2) = ((((((comp @ D) @ A) @ E) @ F4) @ G4) @ X5)))))).
% 3.19/1.64 thf(fact_121_if__prs, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A)]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((((((((map_fun @ $o) @ $o) @ (A > (A > A))) @ (B > (B > B))) @ (id @ $o)) @ ((((((map_fun @ B) @ A) @ (A > A)) @ (B > B)) @ Rep) @ ((((((map_fun @ B) @ A) @ A) @ B) @ Rep) @ Abs))) @ (if @ A)) = (if @ B)))))).
% 3.19/1.64 thf(fact_122_o__prs_I2_J, axiom, (! [F3:$tType,E:$tType,C:$tType,D:$tType,A:$tType,B:$tType,H:$tType,G2:$tType,R1:(A > (A > $o)),Abs12:(A > B),Rep12:(B > A),R2:(C > (C > $o)),Abs22:(C > D),Rep22:(D > C),R32:(E > (E > $o)),Abs32:(E > F3),Rep32:(F3 > E)]: (((((((quotient3 @ A) @ B) @ R1) @ Abs12) @ Rep12) => ((((((quotient3 @ C) @ D) @ R2) @ Abs22) @ Rep22) => ((((((quotient3 @ E) @ F3) @ R32) @ Abs32) @ Rep32) => ((((((((map_fun @ (G2 > H)) @ (G2 > H)) @ ((A > G2) > (A > H))) @ ((B > G2) > (B > H))) @ (id @ (G2 > H))) @ ((((((map_fun @ (B > G2)) @ (A > G2)) @ (A > H)) @ (B > H)) @ ((((((map_fun @ A) @ B) @ G2) @ G2) @ Abs12) @ (id @ G2))) @ ((((((map_fun @ B) @ A) @ H) @ H) @ Rep12) @ (id @ H)))) @ (((comp @ G2) @ H) @ A)) = (((comp @ G2) @ H) @ B)))))))).
% 3.19/1.64 thf(fact_123_fun__ord__parametric, axiom, (! [C:$tType,D:$tType,A:$tType,B:$tType,F3:$tType,E:$tType,C2:(A > (B > $o)),A2:(C > (E > $o)),B2:(D > (F3 > $o))]: (((((bi_total @ A) @ B) @ C2) => ((((((((bNF_rel_fun @ (C > (D > $o))) @ (E > (F3 > $o))) @ ((A > C) > ((A > D) > $o))) @ ((B > E) > ((B > F3) > $o))) @ ((((((bNF_rel_fun @ C) @ E) @ (D > $o)) @ (F3 > $o)) @ A2) @ ((((((bNF_rel_fun @ D) @ F3) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (A > C)) @ (B > E)) @ ((A > D) > $o)) @ ((B > F3) > $o)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ E) @ C2) @ A2)) @ ((((((bNF_rel_fun @ (A > D)) @ (B > F3)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ D) @ F3) @ C2) @ B2)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (((partial_fun_ord @ C) @ D) @ A)) @ (((partial_fun_ord @ E) @ F3) @ B)))))).
% 3.19/1.64 thf(fact_124_id__apply, axiom, (! [A:$tType]: (((id @ A) = (^ [X4:A]: (X4)))))).
% 3.19/1.64 thf(fact_125_fun_Omap__id, axiom, (! [A:$tType,D:$tType,T2:(D > A)]: (((((((comp @ A) @ A) @ D) @ (id @ A)) @ T2) = T2)))).
% 3.19/1.64 thf(fact_126_comp__id, axiom, (! [B:$tType,A:$tType,F:(A > B)]: (((((((comp @ A) @ B) @ A) @ F) @ (id @ A)) = F)))).
% 3.19/1.64 thf(fact_127_id__comp, axiom, (! [B:$tType,A:$tType,G:(A > B)]: (((((((comp @ B) @ B) @ A) @ (id @ B)) @ G) = G)))).
% 3.19/1.64 thf(fact_128_fun_Omap__id0, axiom, (! [A:$tType,D:$tType]: ((((((comp @ A) @ A) @ D) @ (id @ A)) = (id @ (D > A)))))).
% 3.19/1.64 thf(fact_129_map__fun__id, axiom, (! [B:$tType,A:$tType]: ((((((((map_fun @ A) @ A) @ B) @ B) @ (id @ A)) @ (id @ B)) = (id @ (A > B)))))).
% 3.19/1.64 thf(fact_130_llist_Omap__id0, axiom, (! [A:$tType]: (((((coinductive_lmap @ A) @ A) @ (id @ A)) = (id @ (coinductive_llist @ A)))))).
% 3.19/1.64 thf(fact_131_eq__id__iff, axiom, (! [A:$tType,F:(A > A)]: (((! [X4:A]: (((F @ X4) = X4))) = (F = (id @ A)))))).
% 3.19/1.64 thf(fact_132_id__def, axiom, (! [A:$tType]: (((id @ A) = (^ [X4:A]: (X4)))))).
% 3.19/1.64 thf(fact_133_llist_Obi__total__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((bi_total @ A) @ B) @ R) => (((bi_total @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_134_bi__total__def, axiom, (! [B:$tType,A:$tType]: ((((bi_total @ A) @ B) = (^ [R4:(A > (B > $o))]: (((! [X4:A]: (((^ [P4:(B > $o)]: ((? [X6:B]: ((P4 @ X6))))) @ (R4 @ X4)))) & (! [Y5:B]: ((? [X4:A]: (((R4 @ X4) @ Y5)))))))))))).
% 3.19/1.64 thf(fact_135_bi__total__eq, axiom, (! [A:$tType]: ((((bi_total @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_136_id__rsp, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ R) @ R) @ (id @ A)) @ (id @ B))))).
% 3.19/1.64 thf(fact_137_id__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ A) @ B) @ A2) @ A2) @ (id @ A)) @ (id @ B))))).
% 3.19/1.64 thf(fact_138_pointfree__idE, axiom, (! [B:$tType,A:$tType,F:(B > A),G:(A > B),X2:A]: ((((((((comp @ B) @ A) @ A) @ F) @ G) = (id @ A)) => ((F @ (G @ X2)) = X2))))).
% 3.19/1.64 thf(fact_139_comp__eq__id__dest, axiom, (! [C:$tType,B:$tType,A:$tType,A3:(C > B),B3:(A > C),C3:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = (((((comp @ B) @ B) @ A) @ (id @ B)) @ C3)) => ((A3 @ (B3 @ V)) = (C3 @ V)))))).
% 3.19/1.64 thf(fact_140_llist_Omap__id, axiom, (! [A:$tType,T2:(coinductive_llist @ A)]: ((((((coinductive_lmap @ A) @ A) @ (id @ A)) @ T2) = T2)))).
% 3.19/1.64 thf(fact_141_identity__quotient3, axiom, (! [A:$tType]: ((((((quotient3 @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (id @ A)) @ (id @ A))))).
% 3.19/1.64 thf(fact_142_abs__o__rep, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A)]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((((((comp @ A) @ B) @ B) @ Abs) @ Rep) = (id @ B)))))).
% 3.19/1.64 thf(fact_143_id__prs, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Abs:(A > B),Rep:(B > A)]: (((((((quotient3 @ A) @ B) @ R) @ Abs) @ Rep) => ((((((((map_fun @ B) @ A) @ A) @ B) @ Rep) @ Abs) @ (id @ A)) = (id @ B)))))).
% 3.19/1.64 thf(fact_144_transfer__forall__transfer_I1_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ (transfer_forall @ A)) @ (transfer_forall @ B)))))).
% 3.19/1.64 thf(fact_145_monotone__parametric, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ ((C > (C > $o)) > ((A > C) > $o))) @ ((D > (D > $o)) > ((B > D) > $o))) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (C > (C > $o))) @ (D > (D > $o))) @ ((A > C) > $o)) @ ((B > D) > $o)) @ ((((((bNF_rel_fun @ C) @ D) @ (C > $o)) @ (D > $o)) @ B2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2)) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((comple1396247847notone @ A) @ C)) @ ((comple1396247847notone @ B) @ D)))))).
% 3.19/1.64 thf(fact_146_swap__comp__involutory, axiom, (! [B:$tType,A:$tType,A3:A,B3:A]: (((((((comp @ (A > B)) @ (A > B)) @ (A > B)) @ ((((swap @ A) @ B) @ A3) @ B3)) @ ((((swap @ A) @ B) @ A3) @ B3)) = (id @ (A > B)))))).
% 3.19/1.64 thf(fact_147_ex1__prs, axiom, (! [A:$tType,B:$tType,R:(A > (A > $o)),Absf:(A > B),Repf:(B > A),F:(B > $o)]: (((((((quotient3 @ A) @ B) @ R) @ Absf) @ Repf) => (((((((((map_fun @ (B > $o)) @ (A > $o)) @ $o) @ $o) @ ((((((map_fun @ A) @ B) @ $o) @ $o) @ Absf) @ (id @ $o))) @ (id @ $o)) @ ((bex1_rel @ A) @ R)) @ F) = (? [X4:B]: (((F @ X4) & (! [Y5:B]: (((F @ Y5) => (Y5 = X4)))))))))))).
% 3.19/1.64 thf(fact_148_swap__apply_I3_J, axiom, (! [A:$tType,B:$tType,C3:B,A3:B,B3:B,F:(B > A)]: (((C3 != A3) => ((C3 != B3) => (((((((swap @ B) @ A) @ A3) @ B3) @ F) @ C3) = (F @ C3))))))).
% 3.19/1.64 thf(fact_149_swap__apply_I2_J, axiom, (! [A:$tType,B:$tType,A3:B,B3:B,F:(B > A)]: ((((((((swap @ B) @ A) @ A3) @ B3) @ F) @ B3) = (F @ A3))))).
% 3.19/1.64 thf(fact_150_swap__apply_I1_J, axiom, (! [A:$tType,B:$tType,A3:B,B3:B,F:(B > A)]: ((((((((swap @ B) @ A) @ A3) @ B3) @ F) @ A3) = (F @ B3))))).
% 3.19/1.64 thf(fact_151_swap__self, axiom, (! [B:$tType,A:$tType,A3:A,F:(A > B)]: (((((((swap @ A) @ B) @ A3) @ A3) @ F) = F)))).
% 3.19/1.64 thf(fact_152_swap__nilpotent, axiom, (! [B:$tType,A:$tType,A3:A,B3:A,F:(A > B)]: (((((((swap @ A) @ B) @ A3) @ B3) @ (((((swap @ A) @ B) @ A3) @ B3) @ F)) = F)))).
% 3.19/1.64 thf(fact_153_swap__triple, axiom, (! [B:$tType,A:$tType,A3:A,C3:A,B3:A,F:(A > B)]: (((A3 != C3) => ((B3 != C3) => ((((((swap @ A) @ B) @ A3) @ B3) @ (((((swap @ A) @ B) @ B3) @ C3) @ (((((swap @ A) @ B) @ A3) @ B3) @ F))) = (((((swap @ A) @ B) @ A3) @ C3) @ F))))))).
% 3.19/1.64 thf(fact_154_swap__commute, axiom, (! [B:$tType,A:$tType]: ((((swap @ A) @ B) = (^ [A5:A,B5:A]: (((((swap @ A) @ B) @ B5) @ A5))))))).
% 3.19/1.64 thf(fact_155_comp__swap, axiom, (! [B:$tType,C:$tType,A:$tType,F:(C > B),A3:A,B3:A,G:(A > C)]: (((((((comp @ C) @ B) @ A) @ F) @ (((((swap @ A) @ C) @ A3) @ B3) @ G)) = (((((swap @ A) @ B) @ A3) @ B3) @ (((((comp @ C) @ B) @ A) @ F) @ G)))))).
% 3.19/1.64 thf(fact_156_transfer__forall__transfer_I4_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ rev_implies) @ (transfer_forall @ A)) @ (transfer_forall @ B)))))).
% 3.19/1.64 thf(fact_157_transfer__forall__transfer_I5_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ rev_implies)) @ rev_implies) @ (transfer_forall @ A)) @ (transfer_forall @ B)))))).
% 3.19/1.64 thf(fact_158_Domainp__transfer, axiom, (! [C:$tType,A:$tType,B:$tType,D:$tType,B2:(A > (B > $o)),A2:(C > (D > $o))]: (((((bi_total @ A) @ B) @ B2) => ((((((((bNF_rel_fun @ (C > (A > $o))) @ (D > (B > $o))) @ (C > $o)) @ (D > $o)) @ ((((((bNF_rel_fun @ C) @ D) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ ((domainp @ C) @ A)) @ ((domainp @ D) @ B)))))).
% 3.19/1.64 thf(fact_159_rev__implies__def, axiom, (rev_implies = (^ [X4:$o,Y5:$o]: ((Y5 => X4))))).
% 3.19/1.64 thf(fact_160_Domainp__refl, axiom, (! [B:$tType,A:$tType]: ((((domainp @ A) @ B) = ((domainp @ A) @ B))))).
% 3.19/1.64 thf(fact_161_Domainp__iff, axiom, (! [B:$tType,A:$tType]: ((((domainp @ A) @ B) = (^ [T3:(A > (B > $o)),X4:A]: (((^ [P4:(B > $o)]: ((? [X6:B]: ((P4 @ X6))))) @ (T3 @ X4)))))))).
% 3.19/1.64 thf(fact_162_llist_ODomainp__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((domainp @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) = ((coindu543516966_llist @ A) @ (((domainp @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_163_reflp__transfer_I5_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ rev_implies) @ (reflp @ A)) @ (reflp @ B)))))).
% 3.19/1.64 thf(fact_164_reflp__transfer_I4_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ rev_implies))) @ rev_implies) @ (reflp @ A)) @ (reflp @ B)))))).
% 3.19/1.64 thf(fact_165_Ex1__parametric, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ (ex1 @ A)) @ (ex1 @ B))))))).
% 3.19/1.64 thf(fact_166_bi__unique__fun, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((bi_unique @ C) @ D) @ B2) => (((bi_unique @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_167_fun_Orel__reflp, axiom, (! [D:$tType,A:$tType,R:(A > (A > $o))]: ((((reflp @ A) @ R) => ((reflp @ (D > A)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ A) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ R)))))).
% 3.19/1.64 thf(fact_168_DEADID_Orel__reflp, axiom, (! [A:$tType]: (((reflp @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_169_bi__uniqueDl, axiom, (! [B:$tType,A:$tType,A2:(A > (B > $o)),X2:A,Y2:B,Z2:A]: (((((bi_unique @ A) @ B) @ A2) => (((A2 @ X2) @ Y2) => (((A2 @ Z2) @ Y2) => (X2 = Z2))))))).
% 3.19/1.64 thf(fact_170_bi__uniqueDr, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o)),X2:A,Y2:B,Z2:B]: (((((bi_unique @ A) @ B) @ A2) => (((A2 @ X2) @ Y2) => (((A2 @ X2) @ Z2) => (Y2 = Z2))))))).
% 3.19/1.64 thf(fact_171_bi__unique__eq, axiom, (! [A:$tType]: ((((bi_unique @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_172_bi__unique__def, axiom, (! [B:$tType,A:$tType]: ((((bi_unique @ A) @ B) = (^ [R4:(A > (B > $o))]: (((! [X4:A,Y5:B,Z3:B]: ((((R4 @ X4) @ Y5) => (((R4 @ X4) @ Z3) => (Y5 = Z3))))) & (! [X4:A,Y5:A,Z3:B]: ((((R4 @ X4) @ Z3) => (((R4 @ Y5) @ Z3) => (X4 = Y5)))))))))))).
% 3.19/1.64 thf(fact_173_llist_Orel__reflp, axiom, (! [A:$tType,R:(A > (A > $o))]: ((((reflp @ A) @ R) => ((reflp @ (coinductive_llist @ A)) @ (((coindu1486289336t_all2 @ A) @ A) @ R)))))).
% 3.19/1.64 thf(fact_174_llist_Obi__unique__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((bi_unique @ A) @ B) @ R) => (((bi_unique @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_175_bi__total__fun, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((bi_total @ C) @ D) @ B2) => (((bi_total @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_176_eq__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))))))).
% 3.19/1.64 thf(fact_177_bi__unique__alt__def2, axiom, (! [B:$tType,A:$tType]: ((((bi_unique @ A) @ B) = (^ [R4:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ R4) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R4) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))))))))).
% 3.19/1.64 thf(fact_178_reflp__transfer_I1_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ (reflp @ A)) @ (reflp @ B)))))).
% 3.19/1.64 thf(fact_179_fun__upd__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > C)) @ (B > D)) @ (A > (C > (A > C)))) @ (B > (D > (B > D)))) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2)) @ ((((((bNF_rel_fun @ A) @ B) @ (C > (A > C))) @ (D > (B > D))) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ (A > C)) @ (B > D)) @ B2) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2)))) @ ((fun_upd @ A) @ C)) @ ((fun_upd @ B) @ D)))))).
% 3.19/1.64 thf(fact_180_right__unique__parametric, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((bi_unique @ C) @ D) @ B2) => ((((bi_total @ C) @ D) @ B2) => ((((((((bNF_rel_fun @ (A > (C > $o))) @ (B > (D > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (C > $o)) @ (D > $o)) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((right_unique @ A) @ C)) @ ((right_unique @ B) @ D)))))))).
% 3.19/1.64 thf(fact_181_left__unique__parametric, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((bi_total @ A) @ B) @ A2) => ((((bi_total @ C) @ D) @ B2) => ((((((((bNF_rel_fun @ (A > (C > $o))) @ (B > (D > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (C > $o)) @ (D > $o)) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((left_unique @ A) @ C)) @ ((left_unique @ B) @ D)))))))).
% 3.19/1.64 thf(fact_182_fun__upd__apply, axiom, (! [A:$tType,B:$tType]: ((((fun_upd @ B) @ A) = (^ [F2:(B > A),X4:B,Y5:A,Z3:B]: (((((if @ A) @ (Z3 = X4)) @ Y5) @ (F2 @ Z3)))))))).
% 3.19/1.64 thf(fact_183_fun__upd__triv, axiom, (! [B:$tType,A:$tType,F:(A > B),X2:A]: (((((((fun_upd @ A) @ B) @ F) @ X2) @ (F @ X2)) = F)))).
% 3.19/1.64 thf(fact_184_fun__upd__upd, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y2:B,Z2:B]: (((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ F) @ X2) @ Y2)) @ X2) @ Z2) = (((((fun_upd @ A) @ B) @ F) @ X2) @ Z2))))).
% 3.19/1.64 thf(fact_185_bi__uniqueI, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((left_unique @ A) @ B) @ R) => ((((right_unique @ A) @ B) @ R) => (((bi_unique @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_186_bi__unique__alt__def, axiom, (! [B:$tType,A:$tType]: ((((bi_unique @ A) @ B) = (^ [A6:(A > (B > $o))]: (((((left_unique @ A) @ B) @ A6) & (((right_unique @ A) @ B) @ A6)))))))).
% 3.19/1.64 thf(fact_187_fun__upd__comp, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > B),G:(A > C),X2:A,Y2:C]: (((((((comp @ C) @ B) @ A) @ F) @ (((((fun_upd @ A) @ C) @ G) @ X2) @ Y2)) = (((((fun_upd @ A) @ B) @ (((((comp @ C) @ B) @ A) @ F) @ G)) @ X2) @ (F @ Y2)))))).
% 3.19/1.64 thf(fact_188_fun__upd__idem__iff, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y2:B]: ((((((((fun_upd @ A) @ B) @ F) @ X2) @ Y2) = F) = ((F @ X2) = Y2))))).
% 3.19/1.64 thf(fact_189_fun__upd__twist, axiom, (! [A:$tType,B:$tType,A3:A,C3:A,M2:(A > B),B3:B,D3:B]: (((A3 != C3) => ((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M2) @ A3) @ B3)) @ C3) @ D3) = (((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M2) @ C3) @ D3)) @ A3) @ B3)))))).
% 3.19/1.64 thf(fact_190_fun__upd__other, axiom, (! [B:$tType,A:$tType,Z2:A,X2:A,F:(A > B),Y2:B]: (((Z2 != X2) => (((((((fun_upd @ A) @ B) @ F) @ X2) @ Y2) @ Z2) = (F @ Z2)))))).
% 3.19/1.64 thf(fact_191_fun__upd__same, axiom, (! [B:$tType,A:$tType,F:(B > A),X2:B,Y2:A]: ((((((((fun_upd @ B) @ A) @ F) @ X2) @ Y2) @ X2) = Y2)))).
% 3.19/1.64 thf(fact_192_fun__upd__idem, axiom, (! [A:$tType,B:$tType,F:(B > A),X2:B,Y2:A]: ((((F @ X2) = Y2) => ((((((fun_upd @ B) @ A) @ F) @ X2) @ Y2) = F))))).
% 3.19/1.64 thf(fact_193_fun__upd__eqD, axiom, (! [A:$tType,B:$tType,F:(A > B),X2:A,Y2:B,G:(A > B),Z2:B]: ((((((((fun_upd @ A) @ B) @ F) @ X2) @ Y2) = (((((fun_upd @ A) @ B) @ G) @ X2) @ Z2)) => (Y2 = Z2))))).
% 3.19/1.64 thf(fact_194_fun__upd__def, axiom, (! [B:$tType,A:$tType]: ((((fun_upd @ A) @ B) = (^ [F2:(A > B),A5:A,B5:B,X4:A]: (((((if @ B) @ (X4 = A5)) @ B5) @ (F2 @ X4)))))))).
% 3.19/1.64 thf(fact_195_right__unique__def, axiom, (! [B:$tType,A:$tType]: ((((right_unique @ A) @ B) = (^ [R4:(A > (B > $o))]: ((! [X4:A,Y5:B,Z3:B]: ((((R4 @ X4) @ Y5) => (((R4 @ X4) @ Z3) => (Y5 = Z3))))))))))).
% 3.19/1.64 thf(fact_196_right__unique__eq, axiom, (! [A:$tType]: ((((right_unique @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_197_left__unique__def, axiom, (! [B:$tType,A:$tType]: ((((left_unique @ A) @ B) = (^ [R4:(A > (B > $o))]: ((! [X4:A,Y5:A,Z3:B]: ((((R4 @ X4) @ Z3) => (((R4 @ Y5) @ Z3) => (X4 = Y5))))))))))).
% 3.19/1.64 thf(fact_198_left__unique__eq, axiom, (! [A:$tType]: ((((left_unique @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_199_right__uniqueI, axiom, (! [B:$tType,A:$tType,A2:(A > (B > $o))]: (((! [X:A,Y:B,Z4:B]: ((((A2 @ X) @ Y) => (((A2 @ X) @ Z4) => (Y = Z4))))) => (((right_unique @ A) @ B) @ A2))))).
% 3.19/1.64 thf(fact_200_right__uniqueD, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o)),X2:A,Y2:B,Z2:B]: (((((right_unique @ A) @ B) @ A2) => (((A2 @ X2) @ Y2) => (((A2 @ X2) @ Z2) => (Y2 = Z2))))))).
% 3.19/1.64 thf(fact_201_left__uniqueI, axiom, (! [B:$tType,A:$tType,A2:(A > (B > $o))]: (((! [X:A,Y:A,Z4:B]: ((((A2 @ X) @ Z4) => (((A2 @ Y) @ Z4) => (X = Y))))) => (((left_unique @ A) @ B) @ A2))))).
% 3.19/1.64 thf(fact_202_left__uniqueD, axiom, (! [B:$tType,A:$tType,A2:(A > (B > $o)),X2:A,Z2:B,Y2:A]: (((((left_unique @ A) @ B) @ A2) => (((A2 @ X2) @ Z2) => (((A2 @ Y2) @ Z2) => (X2 = Y2))))))).
% 3.19/1.64 thf(fact_203_llist_Oright__unique__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((right_unique @ A) @ B) @ R) => (((right_unique @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_204_llist_Oleft__unique__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((left_unique @ A) @ B) @ R) => (((left_unique @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_205_swap__def, axiom, (! [B:$tType,A:$tType]: ((((swap @ A) @ B) = (^ [A5:A,B5:A,F2:(A > B)]: ((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ F2) @ A5) @ (F2 @ B5))) @ B5) @ (F2 @ A5)))))))).
% 3.19/1.64 thf(fact_206_right__unique__alt__def2, axiom, (! [B:$tType,A:$tType]: ((((right_unique @ A) @ B) = (^ [R4:(A > (B > $o))]: (((((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ R4) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ R4) @ (=>))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))))))))).
% 3.19/1.64 thf(fact_207_eq__imp__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((right_unique @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (=>))) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))))))).
% 3.19/1.64 thf(fact_208_left__unique__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((right_total @ A) @ B) @ A2) => ((((right_total @ C) @ D) @ B2) => ((((bi_unique @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (C > $o))) @ (B > (D > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (C > $o)) @ (D > $o)) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (=>)) @ ((left_unique @ A) @ C)) @ ((left_unique @ B) @ D)))))))).
% 3.19/1.64 thf(fact_209_right__unique__transfer, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((right_total @ A) @ B) @ A2) => ((((right_total @ C) @ D) @ B2) => ((((bi_unique @ C) @ D) @ B2) => ((((((((bNF_rel_fun @ (A > (C > $o))) @ (B > (D > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (C > $o)) @ (D > $o)) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (=>)) @ ((right_unique @ A) @ C)) @ ((right_unique @ B) @ D)))))))).
% 3.19/1.64 thf(fact_210_rtranclp__parametric, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((bi_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ (A > (A > $o))) @ (B > (B > $o))) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (transitive_rtranclp @ A)) @ (transitive_rtranclp @ B))))))).
% 3.19/1.64 thf(fact_211_right__total__fun, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((right_unique @ A) @ B) @ A2) => ((((right_total @ C) @ D) @ B2) => (((right_total @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_212_functional__converse__relation, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((left_unique @ A) @ B) @ R) => ((((right_total @ A) @ B) @ R) => (! [Y6:B]: ((? [X:A]: ((((R @ X) @ Y6) & (! [Ya3:A]: ((((R @ Ya3) @ Y6) => (Ya3 = X)))))))))))))).
% 3.19/1.64 thf(fact_213_right__totalE, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o)),Y2:B]: (((((right_total @ A) @ B) @ A2) => (~ ((! [X:A]: ((~ (((A2 @ X) @ Y2))))))))))).
% 3.19/1.64 thf(fact_214_right__totalI, axiom, (! [A:$tType,B:$tType,A2:(B > (A > $o))]: (((! [Y:A]: ((? [X7:B]: (((A2 @ X7) @ Y))))) => (((right_total @ B) @ A) @ A2))))).
% 3.19/1.64 thf(fact_215_right__total__eq, axiom, (! [A:$tType]: ((((right_total @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_216_right__total__def, axiom, (! [B:$tType,A:$tType]: ((((right_total @ A) @ B) = (^ [R4:(A > (B > $o))]: ((! [Y5:B]: ((? [X4:A]: (((R4 @ X4) @ Y5))))))))))).
% 3.19/1.64 thf(fact_217_llist_Oright__total__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((right_total @ A) @ B) @ R) => (((right_total @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_218_right__unique__fun, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((right_total @ A) @ B) @ A2) => ((((right_unique @ C) @ D) @ B2) => (((right_unique @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_219_transfer__forall__transfer_I3_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((right_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (=>))) @ (=>)) @ (transfer_forall @ A)) @ (transfer_forall @ B)))))).
% 3.19/1.64 thf(fact_220_transfer__forall__transfer_I2_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((right_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (=>)) @ (transfer_forall @ A)) @ (transfer_forall @ B)))))).
% 3.19/1.64 thf(fact_221_right__total__parametric, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((bi_total @ C) @ D) @ B2) => ((((((((bNF_rel_fun @ (A > (C > $o))) @ (B > (D > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (C > $o)) @ (D > $o)) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((right_total @ A) @ C)) @ ((right_total @ B) @ D))))))).
% 3.19/1.64 thf(fact_222_reflp__transfer_I2_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((right_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (=>)))) @ (=>)) @ (reflp @ A)) @ (reflp @ B)))))).
% 3.19/1.64 thf(fact_223_reflp__transfer_I3_J, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((right_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > (A > $o))) @ (B > (B > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (=>)) @ (reflp @ A)) @ (reflp @ B)))))).
% 3.19/1.64 thf(fact_224_Domainp__forall__transfer, axiom, (! [A:$tType,B:$tType,A2:(A > (B > $o))]: (((((right_total @ A) @ B) @ A2) => ((((((((bNF_rel_fun @ (A > $o)) @ (B > $o)) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((transfer_bforall @ A) @ (((domainp @ A) @ B) @ A2))) @ (transfer_forall @ B)))))).
% 3.19/1.64 thf(fact_225_left__total__parametric, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((bi_total @ C) @ D) @ B2) => ((((((((bNF_rel_fun @ (A > (C > $o))) @ (B > (D > $o))) @ $o) @ $o) @ ((((((bNF_rel_fun @ A) @ B) @ (C > $o)) @ (D > $o)) @ A2) @ ((((((bNF_rel_fun @ C) @ D) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ ((left_total @ A) @ C)) @ ((left_total @ B) @ D))))))).
% 3.19/1.64 thf(fact_226_left__total__fun, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((left_unique @ A) @ B) @ A2) => ((((left_total @ C) @ D) @ B2) => (((left_total @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_227_functional__relation, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((right_unique @ A) @ B) @ R) => ((((left_total @ A) @ B) @ R) => (! [X7:A]: ((? [Xa2:B]: ((((R @ X7) @ Xa2) & (! [Y6:B]: ((((R @ X7) @ Y6) => (Y6 = Xa2)))))))))))))).
% 3.19/1.64 thf(fact_228_left__unique__fun, axiom, (! [A:$tType,B:$tType,D:$tType,C:$tType,A2:(A > (B > $o)),B2:(C > (D > $o))]: (((((left_total @ A) @ B) @ A2) => ((((left_unique @ C) @ D) @ B2) => (((left_unique @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_229_left__total__def, axiom, (! [B:$tType,A:$tType]: ((((left_total @ A) @ B) = (^ [R4:(A > (B > $o))]: ((! [X4:A]: (((^ [P4:(B > $o)]: ((? [X6:B]: ((P4 @ X6))))) @ (R4 @ X4)))))))))).
% 3.19/1.64 thf(fact_230_left__total__eq, axiom, (! [A:$tType]: ((((left_total @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))))).
% 3.19/1.64 thf(fact_231_left__totalI, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((! [X:A]: ((? [X12:B]: (((R @ X) @ X12))))) => (((left_total @ A) @ B) @ R))))).
% 3.19/1.64 thf(fact_232_left__totalE, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: (((((left_total @ A) @ B) @ R) => (! [X7:A]: ((? [X13:B]: (((R @ X7) @ X13))))))))).
% 3.19/1.64 thf(fact_233_llist_Oleft__total__rel, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((left_total @ A) @ B) @ R) => (((left_total @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_234_bi__totalI, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o))]: (((((left_total @ A) @ B) @ R) => ((((right_total @ A) @ B) @ R) => (((bi_total @ A) @ B) @ R)))))).
% 3.19/1.64 thf(fact_235_bi__total__alt__def, axiom, (! [B:$tType,A:$tType]: ((((bi_total @ A) @ B) = (^ [A6:(A > (B > $o))]: (((((left_total @ A) @ B) @ A6) & (((right_total @ A) @ B) @ A6)))))))).
% 3.19/1.64 thf(fact_236_lhd__lfilter, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lhd @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = ((coinductive_lhd @ A) @ (((coindu218763757pWhile @ A) @ (((((comp @ $o) @ $o) @ A) @ (~)) @ P)) @ Xs)))))).
% 3.19/1.64 thf(fact_237_relcompp__transfer, axiom, (! [C:$tType,A:$tType,E:$tType,F3:$tType,B:$tType,D:$tType,B2:(A > (B > $o)),A2:(C > (D > $o)),C2:(E > (F3 > $o))]: (((((bi_total @ A) @ B) @ B2) => ((((((((bNF_rel_fun @ (C > (A > $o))) @ (D > (B > $o))) @ ((A > (E > $o)) > (C > (E > $o)))) @ ((B > (F3 > $o)) > (D > (F3 > $o)))) @ ((((((bNF_rel_fun @ C) @ D) @ (A > $o)) @ (B > $o)) @ A2) @ ((((((bNF_rel_fun @ A) @ B) @ $o) @ $o) @ B2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ (A > (E > $o))) @ (B > (F3 > $o))) @ (C > (E > $o))) @ (D > (F3 > $o))) @ ((((((bNF_rel_fun @ A) @ B) @ (E > $o)) @ (F3 > $o)) @ B2) @ ((((((bNF_rel_fun @ E) @ F3) @ $o) @ $o) @ C2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))))) @ ((((((bNF_rel_fun @ C) @ D) @ (E > $o)) @ (F3 > $o)) @ A2) @ ((((((bNF_rel_fun @ E) @ F3) @ $o) @ $o) @ C2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z))))))) @ (((relcompp @ C) @ A) @ E)) @ (((relcompp @ D) @ B) @ F3)))))).
% 3.19/1.64 thf(fact_238_pcr__Domainp__par__left__total, axiom, (! [A:$tType,B:$tType,C:$tType,B2:(A > (B > $o)),P:(A > $o),A2:(C > (A > $o)),P2:(C > $o)]: ((((((domainp @ A) @ B) @ B2) = P) => ((((left_total @ C) @ A) @ A2) => (((((((((bNF_rel_fun @ C) @ A) @ $o) @ $o) @ A2) @ (^ [Y3:$o,Z:$o]: ((Y3 = Z)))) @ P2) @ P) => ((((domainp @ C) @ B) @ (((((relcompp @ C) @ A) @ B) @ A2) @ B2)) = P2))))))).
% 3.19/1.64 thf(fact_239_right__unique__OO, axiom, (! [A:$tType,C:$tType,B:$tType,A2:(A > (B > $o)),B2:(B > (C > $o))]: (((((right_unique @ A) @ B) @ A2) => ((((right_unique @ B) @ C) @ B2) => (((right_unique @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_240_right__total__OO, axiom, (! [A:$tType,C:$tType,B:$tType,A2:(A > (B > $o)),B2:(B > (C > $o))]: (((((right_total @ A) @ B) @ A2) => ((((right_total @ B) @ C) @ B2) => (((right_total @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_241_pcr__Domainp__total, axiom, (! [A:$tType,B:$tType,C:$tType,B2:(A > (B > $o)),A2:(C > (A > $o)),P:(C > $o)]: (((((left_total @ A) @ B) @ B2) => (((((domainp @ C) @ A) @ A2) = P) => ((((domainp @ C) @ B) @ (((((relcompp @ C) @ A) @ B) @ A2) @ B2)) = P)))))).
% 3.19/1.64 thf(fact_242_left__total__OO, axiom, (! [A:$tType,C:$tType,B:$tType,R:(A > (B > $o)),S:(B > (C > $o))]: (((((left_total @ A) @ B) @ R) => ((((left_total @ B) @ C) @ S) => (((left_total @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ R) @ S))))))).
% 3.19/1.64 thf(fact_243_bi__unique__OO, axiom, (! [A:$tType,C:$tType,B:$tType,A2:(A > (B > $o)),B2:(B > (C > $o))]: (((((bi_unique @ A) @ B) @ A2) => ((((bi_unique @ B) @ C) @ B2) => (((bi_unique @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_244_bi__total__OO, axiom, (! [A:$tType,C:$tType,B:$tType,A2:(A > (B > $o)),B2:(B > (C > $o))]: (((((bi_total @ A) @ B) @ A2) => ((((bi_total @ B) @ C) @ B2) => (((bi_total @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ A2) @ B2))))))).
% 3.19/1.64 thf(fact_245_lhd__LCons, axiom, (! [A:$tType,X21:A,X222:(coinductive_llist @ A)]: ((((coinductive_lhd @ A) @ (((coinductive_LCons @ A) @ X21) @ X222)) = X21)))).
% 3.19/1.64 thf(fact_246_lhd__iterates, axiom, (! [A:$tType,F:(A > A),X2:A]: ((((coinductive_lhd @ A) @ (((coinductive_iterates @ A) @ F) @ X2)) = X2)))).
% 3.19/1.64 thf(fact_247_unfold__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A3:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A3))) => (((coinductive_lhd @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A3)) = (G21 @ A3)))))).
% 3.19/1.64 thf(fact_248_llist_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,P3:(C > $o),A3:C,G21:(C > A),Q22:(C > $o),G221:(C > (coinductive_llist @ A)),G222:(C > C)]: (((~ ((P3 @ A3))) => (((coinductive_lhd @ A) @ ((((((((coindu1259883913_llist @ C) @ A) @ P3) @ G21) @ Q22) @ G221) @ G222) @ A3)) = (G21 @ A3)))))).
% 3.19/1.64 thf(fact_249_eq__comp__r, axiom, (! [A:$tType,R:(A > (A > $o))]: (((((((relcompp @ A) @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ (((((relcompp @ A) @ A) @ A) @ R) @ (^ [Y3:A,Z:A]: ((Y3 = Z))))) = R)))).
% 3.19/1.64 thf(fact_250_llist_Orel__compp, axiom, (! [A:$tType,C:$tType,B:$tType,R:(A > (B > $o)),S:(B > (C > $o))]: (((((coindu1486289336t_all2 @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ R) @ S)) = (((((relcompp @ (coinductive_llist @ A)) @ (coinductive_llist @ B)) @ (coinductive_llist @ C)) @ (((coindu1486289336t_all2 @ A) @ B) @ R)) @ (((coindu1486289336t_all2 @ B) @ C) @ S)))))).
% 3.19/1.64 thf(fact_251_OOO__eq__quotient3, axiom, (! [A:$tType,B:$tType,C:$tType,R1:(A > (A > $o)),Abs12:(A > B),Rep12:(B > A),Abs22:(B > C),Rep22:(C > B)]: (((((((quotient3 @ A) @ B) @ R1) @ Abs12) @ Rep12) => ((((((quotient3 @ B) @ C) @ (^ [Y3:B,Z:B]: ((Y3 = Z)))) @ Abs22) @ Rep22) => (((((quotient3 @ A) @ C) @ (((((relcompp @ A) @ A) @ A) @ R1) @ (((((relcompp @ A) @ A) @ A) @ (^ [Y3:A,Z:A]: ((Y3 = Z)))) @ R1))) @ (((((comp @ B) @ C) @ A) @ Abs22) @ Abs12)) @ (((((comp @ B) @ A) @ C) @ Rep12) @ Rep22))))))).
% 3.19/1.64 thf(fact_252_OOO__quotient3, axiom, (! [A:$tType,B:$tType,C:$tType,R1:(A > (A > $o)),Abs12:(A > B),Rep12:(B > A),R2:(B > (B > $o)),Abs22:(B > C),Rep22:(C > B),R23:(A > (A > $o))]: (((((((quotient3 @ A) @ B) @ R1) @ Abs12) @ Rep12) => ((((((quotient3 @ B) @ C) @ R2) @ Abs22) @ Rep22) => ((! [X:A,Y:A]: ((((R23 @ X) @ Y) => (((R1 @ X) @ X) => (((R1 @ Y) @ Y) => ((R2 @ (Abs12 @ X)) @ (Abs12 @ Y))))))) => ((! [X:B,Y:B]: ((((R2 @ X) @ Y) => ((R23 @ (Rep12 @ X)) @ (Rep12 @ Y))))) => (((((quotient3 @ A) @ C) @ (((((relcompp @ A) @ A) @ A) @ R1) @ (((((relcompp @ A) @ A) @ A) @ R23) @ R1))) @ (((((comp @ B) @ C) @ A) @ Abs22) @ Abs12)) @ (((((comp @ B) @ A) @ C) @ Rep12) @ Rep22))))))))).
% 3.19/1.64 thf(fact_253_left__unique__OO, axiom, (! [A:$tType,C:$tType,B:$tType,R:(A > (B > $o)),S:(B > (C > $o))]: (((((left_unique @ A) @ B) @ R) => ((((left_unique @ B) @ C) @ S) => (((left_unique @ A) @ C) @ (((((relcompp @ A) @ B) @ C) @ R) @ S))))))).
% 3.19/1.64 thf(fact_254_fun_Orel__compp, axiom, (! [A:$tType,D:$tType,C:$tType,B:$tType,R:(A > (B > $o)),S:(B > (C > $o))]: ((((((((bNF_rel_fun @ D) @ D) @ A) @ C) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ (((((relcompp @ A) @ B) @ C) @ R) @ S)) = (((((relcompp @ (D > A)) @ (D > B)) @ (D > C)) @ ((((((bNF_rel_fun @ D) @ D) @ A) @ B) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ R)) @ ((((((bNF_rel_fun @ D) @ D) @ B) @ C) @ (^ [Y3:D,Z:D]: ((Y3 = Z)))) @ S)))))).
% 3.19/1.64 thf(fact_255_neg__fun__distr2, axiom, (! [F3:$tType,E:$tType,A:$tType,B:$tType,D:$tType,C:$tType,R7:(A > (B > $o)),S5:(C > (D > $o)),R:(E > (A > $o)),S:(F3 > (C > $o))]: (((((right_unique @ A) @ B) @ R7) => ((((left_total @ A) @ B) @ R7) => ((((left_unique @ C) @ D) @ S5) => ((((right_total @ C) @ D) @ S5) => (((ord_less_eq @ ((E > F3) > ((B > D) > $o))) @ ((((((bNF_rel_fun @ E) @ B) @ F3) @ D) @ (((((relcompp @ E) @ A) @ B) @ R) @ R7)) @ (((((relcompp @ F3) @ C) @ D) @ S) @ S5))) @ (((((relcompp @ (E > F3)) @ (A > C)) @ (B > D)) @ ((((((bNF_rel_fun @ E) @ A) @ F3) @ C) @ R) @ S)) @ ((((((bNF_rel_fun @ A) @ B) @ C) @ D) @ R7) @ S5)))))))))).
% 3.19/1.64 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.19/1.64 thf(help_If_2_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $false) @ X2) @ Y2) = Y2)))).
% 3.19/1.64 thf(help_If_1_1_T, axiom, (! [A:$tType,X2:A,Y2:A]: ((((((if @ A) @ $true) @ X2) @ Y2) = X2)))).
% 3.19/1.64 thf(conj_0, conjecture, ((((((((bNF_rel_fun @ (coinductive_llist @ a)) @ (coinductive_llist @ b)) @ (coinductive_llist @ a)) @ (coinductive_llist @ b)) @ (((coindu1486289336t_all2 @ a) @ b) @ a2)) @ (((coindu1486289336t_all2 @ a) @ b) @ a2)) @ (lMirro427583474mirror @ a)) @ (lMirro427583474mirror @ b))).
% 3.19/1.64 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7OvFDdixfL/DTF2DTF25247.p
% 3.19/1.64 ------------------------
% 3.30/1.70 ---- Cleaned THF ---
% 3.30/1.70 thf(ty_t_Coinductive__List_Ollist,type,
% 3.30/1.70 coinductive_llist: $tType > $tType ).
% 3.30/1.70
% 3.30/1.70 thf(ty_t_itself,type,
% 3.30/1.70 itself: $tType > $tType ).
% 3.30/1.70
% 3.30/1.70 thf(ty_tf_b,type,
% 3.30/1.70 b: $tType ).
% 3.30/1.70
% 3.30/1.70 thf(ty_tf_a,type,
% 3.30/1.70 a: $tType ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_BNF__Def_Orel__fun,type,
% 3.30/1.70 bNF_rel_fun:
% 3.30/1.70 !>[A: $tType,C: $tType,B: $tType,D: $tType] : ( ( A > C > $o ) > ( B > D > $o ) > ( A > B ) > ( C > D ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Oiterates,type,
% 3.30/1.70 coinductive_iterates:
% 3.30/1.70 !>[A: $tType] : ( ( A > A ) > A > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_OldropWhile,type,
% 3.30/1.70 coindu218763757pWhile:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Olfilter,type,
% 3.30/1.70 coinductive_lfilter:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 3.30/1.70 coinductive_LCons:
% 3.30/1.70 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_Ocase__llist,type,
% 3.30/1.70 coindu1381640503_llist:
% 3.30/1.70 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B ) > ( coinductive_llist @ A ) > B ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_Ocorec__llist,type,
% 3.30/1.70 coindu1259883913_llist:
% 3.30/1.70 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 3.30/1.70 coinductive_lhd:
% 3.30/1.70 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_Ollist__all2,type,
% 3.30/1.70 coindu1486289336t_all2:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_Olmap,type,
% 3.30/1.70 coinductive_lmap:
% 3.30/1.70 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coinductive_llist @ A ) > ( coinductive_llist @ Aa ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ollist_Opred__llist,type,
% 3.30/1.70 coindu543516966_llist:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Olmember,type,
% 3.30/1.70 coinductive_lmember:
% 3.30/1.70 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_OltakeWhile,type,
% 3.30/1.70 coindu501562517eWhile:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Coinductive__List_Ounfold__llist,type,
% 3.30/1.70 coindu1441602521_llist:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coinductive_llist @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Complete__Partial__Order_Omonotone,type,
% 3.30/1.70 comple1396247847notone:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( B > B > $o ) > ( A > B ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Fun_Ocomp,type,
% 3.30/1.70 comp:
% 3.30/1.70 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Fun_Ofun__upd,type,
% 3.30/1.70 fun_upd:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Fun_Oid,type,
% 3.30/1.70 id:
% 3.30/1.70 !>[A: $tType] : ( A > A ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Fun_Omap__fun,type,
% 3.30/1.70 map_fun:
% 3.30/1.70 !>[C: $tType,A: $tType,B: $tType,D: $tType] : ( ( C > A ) > ( B > D ) > ( A > B ) > C > D ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Fun_Oswap,type,
% 3.30/1.70 swap:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( A > A > ( A > B ) > A > B ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_HOL_OEx1,type,
% 3.30/1.70 ex1:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_If,type,
% 3.30/1.70 if:
% 3.30/1.70 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror,type,
% 3.30/1.70 lMirro427583474mirror:
% 3.30/1.70 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.30/1.70 ord_less_eq:
% 3.30/1.70 !>[A: $tType] : ( A > A > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Partial__Function_Ofun__ord,type,
% 3.30/1.70 partial_fun_ord:
% 3.30/1.70 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( C > A ) > ( C > B ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Pure_Otype,type,
% 3.30/1.70 type:
% 3.30/1.70 !>[A: $tType] : ( itself @ A ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Quotient_OBex1__rel,type,
% 3.30/1.70 bex1_rel:
% 3.30/1.70 !>[A: $tType] : ( ( A > A > $o ) > ( A > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Quotient_OQuotient3,type,
% 3.30/1.70 quotient3:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > A > $o ) > ( A > B ) > ( B > A ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Relation_ODomainp,type,
% 3.30/1.70 domainp:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > A > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Relation_Oreflp,type,
% 3.30/1.70 reflp:
% 3.30/1.70 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Relation_Orelcompp,type,
% 3.30/1.70 relcompp:
% 3.30/1.70 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > $o ) > ( B > C > $o ) > A > C > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Obi__total,type,
% 3.30/1.70 bi_total:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Obi__unique,type,
% 3.30/1.70 bi_unique:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Oleft__total,type,
% 3.30/1.70 left_total:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Oleft__unique,type,
% 3.30/1.70 left_unique:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Orev__implies,type,
% 3.30/1.70 rev_implies: $o > $o > $o ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Oright__total,type,
% 3.30/1.70 right_total:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Oright__unique,type,
% 3.30/1.70 right_unique:
% 3.30/1.70 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Otransfer__bforall,type,
% 3.30/1.70 transfer_bforall:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transfer_Otransfer__forall,type,
% 3.30/1.70 transfer_forall:
% 3.30/1.70 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_c_Transitive__Closure_Ortranclp,type,
% 3.30/1.70 transitive_rtranclp:
% 3.30/1.70 !>[A: $tType] : ( ( A > A > $o ) > A > A > $o ) ).
% 3.30/1.70
% 3.30/1.70 thf(sy_v_A,type,
% 3.30/1.70 a2: a > b > $o ).
% 3.30/1.70
% 3.30/1.70 thf(fact_0_llist__all2__lmirror,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( lMirro427583474mirror @ A @ Xs ) @ ( lMirro427583474mirror @ B @ Ys ) )
% 3.30/1.70 = ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_1_llist__all2__lmirrorD,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( lMirro427583474mirror @ A @ Xs ) @ ( lMirro427583474mirror @ B @ Ys ) )
% 3.30/1.70 => ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_2_llist__all2__lmirrorI,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 3.30/1.70 => ( coindu1486289336t_all2 @ A @ B @ P @ ( lMirro427583474mirror @ A @ Xs ) @ ( lMirro427583474mirror @ B @ Ys ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_3_rel__funI,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 3.30/1.70 ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( A2 @ X @ Y )
% 3.30/1.70 => ( B2 @ ( F @ X ) @ ( G @ Y ) ) )
% 3.30/1.70 => ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 @ F @ G ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_4_llist__all2__rsp,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > B > $o,S: A > A > $o,T: B > B > $o,X2: coinductive_llist @ A,Y2: coinductive_llist @ B,A3: coinductive_llist @ A,B3: coinductive_llist @ B] :
% 3.30/1.70 ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( R @ X @ Y )
% 3.30/1.70 => ! [A4: A,B4: B] :
% 3.30/1.70 ( ( R @ A4 @ B4 )
% 3.30/1.70 => ( ( S @ X @ A4 )
% 3.30/1.70 = ( T @ Y @ B4 ) ) ) )
% 3.30/1.70 => ( ( coindu1486289336t_all2 @ A @ B @ R @ X2 @ Y2 )
% 3.30/1.70 => ( ( coindu1486289336t_all2 @ A @ B @ R @ A3 @ B3 )
% 3.30/1.70 => ( ( coindu1486289336t_all2 @ A @ A @ S @ X2 @ A3 )
% 3.30/1.70 = ( coindu1486289336t_all2 @ B @ B @ T @ Y2 @ B3 ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_5_llist__all2__mono,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,P2: A > B > $o] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 3.30/1.70 => ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( P @ X @ Y )
% 3.30/1.70 => ( P2 @ X @ Y ) )
% 3.30/1.70 => ( coindu1486289336t_all2 @ A @ B @ P2 @ Xs @ Ys ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_6_llist_Orel__eq,axiom,
% 3.30/1.70 ! [A: $tType] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ A
% 3.30/1.70 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.30/1.70 = ( ^ [Y3: coinductive_llist @ A,Z: coinductive_llist @ A] : ( Y3 = Z ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_7_llist_Orel__refl,axiom,
% 3.30/1.70 ! [B: $tType,Ra: B > B > $o,X2: coinductive_llist @ B] :
% 3.30/1.70 ( ! [X: B] : ( Ra @ X @ X )
% 3.30/1.70 => ( coindu1486289336t_all2 @ B @ B @ Ra @ X2 @ X2 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_8_rel__funD,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y2: B] :
% 3.30/1.70 ( ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 @ F @ G )
% 3.30/1.70 => ( ( A2 @ X2 @ Y2 )
% 3.30/1.70 => ( B2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_9_let__rsp,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o] :
% 3.30/1.70 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ R1 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 ) @ R2 )
% 3.30/1.70 @ ^ [S2: A,F2: A > C] : ( F2 @ S2 )
% 3.30/1.70 @ ^ [S2: B,F2: B > D] : ( F2 @ S2 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_10_rel__funE,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o,F: A > C,G: B > D,X2: A,Y2: B] :
% 3.30/1.70 ( ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 @ F @ G )
% 3.30/1.70 => ( ( A2 @ X2 @ Y2 )
% 3.30/1.70 => ( B2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_11_apply__rsp_H,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,R1: A > B > $o,R2: C > D > $o,F: A > C,G: B > D,X2: A,Y2: B] :
% 3.30/1.70 ( ( bNF_rel_fun @ A @ B @ C @ D @ R1 @ R2 @ F @ G )
% 3.30/1.70 => ( ( R1 @ X2 @ Y2 )
% 3.30/1.70 => ( R2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_12_rel__funD2,axiom,
% 3.30/1.70 ! [B: $tType,C: $tType,A: $tType,A2: A > A > $o,B2: B > C > $o,F: A > B,G: A > C,X2: A] :
% 3.30/1.70 ( ( bNF_rel_fun @ A @ A @ B @ C @ A2 @ B2 @ F @ G )
% 3.30/1.70 => ( ( A2 @ X2 @ X2 )
% 3.30/1.70 => ( B2 @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_13_rel__fun__mono,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,X3: A > B > $o,A2: C > D > $o,F: A > C,G: B > D,Y4: A > B > $o,B2: C > D > $o] :
% 3.30/1.70 ( ( bNF_rel_fun @ A @ B @ C @ D @ X3 @ A2 @ F @ G )
% 3.30/1.70 => ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( Y4 @ X @ Y )
% 3.30/1.70 => ( X3 @ X @ Y ) )
% 3.30/1.70 => ( ! [X: C,Y: D] :
% 3.30/1.70 ( ( A2 @ X @ Y )
% 3.30/1.70 => ( B2 @ X @ Y ) )
% 3.30/1.70 => ( bNF_rel_fun @ A @ B @ C @ D @ Y4 @ B2 @ F @ G ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_14_rel__fun__mono_H,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,Y4: A > B > $o,X3: A > B > $o,A2: C > D > $o,B2: C > D > $o,F: A > C,G: B > D] :
% 3.30/1.70 ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( Y4 @ X @ Y )
% 3.30/1.70 => ( X3 @ X @ Y ) )
% 3.30/1.70 => ( ! [X: C,Y: D] :
% 3.30/1.70 ( ( A2 @ X @ Y )
% 3.30/1.70 => ( B2 @ X @ Y ) )
% 3.30/1.70 => ( ( bNF_rel_fun @ A @ B @ C @ D @ X3 @ A2 @ F @ G )
% 3.30/1.70 => ( bNF_rel_fun @ A @ B @ C @ D @ Y4 @ B2 @ F @ G ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_15_llist__all2__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) > $o )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ R
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > $o ) @ ( coindu1486289336t_all2 @ A @ B @ R )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ $o @ $o @ ( coindu1486289336t_all2 @ A @ B @ R )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.70 @ ( coindu1486289336t_all2 @ A @ A )
% 3.30/1.70 @ ( coindu1486289336t_all2 @ B @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_16_llist_Orel__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,D: $tType,C: $tType,Sa: A > C > $o,Sc: B > D > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > D > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > $o ) @ ( ( coinductive_llist @ C ) > ( coinductive_llist @ D ) > $o )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( D > $o ) @ Sa
% 3.30/1.70 @ ( bNF_rel_fun @ B @ D @ $o @ $o @ Sc
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ C ) @ ( ( coinductive_llist @ B ) > $o ) @ ( ( coinductive_llist @ D ) > $o ) @ ( coindu1486289336t_all2 @ A @ C @ Sa )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ B ) @ ( coinductive_llist @ D ) @ $o @ $o @ ( coindu1486289336t_all2 @ B @ D @ Sc )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.70 @ ( coindu1486289336t_all2 @ A @ B )
% 3.30/1.70 @ ( coindu1486289336t_all2 @ C @ D ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_17_Let__transfer,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.70 ( bNF_rel_fun @ A @ B @ ( ( A > C ) > C ) @ ( ( B > D ) > D ) @ A2 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ C @ D @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) @ B2 )
% 3.30/1.70 @ ^ [S2: A,F2: A > C] : ( F2 @ S2 )
% 3.30/1.70 @ ^ [S2: B,F2: B > D] : ( F2 @ S2 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_18_rel__fun__def__butlast,axiom,
% 3.30/1.70 ! [B: $tType,D: $tType,C: $tType,E: $tType,F3: $tType,A: $tType,R: A > B > $o,S: C > E > $o,T: D > F3 > $o,F: A > C > D,G: B > E > F3] :
% 3.30/1.70 ( ( bNF_rel_fun @ A @ B @ ( C > D ) @ ( E > F3 ) @ R @ ( bNF_rel_fun @ C @ E @ D @ F3 @ S @ T ) @ F @ G )
% 3.30/1.70 = ( ! [X4: A,Y5: B] :
% 3.30/1.70 ( ( R @ X4 @ Y5 )
% 3.30/1.70 => ( bNF_rel_fun @ C @ E @ D @ F3 @ S @ T @ ( F @ X4 ) @ ( G @ Y5 ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_19_If__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ $o @ $o @ ( A > A > A ) @ ( B > B > B )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ ( A > A ) @ ( B > B ) @ A2 @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) )
% 3.30/1.70 @ ( if @ A )
% 3.30/1.70 @ ( if @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_20_llist__corec__transfer,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( A > C ) > ( A > $o ) > ( A > ( coinductive_llist @ C ) ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > D ) > ( B > $o ) > ( B > ( coinductive_llist @ D ) ) > ( B > B ) > B > ( coinductive_llist @ D ) )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ ( ( A > $o ) > ( A > ( coinductive_llist @ C ) ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > $o ) > ( B > ( coinductive_llist @ D ) ) > ( B > B ) > B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 )
% 3.30/1.70 @ ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( A > ( coinductive_llist @ C ) ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > ( coinductive_llist @ D ) ) > ( B > B ) > B > ( coinductive_llist @ D ) )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( A > ( coinductive_llist @ C ) ) @ ( B > ( coinductive_llist @ D ) ) @ ( ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > B ) > B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A2 @ ( coindu1486289336t_all2 @ C @ D @ B2 ) ) @ ( bNF_rel_fun @ ( A > A ) @ ( B > B ) @ ( A > ( coinductive_llist @ C ) ) @ ( B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A2 @ ( coindu1486289336t_all2 @ C @ D @ B2 ) ) ) ) ) )
% 3.30/1.70 @ ( coindu1259883913_llist @ A @ C )
% 3.30/1.70 @ ( coindu1259883913_llist @ B @ D ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_21_llist_Ocorec__transfer,axiom,
% 3.30/1.70 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > A ) > ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > B ) > ( D > $o ) > ( D > ( coinductive_llist @ B ) ) > ( D > D ) > D > ( coinductive_llist @ B ) )
% 3.30/1.70 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( C > A ) @ ( D > B ) @ ( ( C > $o ) > ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > $o ) > ( D > ( coinductive_llist @ B ) ) > ( D > D ) > D > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ C @ D @ A @ B @ S @ R )
% 3.30/1.70 @ ( bNF_rel_fun @ ( C > $o ) @ ( D > $o ) @ ( ( C > ( coinductive_llist @ A ) ) > ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > ( coinductive_llist @ B ) ) > ( D > D ) > D > ( coinductive_llist @ B ) )
% 3.30/1.70 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ S
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( C > ( coinductive_llist @ A ) ) @ ( D > ( coinductive_llist @ B ) ) @ ( ( C > C ) > C > ( coinductive_llist @ A ) ) @ ( ( D > D ) > D > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ C @ D @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ S @ ( coindu1486289336t_all2 @ A @ B @ R ) ) @ ( bNF_rel_fun @ ( C > C ) @ ( D > D ) @ ( C > ( coinductive_llist @ A ) ) @ ( D > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ C @ D @ C @ D @ S @ S ) @ ( bNF_rel_fun @ C @ D @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ S @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ) ) )
% 3.30/1.70 @ ( coindu1259883913_llist @ C @ A )
% 3.30/1.70 @ ( coindu1259883913_llist @ D @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_22_unfold__llist__transfer,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( A > C ) > ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > D ) > ( B > B ) > B > ( coinductive_llist @ D ) )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ ( ( A > A ) > A > ( coinductive_llist @ C ) ) @ ( ( B > B ) > B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ ( A > A ) @ ( B > B ) @ ( A > ( coinductive_llist @ C ) ) @ ( B > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A2 @ ( coindu1486289336t_all2 @ C @ D @ B2 ) ) ) )
% 3.30/1.70 @ ( coindu1441602521_llist @ A @ C )
% 3.30/1.70 @ ( coindu1441602521_llist @ B @ D ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_23_iterates__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,A2: A > B > $o] : ( bNF_rel_fun @ ( A > A ) @ ( B > B ) @ ( A > ( coinductive_llist @ A ) ) @ ( B > ( coinductive_llist @ B ) ) @ ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 ) @ ( bNF_rel_fun @ A @ B @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ A2 @ ( coindu1486289336t_all2 @ A @ B @ A2 ) ) @ ( coinductive_iterates @ A ) @ ( coinductive_iterates @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_24_fun_Orel__transfer,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,C: $tType,E: $tType,D: $tType,Sa: A > C > $o,Sc: B > E > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > B > $o ) @ ( C > E > $o ) @ ( ( D > A ) > ( D > B ) > $o ) @ ( ( D > C ) > ( D > E ) > $o )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ C @ ( B > $o ) @ ( E > $o ) @ Sa
% 3.30/1.70 @ ( bNF_rel_fun @ B @ E @ $o @ $o @ Sc
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( D > A ) @ ( D > C ) @ ( ( D > B ) > $o ) @ ( ( D > E ) > $o )
% 3.30/1.70 @ ( bNF_rel_fun @ D @ D @ A @ C
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.70 @ Sa )
% 3.30/1.70 @ ( bNF_rel_fun @ ( D > B ) @ ( D > E ) @ $o @ $o
% 3.30/1.70 @ ( bNF_rel_fun @ D @ D @ B @ E
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.70 @ Sc )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.70 @ ( bNF_rel_fun @ D @ D @ A @ B
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ D @ D @ C @ E
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_25_fun_Orel__refl,axiom,
% 3.30/1.70 ! [B: $tType,D: $tType,Ra: B > B > $o,X2: D > B] :
% 3.30/1.70 ( ! [X: B] : ( Ra @ X @ X )
% 3.30/1.70 => ( bNF_rel_fun @ D @ D @ B @ B
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.70 @ Ra
% 3.30/1.70 @ X2
% 3.30/1.70 @ X2 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_26_fun_Orel__eq,axiom,
% 3.30/1.70 ! [A: $tType,D: $tType] :
% 3.30/1.70 ( ( bNF_rel_fun @ D @ D @ A @ A
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.70 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.30/1.70 = ( ^ [Y3: D > A,Z: D > A] : ( Y3 = Z ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_27_case__llist__transfer,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,D: $tType,B: $tType,B2: A > B > $o,A2: C > D > $o] : ( bNF_rel_fun @ A @ B @ ( ( C > ( coinductive_llist @ C ) > A ) > ( coinductive_llist @ C ) > A ) @ ( ( D > ( coinductive_llist @ D ) > B ) > ( coinductive_llist @ D ) > B ) @ B2 @ ( bNF_rel_fun @ ( C > ( coinductive_llist @ C ) > A ) @ ( D > ( coinductive_llist @ D ) > B ) @ ( ( coinductive_llist @ C ) > A ) @ ( ( coinductive_llist @ D ) > B ) @ ( bNF_rel_fun @ C @ D @ ( ( coinductive_llist @ C ) > A ) @ ( ( coinductive_llist @ D ) > B ) @ A2 @ ( bNF_rel_fun @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A @ B @ ( coindu1486289336t_all2 @ C @ D @ A2 ) @ B2 ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ C ) @ ( coinductive_llist @ D ) @ A @ B @ ( coindu1486289336t_all2 @ C @ D @ A2 ) @ B2 ) ) @ ( coindu1381640503_llist @ A @ C ) @ ( coindu1381640503_llist @ B @ D ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_28_llist_Ocase__transfer,axiom,
% 3.30/1.70 ! [C: $tType,A: $tType,B: $tType,D: $tType,S: C > D > $o,R: A > B > $o] : ( bNF_rel_fun @ C @ D @ ( ( A > ( coinductive_llist @ A ) > C ) > ( coinductive_llist @ A ) > C ) @ ( ( B > ( coinductive_llist @ B ) > D ) > ( coinductive_llist @ B ) > D ) @ S @ ( bNF_rel_fun @ ( A > ( coinductive_llist @ A ) > C ) @ ( B > ( coinductive_llist @ B ) > D ) @ ( ( coinductive_llist @ A ) > C ) @ ( ( coinductive_llist @ B ) > D ) @ ( bNF_rel_fun @ A @ B @ ( ( coinductive_llist @ A ) > C ) @ ( ( coinductive_llist @ B ) > D ) @ R @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ D @ ( coindu1486289336t_all2 @ A @ B @ R ) @ S ) ) @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ D @ ( coindu1486289336t_all2 @ A @ B @ R ) @ S ) ) @ ( coindu1381640503_llist @ C @ A ) @ ( coindu1381640503_llist @ D @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_29_map__fun__parametric,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,E: $tType,F3: $tType,H: $tType,G2: $tType,D: $tType,C: $tType,A2: A > C > $o,B2: B > D > $o,C2: E > G2 > $o,D2: F3 > H > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > F3 ) > ( B > E ) > A > F3 ) @ ( ( G2 > H ) > ( D > G2 ) > C > H ) @ ( bNF_rel_fun @ A @ C @ B @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ ( E > F3 ) @ ( G2 > H ) @ ( ( B > E ) > A > F3 ) @ ( ( D > G2 ) > C > H ) @ ( bNF_rel_fun @ E @ G2 @ F3 @ H @ C2 @ D2 ) @ ( bNF_rel_fun @ ( B > E ) @ ( D > G2 ) @ ( A > F3 ) @ ( C > H ) @ ( bNF_rel_fun @ B @ D @ E @ G2 @ B2 @ C2 ) @ ( bNF_rel_fun @ A @ C @ F3 @ H @ A2 @ D2 ) ) ) @ ( map_fun @ A @ B @ E @ F3 ) @ ( map_fun @ C @ D @ G2 @ H ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_30_llist_Opred__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > $o )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ $o @ $o @ ( coindu1486289336t_all2 @ A @ B @ R )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( coindu543516966_llist @ A )
% 3.30/1.70 @ ( coindu543516966_llist @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_31_llist__all__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > $o ) @ ( ( coinductive_llist @ B ) > $o )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ $o @ $o @ ( coindu1486289336t_all2 @ A @ B @ A2 )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( coindu543516966_llist @ A )
% 3.30/1.70 @ ( coindu543516966_llist @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_32_if__rsp,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( bNF_rel_fun @ $o @ $o @ ( A > A > A ) @ ( A > A > A )
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ A @ ( A > A ) @ ( A > A ) @ R @ ( bNF_rel_fun @ A @ A @ A @ A @ R @ R ) )
% 3.30/1.70 @ ( if @ A )
% 3.30/1.70 @ ( if @ A ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_33_ldropWhile__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) )
% 3.30/1.70 @ ( coindu218763757pWhile @ A )
% 3.30/1.70 @ ( coindu218763757pWhile @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_34_ltakeWhile__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) )
% 3.30/1.70 @ ( coindu501562517eWhile @ A )
% 3.30/1.70 @ ( coindu501562517eWhile @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_35_lfilter__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) )
% 3.30/1.70 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) )
% 3.30/1.70 @ ( coinductive_lfilter @ A )
% 3.30/1.70 @ ( coinductive_lfilter @ B ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_36_fun_Omap__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,D: $tType,G2: $tType,F3: $tType,Rb: A > F3 > $o,Sd: B > G2 > $o] :
% 3.30/1.70 ( bNF_rel_fun @ ( A > B ) @ ( F3 > G2 ) @ ( ( D > A ) > D > B ) @ ( ( D > F3 ) > D > G2 ) @ ( bNF_rel_fun @ A @ F3 @ B @ G2 @ Rb @ Sd )
% 3.30/1.70 @ ( bNF_rel_fun @ ( D > A ) @ ( D > F3 ) @ ( D > B ) @ ( D > G2 )
% 3.30/1.70 @ ( bNF_rel_fun @ D @ D @ A @ F3
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.70 @ Rb )
% 3.30/1.70 @ ( bNF_rel_fun @ D @ D @ B @ G2
% 3.30/1.70 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.70 @ Sd ) )
% 3.30/1.70 @ ( comp @ A @ B @ D )
% 3.30/1.70 @ ( comp @ F3 @ G2 @ D ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_37_comp__transfer,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,E: $tType,F3: $tType,D: $tType,C: $tType,B2: A > C > $o,C2: B > D > $o,A2: E > F3 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > A ) > E > B ) @ ( ( F3 > C ) > F3 > D ) @ ( bNF_rel_fun @ A @ C @ B @ D @ B2 @ C2 ) @ ( bNF_rel_fun @ ( E > A ) @ ( F3 > C ) @ ( E > B ) @ ( F3 > D ) @ ( bNF_rel_fun @ E @ F3 @ A @ C @ A2 @ B2 ) @ ( bNF_rel_fun @ E @ F3 @ B @ D @ A2 @ C2 ) ) @ ( comp @ A @ B @ E ) @ ( comp @ C @ D @ F3 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_38_lfilter__idem,axiom,
% 3.30/1.70 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 3.30/1.70 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 3.30/1.70 = ( coinductive_lfilter @ A @ P @ Xs ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_39_fun__quotient3,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,C: $tType,D: $tType,R1: A > A > $o,Abs1: A > B,Rep1: B > A,R2: C > C > $o,Abs2: C > D,Rep2: D > C] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R1 @ Abs1 @ Rep1 )
% 3.30/1.70 => ( ( quotient3 @ C @ D @ R2 @ Abs2 @ Rep2 )
% 3.30/1.70 => ( quotient3 @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ A @ C @ C @ R1 @ R2 ) @ ( map_fun @ B @ A @ C @ D @ Rep1 @ Abs2 ) @ ( map_fun @ A @ B @ D @ C @ Abs1 @ Rep2 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_40_unfold__llist__ltl__unroll,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B] :
% 3.30/1.70 ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) )
% 3.30/1.70 = ( coindu1441602521_llist @ B @ A @ ( comp @ B @ $o @ B @ IS_LNIL @ LTL ) @ ( comp @ B @ A @ B @ LHD @ LTL ) @ LTL @ B3 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_41_rewriteR__comp__comp2,axiom,
% 3.30/1.70 ! [C: $tType,B: $tType,E: $tType,D: $tType,A: $tType,G: C > B,H2: A > C,R12: D > B,R22: A > D,F: B > E,L: D > E] :
% 3.30/1.70 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 3.30/1.70 = ( comp @ D @ B @ A @ R12 @ R22 ) )
% 3.30/1.70 => ( ( ( comp @ B @ E @ D @ F @ R12 )
% 3.30/1.70 = L )
% 3.30/1.70 => ( ( comp @ C @ E @ A @ ( comp @ B @ E @ C @ F @ G ) @ H2 )
% 3.30/1.70 = ( comp @ D @ E @ A @ L @ R22 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_42_rewriteL__comp__comp2,axiom,
% 3.30/1.70 ! [A: $tType,C: $tType,B: $tType,D: $tType,E: $tType,F: C > B,G: A > C,L1: D > B,L2: A > D,H2: E > A,R3: E > D] :
% 3.30/1.70 ( ( ( comp @ C @ B @ A @ F @ G )
% 3.30/1.70 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 3.30/1.70 => ( ( ( comp @ A @ D @ E @ L2 @ H2 )
% 3.30/1.70 = R3 )
% 3.30/1.70 => ( ( comp @ C @ B @ E @ F @ ( comp @ A @ C @ E @ G @ H2 ) )
% 3.30/1.70 = ( comp @ D @ B @ E @ L1 @ R3 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_43_rewriteR__comp__comp,axiom,
% 3.30/1.70 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H2: A > C,R3: A > B,F: B > D] :
% 3.30/1.70 ( ( ( comp @ C @ B @ A @ G @ H2 )
% 3.30/1.70 = R3 )
% 3.30/1.70 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F @ G ) @ H2 )
% 3.30/1.70 = ( comp @ B @ D @ A @ F @ R3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_44_rewriteL__comp__comp,axiom,
% 3.30/1.70 ! [C: $tType,B: $tType,A: $tType,D: $tType,F: C > B,G: A > C,L: A > B,H2: D > A] :
% 3.30/1.70 ( ( ( comp @ C @ B @ A @ F @ G )
% 3.30/1.70 = L )
% 3.30/1.70 => ( ( comp @ C @ B @ D @ F @ ( comp @ A @ C @ D @ G @ H2 ) )
% 3.30/1.70 = ( comp @ A @ B @ D @ L @ H2 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_45_ext,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.30/1.70 ( ! [X: A] :
% 3.30/1.70 ( ( F @ X )
% 3.30/1.70 = ( G @ X ) )
% 3.30/1.70 => ( F = G ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_46_fun_Omap__comp,axiom,
% 3.30/1.70 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F: A > B,V: D > A] :
% 3.30/1.70 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F @ V ) )
% 3.30/1.70 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_47_Quotient3__rep__reflp,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,A3: B] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( R @ ( Rep @ A3 ) @ ( Rep @ A3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_48_Quotient3__rep__abs,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ R3 @ R3 )
% 3.30/1.70 => ( R @ ( Rep @ ( Abs @ R3 ) ) @ R3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_49_Quotient3__rel__rep,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,A3: B,B3: B] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ ( Rep @ A3 ) @ ( Rep @ B3 ) )
% 3.30/1.70 = ( A3 = B3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_50_Quotient3__rel__abs,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ R3 @ S3 )
% 3.30/1.70 => ( ( Abs @ R3 )
% 3.30/1.70 = ( Abs @ S3 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_51_Quotient3__abs__rep,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,A3: B] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( Abs @ ( Rep @ A3 ) )
% 3.30/1.70 = A3 ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_52_rep__abs__rsp__left,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,X1: A,X22: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ X1 @ X22 )
% 3.30/1.70 => ( R @ ( Rep @ ( Abs @ X1 ) ) @ X22 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_53_Quotient3__refl2,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ R3 @ S3 )
% 3.30/1.70 => ( R @ S3 @ S3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_54_Quotient3__refl1,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ R3 @ S3 )
% 3.30/1.70 => ( R @ R3 @ R3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_55_Quotient3__rel,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,R3: A,S3: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( ( R @ R3 @ R3 )
% 3.30/1.70 & ( R @ S3 @ S3 )
% 3.30/1.70 & ( ( Abs @ R3 )
% 3.30/1.70 = ( Abs @ S3 ) ) )
% 3.30/1.70 = ( R @ R3 @ S3 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_56_Quotient3__def,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType] :
% 3.30/1.70 ( ( quotient3 @ A @ B )
% 3.30/1.70 = ( ^ [R4: A > A > $o,Abs3: A > B,Rep3: B > A] :
% 3.30/1.70 ( ! [A5: B] :
% 3.30/1.70 ( ( Abs3 @ ( Rep3 @ A5 ) )
% 3.30/1.70 = A5 )
% 3.30/1.70 & ! [A5: B] : ( R4 @ ( Rep3 @ A5 ) @ ( Rep3 @ A5 ) )
% 3.30/1.70 & ! [R5: A,S2: A] :
% 3.30/1.70 ( ( R4 @ R5 @ S2 )
% 3.30/1.70 = ( ( R4 @ R5 @ R5 )
% 3.30/1.70 & ( R4 @ S2 @ S2 )
% 3.30/1.70 & ( ( Abs3 @ R5 )
% 3.30/1.70 = ( Abs3 @ S2 ) ) ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_57_comp__apply__eq,axiom,
% 3.30/1.70 ! [B: $tType,D: $tType,A: $tType,C: $tType,F: B > A,G: C > B,X2: C,H2: D > A,K: C > D] :
% 3.30/1.70 ( ( ( F @ ( G @ X2 ) )
% 3.30/1.70 = ( H2 @ ( K @ X2 ) ) )
% 3.30/1.70 => ( ( comp @ B @ A @ C @ F @ G @ X2 )
% 3.30/1.70 = ( comp @ D @ A @ C @ H2 @ K @ X2 ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_58_rep__abs__rsp,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,X1: A,X22: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ X1 @ X22 )
% 3.30/1.70 => ( R @ X1 @ ( Rep @ ( Abs @ X22 ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_59_equals__rsp,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,Xa: A,Xb: A,Ya: A,Yb: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( R @ Xa @ Xb )
% 3.30/1.70 => ( ( R @ Ya @ Yb )
% 3.30/1.70 => ( ( R @ Xa @ Ya )
% 3.30/1.70 = ( R @ Xb @ Yb ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_60_Quotient3I,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,Abs: B > A,Rep: A > B,R: B > B > $o] :
% 3.30/1.70 ( ! [A4: A] :
% 3.30/1.70 ( ( Abs @ ( Rep @ A4 ) )
% 3.30/1.70 = A4 )
% 3.30/1.70 => ( ! [A4: A] : ( R @ ( Rep @ A4 ) @ ( Rep @ A4 ) )
% 3.30/1.70 => ( ! [R6: B,S4: B] :
% 3.30/1.70 ( ( R @ R6 @ S4 )
% 3.30/1.70 = ( ( R @ R6 @ R6 )
% 3.30/1.70 & ( R @ S4 @ S4 )
% 3.30/1.70 & ( ( Abs @ R6 )
% 3.30/1.70 = ( Abs @ S4 ) ) ) )
% 3.30/1.70 => ( quotient3 @ B @ A @ R @ Abs @ Rep ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_61_cond__prs,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,R: A > A > $o,Absf: A > B,Repf: B > A,A3: $o,B3: B,C3: B] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Absf @ Repf )
% 3.30/1.70 => ( ( A3
% 3.30/1.70 => ( ( Absf @ ( if @ A @ A3 @ ( Repf @ B3 ) @ ( Repf @ C3 ) ) )
% 3.30/1.70 = B3 ) )
% 3.30/1.70 & ( ~ A3
% 3.30/1.70 => ( ( Absf @ ( if @ A @ A3 @ ( Repf @ B3 ) @ ( Repf @ C3 ) ) )
% 3.30/1.70 = C3 ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_62_let__prs,axiom,
% 3.30/1.70 ! [C: $tType,A: $tType,B: $tType,D: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,Abs22: C > D,Rep22: D > C] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 3.30/1.70 => ( ( quotient3 @ C @ D @ R2 @ Abs22 @ Rep22 )
% 3.30/1.70 => ( ( map_fun @ D @ C @ ( ( C > A ) > A ) @ ( ( D > B ) > B ) @ Rep22 @ ( map_fun @ ( D > B ) @ ( C > A ) @ A @ B @ ( map_fun @ C @ D @ B @ A @ Abs22 @ Rep12 ) @ Abs12 )
% 3.30/1.70 @ ^ [S2: C,F2: C > A] : ( F2 @ S2 ) )
% 3.30/1.70 = ( ^ [S2: D,F2: D > B] : ( F2 @ S2 ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_63_o__prs_I1_J,axiom,
% 3.30/1.70 ! [C: $tType,E: $tType,A: $tType,B: $tType,F3: $tType,D: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,Abs22: C > D,Rep22: D > C,R32: E > E > $o,Abs32: E > F3,Rep32: F3 > E] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 3.30/1.70 => ( ( quotient3 @ C @ D @ R2 @ Abs22 @ Rep22 )
% 3.30/1.70 => ( ( quotient3 @ E @ F3 @ R32 @ Abs32 @ Rep32 )
% 3.30/1.70 => ( ( map_fun @ ( D > F3 ) @ ( C > E ) @ ( ( A > C ) > A > E ) @ ( ( B > D ) > B > F3 ) @ ( map_fun @ C @ D @ F3 @ E @ Abs22 @ Rep32 ) @ ( map_fun @ ( B > D ) @ ( A > C ) @ ( A > E ) @ ( B > F3 ) @ ( map_fun @ A @ B @ D @ C @ Abs12 @ Rep22 ) @ ( map_fun @ B @ A @ E @ F3 @ Rep12 @ Abs32 ) ) @ ( comp @ C @ E @ A ) )
% 3.30/1.70 = ( comp @ D @ F3 @ B ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_64_llist__all2__lfilterI,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Q1: A > $o,Q2: B > $o] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 3.30/1.70 => ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( P @ X @ Y )
% 3.30/1.70 => ( ( Q1 @ X )
% 3.30/1.70 = ( Q2 @ Y ) ) )
% 3.30/1.70 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_lfilter @ A @ Q1 @ Xs ) @ ( coinductive_lfilter @ B @ Q2 @ Ys ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_65_apply__rspQ3_H_H,axiom,
% 3.30/1.70 ! [C: $tType,A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A,S: C > C > $o,F: A > C,X2: B] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( ( bNF_rel_fun @ A @ A @ C @ C @ R @ S @ F @ F )
% 3.30/1.70 => ( S @ ( F @ ( Rep @ X2 ) ) @ ( F @ ( Rep @ X2 ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_66_apply__rspQ3,axiom,
% 3.30/1.70 ! [B: $tType,C: $tType,A: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,F: A > C,G: A > C,X2: A,Y2: A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 3.30/1.70 => ( ( bNF_rel_fun @ A @ A @ C @ C @ R1 @ R2 @ F @ G )
% 3.30/1.70 => ( ( R1 @ X2 @ Y2 )
% 3.30/1.70 => ( R2 @ ( F @ X2 ) @ ( G @ Y2 ) ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_67_llist__all2__ldropWhileI,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Q1: A > $o,Q2: B > $o] :
% 3.30/1.70 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 3.30/1.70 => ( ! [X: A,Y: B] :
% 3.30/1.70 ( ( P @ X @ Y )
% 3.30/1.70 => ( ( Q1 @ X )
% 3.30/1.70 = ( Q2 @ Y ) ) )
% 3.30/1.70 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coindu218763757pWhile @ A @ Q1 @ Xs ) @ ( coindu218763757pWhile @ B @ Q2 @ Ys ) ) ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_68_quot__rel__rsp,axiom,
% 3.30/1.70 ! [B: $tType,A: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 3.30/1.70 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.70 => ( bNF_rel_fun @ A @ A @ ( A > $o ) @ ( A > $o ) @ R
% 3.30/1.70 @ ( bNF_rel_fun @ A @ A @ $o @ $o @ R
% 3.30/1.70 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.70 @ R
% 3.30/1.70 @ R ) ) ).
% 3.30/1.70
% 3.30/1.70 thf(fact_69_o__rsp_I1_J,axiom,
% 3.30/1.70 ! [A: $tType,B: $tType,E: $tType,F3: $tType,D: $tType,C: $tType,R2: A > C > $o,R32: B > D > $o,R1: E > F3 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( E > A ) > E > B ) @ ( ( F3 > C ) > F3 > D ) @ ( bNF_rel_fun @ A @ C @ B @ D @ R2 @ R32 ) @ ( bNF_rel_fun @ ( E > A ) @ ( F3 > C ) @ ( E > B ) @ ( F3 > D ) @ ( bNF_rel_fun @ E @ F3 @ A @ C @ R1 @ R2 ) @ ( bNF_rel_fun @ E @ F3 @ B @ D @ R1 @ R32 ) ) @ ( comp @ A @ B @ E ) @ ( comp @ C @ D @ F3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_70_o__rsp_I2_J,axiom,
% 3.30/1.71 ! [E: $tType,F3: $tType,H: $tType,G2: $tType,R1: E > F3 > $o] :
% 3.30/1.71 ( bNF_rel_fun @ ( G2 > H ) @ ( G2 > H ) @ ( ( E > G2 ) > E > H ) @ ( ( F3 > G2 ) > F3 > H )
% 3.30/1.71 @ ^ [Y3: G2 > H,Z: G2 > H] : ( Y3 = Z )
% 3.30/1.71 @ ( bNF_rel_fun @ ( E > G2 ) @ ( F3 > G2 ) @ ( E > H ) @ ( F3 > H )
% 3.30/1.71 @ ( bNF_rel_fun @ E @ F3 @ G2 @ G2 @ R1
% 3.30/1.71 @ ^ [Y3: G2,Z: G2] : ( Y3 = Z ) )
% 3.30/1.71 @ ( bNF_rel_fun @ E @ F3 @ H @ H @ R1
% 3.30/1.71 @ ^ [Y3: H,Z: H] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( comp @ G2 @ H @ E )
% 3.30/1.71 @ ( comp @ G2 @ H @ F3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_71_map__fun__apply,axiom,
% 3.30/1.71 ! [D: $tType,A: $tType,C: $tType,B: $tType] :
% 3.30/1.71 ( ( map_fun @ B @ C @ D @ A )
% 3.30/1.71 = ( ^ [F2: B > C,G3: D > A,H3: C > D,X4: B] : ( G3 @ ( H3 @ ( F2 @ X4 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_72_comp__apply,axiom,
% 3.30/1.71 ! [C: $tType,A: $tType,B: $tType] :
% 3.30/1.71 ( ( comp @ B @ A @ C )
% 3.30/1.71 = ( ^ [F2: B > A,G3: C > B,X4: C] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_73_map__fun__def,axiom,
% 3.30/1.71 ! [B: $tType,D: $tType,A: $tType,C: $tType] :
% 3.30/1.71 ( ( map_fun @ C @ A @ B @ D )
% 3.30/1.71 = ( ^ [F2: C > A,G3: B > D,H3: A > B] : ( comp @ A @ D @ C @ ( comp @ B @ D @ A @ G3 @ H3 ) @ F2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_74_map__fun_Ocomp,axiom,
% 3.30/1.71 ! [E: $tType,C: $tType,A: $tType,F3: $tType,D: $tType,B: $tType,F: E > C,G: D > F3,H2: C > A,I: B > D] :
% 3.30/1.71 ( ( comp @ ( C > D ) @ ( E > F3 ) @ ( A > B ) @ ( map_fun @ E @ C @ D @ F3 @ F @ G ) @ ( map_fun @ C @ A @ B @ D @ H2 @ I ) )
% 3.30/1.71 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H2 @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_75_map__fun_Ocompositionality,axiom,
% 3.30/1.71 ! [D: $tType,F3: $tType,C: $tType,E: $tType,B: $tType,A: $tType,F: E > C,G: D > F3,H2: C > A,I: B > D,Fun: A > B] :
% 3.30/1.71 ( ( map_fun @ E @ C @ D @ F3 @ F @ G @ ( map_fun @ C @ A @ B @ D @ H2 @ I @ Fun ) )
% 3.30/1.71 = ( map_fun @ E @ A @ B @ F3 @ ( comp @ C @ A @ E @ H2 @ F ) @ ( comp @ D @ F3 @ B @ G @ I ) @ Fun ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_76_llist_Omap__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F3: $tType,E: $tType,Rb: A > E > $o,Sd: B > F3 > $o] : ( bNF_rel_fun @ ( A > B ) @ ( E > F3 ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) ) @ ( ( coinductive_llist @ E ) > ( coinductive_llist @ F3 ) ) @ ( bNF_rel_fun @ A @ E @ B @ F3 @ Rb @ Sd ) @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ E ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ F3 ) @ ( coindu1486289336t_all2 @ A @ E @ Rb ) @ ( coindu1486289336t_all2 @ B @ F3 @ Sd ) ) @ ( coinductive_lmap @ A @ B ) @ ( coinductive_lmap @ E @ F3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_77_lmap__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > C > $o,B2: B > D > $o] : ( bNF_rel_fun @ ( A > B ) @ ( C > D ) @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) ) @ ( ( coinductive_llist @ C ) > ( coinductive_llist @ D ) ) @ ( bNF_rel_fun @ A @ C @ B @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ C ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ D ) @ ( coindu1486289336t_all2 @ A @ C @ A2 ) @ ( coindu1486289336t_all2 @ B @ D @ B2 ) ) @ ( coinductive_lmap @ A @ B ) @ ( coinductive_lmap @ C @ D ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_78_bex1__rel__rsp,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > A > $o,Absf: A > B,Repf: B > A] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R @ Absf @ Repf )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( A > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ A @ $o @ $o @ R
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( bex1_rel @ A @ R )
% 3.30/1.71 @ ( bex1_rel @ A @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_79_LCons__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) ) @ A2 @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) @ ( coindu1486289336t_all2 @ A @ B @ A2 ) ) @ ( coinductive_LCons @ A ) @ ( coinductive_LCons @ B ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_80_llist_Oinject,axiom,
% 3.30/1.71 ! [A: $tType,X21: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 3.30/1.71 ( ( ( coinductive_LCons @ A @ X21 @ X222 )
% 3.30/1.71 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 3.30/1.71 = ( ( X21 = Y21 )
% 3.30/1.71 & ( X222 = Y22 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_81_llist__all2__LCons__LCons,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X222: coinductive_llist @ A,Y21: B,Y22: coinductive_llist @ B] :
% 3.30/1.71 ( ( coindu1486289336t_all2 @ A @ B @ R @ ( coinductive_LCons @ A @ X21 @ X222 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) )
% 3.30/1.71 = ( ( R @ X21 @ Y21 )
% 3.30/1.71 & ( coindu1486289336t_all2 @ A @ B @ R @ X222 @ Y22 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_82_lfilter__LCons,axiom,
% 3.30/1.71 ! [A: $tType,P: A > $o,X2: A,Xs: coinductive_llist @ A] :
% 3.30/1.71 ( ( ( P @ X2 )
% 3.30/1.71 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 3.30/1.71 = ( coinductive_LCons @ A @ X2 @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) )
% 3.30/1.71 & ( ~ ( P @ X2 )
% 3.30/1.71 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 3.30/1.71 = ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_83_ldropWhile__LCons,axiom,
% 3.30/1.71 ! [A: $tType,P: A > $o,X2: A,Xs: coinductive_llist @ A] :
% 3.30/1.71 ( ( ( P @ X2 )
% 3.30/1.71 => ( ( coindu218763757pWhile @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 3.30/1.71 = ( coindu218763757pWhile @ A @ P @ Xs ) ) )
% 3.30/1.71 & ( ~ ( P @ X2 )
% 3.30/1.71 => ( ( coindu218763757pWhile @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 3.30/1.71 = ( coinductive_LCons @ A @ X2 @ Xs ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_84_unfold__llist__eq__LCons,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B,X2: A,Xs: coinductive_llist @ A] :
% 3.30/1.71 ( ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B3 )
% 3.30/1.71 = ( coinductive_LCons @ A @ X2 @ Xs ) )
% 3.30/1.71 = ( ~ ( IS_LNIL @ B3 )
% 3.30/1.71 & ( X2
% 3.30/1.71 = ( LHD @ B3 ) )
% 3.30/1.71 & ( Xs
% 3.30/1.71 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_85_llist_Opred__inject_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,P: A > $o,A3: A,Aa2: coinductive_llist @ A] :
% 3.30/1.71 ( ( coindu543516966_llist @ A @ P @ ( coinductive_LCons @ A @ A3 @ Aa2 ) )
% 3.30/1.71 = ( ( P @ A3 )
% 3.30/1.71 & ( coindu543516966_llist @ A @ P @ Aa2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_86_llist_Osimps_I13_J,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,F: A > B,X21: A,X222: coinductive_llist @ A] :
% 3.30/1.71 ( ( coinductive_lmap @ A @ B @ F @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 3.30/1.71 = ( coinductive_LCons @ B @ ( F @ X21 ) @ ( coinductive_lmap @ A @ B @ F @ X222 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_87_bex1__rel__aux,axiom,
% 3.30/1.71 ! [A: $tType,R: A > A > $o,X2: A > $o,Y2: A > $o] :
% 3.30/1.71 ( ! [Xa2: A,Ya2: A] :
% 3.30/1.71 ( ( R @ Xa2 @ Ya2 )
% 3.30/1.71 => ( ( X2 @ Xa2 )
% 3.30/1.71 = ( Y2 @ Ya2 ) ) )
% 3.30/1.71 => ( ( bex1_rel @ A @ R @ X2 )
% 3.30/1.71 => ( bex1_rel @ A @ R @ Y2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_88_bex1__rel__aux2,axiom,
% 3.30/1.71 ! [A: $tType,R: A > A > $o,X2: A > $o,Y2: A > $o] :
% 3.30/1.71 ( ! [Xa2: A,Ya2: A] :
% 3.30/1.71 ( ( R @ Xa2 @ Ya2 )
% 3.30/1.71 => ( ( X2 @ Xa2 )
% 3.30/1.71 = ( Y2 @ Ya2 ) ) )
% 3.30/1.71 => ( ( bex1_rel @ A @ R @ Y2 )
% 3.30/1.71 => ( bex1_rel @ A @ R @ X2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_89_lmap__eq__LCons__conv,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B,Y2: A,Ys: coinductive_llist @ A] :
% 3.30/1.71 ( ( ( coinductive_lmap @ B @ A @ F @ Xs )
% 3.30/1.71 = ( coinductive_LCons @ A @ Y2 @ Ys ) )
% 3.30/1.71 = ( ? [X4: B,Xs2: coinductive_llist @ B] :
% 3.30/1.71 ( ( Xs
% 3.30/1.71 = ( coinductive_LCons @ B @ X4 @ Xs2 ) )
% 3.30/1.71 & ( Y2
% 3.30/1.71 = ( F @ X4 ) )
% 3.30/1.71 & ( Ys
% 3.30/1.71 = ( coinductive_lmap @ B @ A @ F @ Xs2 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_90_iterates__equality,axiom,
% 3.30/1.71 ! [A: $tType,H2: A > ( coinductive_llist @ A ),F: A > A] :
% 3.30/1.71 ( ! [X: A] :
% 3.30/1.71 ( ( H2 @ X )
% 3.30/1.71 = ( coinductive_LCons @ A @ X @ ( coinductive_lmap @ A @ A @ F @ ( H2 @ X ) ) ) )
% 3.30/1.71 => ( H2
% 3.30/1.71 = ( coinductive_iterates @ A @ F ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_91_iterates__lmap,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( ( coinductive_iterates @ A )
% 3.30/1.71 = ( ^ [F2: A > A,X4: A] : ( coinductive_LCons @ A @ X4 @ ( coinductive_lmap @ A @ A @ F2 @ ( coinductive_iterates @ A @ F2 @ X4 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_92_llist_Omap__comp,axiom,
% 3.30/1.71 ! [B: $tType,C: $tType,A: $tType,G: B > C,F: A > B,V: coinductive_llist @ A] :
% 3.30/1.71 ( ( coinductive_lmap @ B @ C @ G @ ( coinductive_lmap @ A @ B @ F @ V ) )
% 3.30/1.71 = ( coinductive_lmap @ A @ C @ ( comp @ B @ C @ A @ G @ F ) @ V ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_93_lfilter__lmap,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,P: A > $o,F: B > A,Xs: coinductive_llist @ B] :
% 3.30/1.71 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 3.30/1.71 = ( coinductive_lmap @ B @ A @ F @ ( coinductive_lfilter @ B @ ( comp @ A @ $o @ B @ P @ F ) @ Xs ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_94_ltakeWhile__lmap,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,P: A > $o,F: B > A,Xs: coinductive_llist @ B] :
% 3.30/1.71 ( ( coindu501562517eWhile @ A @ P @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 3.30/1.71 = ( coinductive_lmap @ B @ A @ F @ ( coindu501562517eWhile @ B @ ( comp @ A @ $o @ B @ P @ F ) @ Xs ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_95_ldropWhile__lmap,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,P: A > $o,F: B > A,Xs: coinductive_llist @ B] :
% 3.30/1.71 ( ( coindu218763757pWhile @ A @ P @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 3.30/1.71 = ( coinductive_lmap @ B @ A @ F @ ( coindu218763757pWhile @ B @ ( comp @ A @ $o @ B @ P @ F ) @ Xs ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_96_lmap__iterates,axiom,
% 3.30/1.71 ! [A: $tType,F: A > A,X2: A] :
% 3.30/1.71 ( ( coinductive_lmap @ A @ A @ F @ ( coinductive_iterates @ A @ F @ X2 ) )
% 3.30/1.71 = ( coinductive_iterates @ A @ F @ ( F @ X2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_97_llist_Orel__intros_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X222: coinductive_llist @ A,Y22: coinductive_llist @ B] :
% 3.30/1.71 ( ( R @ X21 @ Y21 )
% 3.30/1.71 => ( ( coindu1486289336t_all2 @ A @ B @ R @ X222 @ Y22 )
% 3.30/1.71 => ( coindu1486289336t_all2 @ A @ B @ R @ ( coinductive_LCons @ A @ X21 @ X222 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_98_llist__all2__LCons1,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,P: A > B > $o,X2: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 3.30/1.71 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) @ Ys )
% 3.30/1.71 = ( ? [Y5: B,Ys2: coinductive_llist @ B] :
% 3.30/1.71 ( ( Ys
% 3.30/1.71 = ( coinductive_LCons @ B @ Y5 @ Ys2 ) )
% 3.30/1.71 & ( P @ X2 @ Y5 )
% 3.30/1.71 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_99_llist__all2__LCons2,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Y2: B,Ys: coinductive_llist @ B] :
% 3.30/1.71 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ ( coinductive_LCons @ B @ Y2 @ Ys ) )
% 3.30/1.71 = ( ? [X4: A,Xs2: coinductive_llist @ A] :
% 3.30/1.71 ( ( Xs
% 3.30/1.71 = ( coinductive_LCons @ A @ X4 @ Xs2 ) )
% 3.30/1.71 & ( P @ X4 @ Y2 )
% 3.30/1.71 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs2 @ Ys ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_100_lmap__lmirror,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 3.30/1.71 ( ( coinductive_lmap @ B @ A @ F @ ( lMirro427583474mirror @ B @ Xs ) )
% 3.30/1.71 = ( lMirro427583474mirror @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_101_llist_Opred__map,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,Q: B > $o,F: A > B,X2: coinductive_llist @ A] :
% 3.30/1.71 ( ( coindu543516966_llist @ B @ Q @ ( coinductive_lmap @ A @ B @ F @ X2 ) )
% 3.30/1.71 = ( coindu543516966_llist @ A @ ( comp @ B @ $o @ A @ Q @ F ) @ X2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_102_llist_Osimps_I5_J,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,F1: B,F22: A > ( coinductive_llist @ A ) > B,X21: A,X222: coinductive_llist @ A] :
% 3.30/1.71 ( ( coindu1381640503_llist @ B @ A @ F1 @ F22 @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 3.30/1.71 = ( F22 @ X21 @ X222 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_103_lfilter__LCons__seek,axiom,
% 3.30/1.71 ! [A: $tType,P3: A > $o,X2: A,L: coinductive_llist @ A] :
% 3.30/1.71 ( ~ ( P3 @ X2 )
% 3.30/1.71 => ( ( coinductive_lfilter @ A @ P3 @ ( coinductive_LCons @ A @ X2 @ L ) )
% 3.30/1.71 = ( coinductive_lfilter @ A @ P3 @ L ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_104_lfilter__LCons__found,axiom,
% 3.30/1.71 ! [A: $tType,P: A > $o,X2: A,Xs: coinductive_llist @ A] :
% 3.30/1.71 ( ( P @ X2 )
% 3.30/1.71 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X2 @ Xs ) )
% 3.30/1.71 = ( coinductive_LCons @ A @ X2 @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_105_iterates_Ocode,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( ( coinductive_iterates @ A )
% 3.30/1.71 = ( ^ [F2: A > A,X4: A] : ( coinductive_LCons @ A @ X4 @ ( coinductive_iterates @ A @ F2 @ ( F2 @ X4 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_106_unfold__llist_Octr_I2_J,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,P3: A > $o,A3: A,G21: A > B,G22: A > A] :
% 3.30/1.71 ( ~ ( P3 @ A3 )
% 3.30/1.71 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A3 )
% 3.30/1.71 = ( coinductive_LCons @ B @ ( G21 @ A3 ) @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_107_llist_Ocorec_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,P3: C > $o,A3: C,G21: C > A,Q22: C > $o,G221: C > ( coinductive_llist @ A ),G222: C > C] :
% 3.30/1.71 ( ~ ( P3 @ A3 )
% 3.30/1.71 => ( ( coindu1259883913_llist @ C @ A @ P3 @ G21 @ Q22 @ G221 @ G222 @ A3 )
% 3.30/1.71 = ( coinductive_LCons @ A @ ( G21 @ A3 ) @ ( if @ ( coinductive_llist @ A ) @ ( Q22 @ A3 ) @ ( G221 @ A3 ) @ ( coindu1259883913_llist @ C @ A @ P3 @ G21 @ Q22 @ G221 @ G222 @ ( G222 @ A3 ) ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_108_lmap__unfold__llist,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,F: B > A,IS_LNIL: C > $o,LHD: C > B,LTL: C > C,B3: C] :
% 3.30/1.71 ( ( coinductive_lmap @ B @ A @ F @ ( coindu1441602521_llist @ C @ B @ IS_LNIL @ LHD @ LTL @ B3 ) )
% 3.30/1.71 = ( coindu1441602521_llist @ C @ A @ IS_LNIL @ ( comp @ B @ A @ C @ F @ LHD ) @ LTL @ B3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_109_llist_Omap__o__corec,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,F: A > B,G: C > $o,Ga: C > A,Gb: C > $o,Gc: C > ( coinductive_llist @ A ),Gd: C > C] :
% 3.30/1.71 ( ( comp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ ( coinductive_lmap @ A @ B @ F ) @ ( coindu1259883913_llist @ C @ A @ G @ Ga @ Gb @ Gc @ Gd ) )
% 3.30/1.71 = ( coindu1259883913_llist @ C @ B @ G @ ( comp @ A @ B @ C @ F @ Ga ) @ Gb @ ( comp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ C @ ( coinductive_lmap @ A @ B @ F ) @ Gc ) @ Gd ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_110_lmap__corec__llist,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,F: B > A,IS_LNIL: C > $o,LHD: C > B,EndORmore: C > $o,TTL_end: C > ( coinductive_llist @ B ),TTL_more: C > C,B3: C] :
% 3.30/1.71 ( ( coinductive_lmap @ B @ A @ F @ ( coindu1259883913_llist @ C @ B @ IS_LNIL @ LHD @ EndORmore @ TTL_end @ TTL_more @ B3 ) )
% 3.30/1.71 = ( coindu1259883913_llist @ C @ A @ IS_LNIL @ ( comp @ B @ A @ C @ F @ LHD ) @ EndORmore @ ( comp @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ C @ ( coinductive_lmap @ B @ A @ F ) @ TTL_end ) @ TTL_more @ B3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_111_lfilter__eq__LCons,axiom,
% 3.30/1.71 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A,X2: A,Xs3: coinductive_llist @ A] :
% 3.30/1.71 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 3.30/1.71 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 3.30/1.71 => ? [Xs4: coinductive_llist @ A] :
% 3.30/1.71 ( ( Xs3
% 3.30/1.71 = ( coinductive_lfilter @ A @ P @ Xs4 ) )
% 3.30/1.71 & ( ( coindu218763757pWhile @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ Xs )
% 3.30/1.71 = ( coinductive_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_112_comp__eq__dest__lhs,axiom,
% 3.30/1.71 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B3: A > C,C3: A > B,V: A] :
% 3.30/1.71 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.30/1.71 = C3 )
% 3.30/1.71 => ( ( A3 @ ( B3 @ V ) )
% 3.30/1.71 = ( C3 @ V ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_113_comp__eq__elim,axiom,
% 3.30/1.71 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C3: D > B,D3: A > D] :
% 3.30/1.71 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.30/1.71 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 3.30/1.71 => ! [V2: A] :
% 3.30/1.71 ( ( A3 @ ( B3 @ V2 ) )
% 3.30/1.71 = ( C3 @ ( D3 @ V2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_114_comp__eq__dest,axiom,
% 3.30/1.71 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C3: D > B,D3: A > D,V: A] :
% 3.30/1.71 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.30/1.71 = ( comp @ D @ B @ A @ C3 @ D3 ) )
% 3.30/1.71 => ( ( A3 @ ( B3 @ V ) )
% 3.30/1.71 = ( C3 @ ( D3 @ V ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_115_comp__assoc,axiom,
% 3.30/1.71 ! [B: $tType,D: $tType,C: $tType,A: $tType,F: D > B,G: C > D,H2: A > C] :
% 3.30/1.71 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F @ G ) @ H2 )
% 3.30/1.71 = ( comp @ D @ B @ A @ F @ ( comp @ C @ D @ A @ G @ H2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_116_comp__def,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType] :
% 3.30/1.71 ( ( comp @ B @ C @ A )
% 3.30/1.71 = ( ^ [F2: B > C,G3: A > B,X4: A] : ( F2 @ ( G3 @ X4 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_117_llist_Octr__transfer_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) @ ( ( coinductive_llist @ B ) > ( coinductive_llist @ B ) ) @ R @ ( bNF_rel_fun @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) @ ( coinductive_LCons @ A ) @ ( coinductive_LCons @ B ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_118_lmember__code_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,X2: A,Y2: A,Ys: coinductive_llist @ A] :
% 3.30/1.71 ( ( coinductive_lmember @ A @ X2 @ ( coinductive_LCons @ A @ Y2 @ Ys ) )
% 3.30/1.71 = ( ( X2 = Y2 )
% 3.30/1.71 | ( coinductive_lmember @ A @ X2 @ Ys ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_119_type__copy__map__cong0,axiom,
% 3.30/1.71 ! [B: $tType,D: $tType,E: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X2: C,N: D > A,H2: C > D,F: A > E] :
% 3.30/1.71 ( ( ( M @ ( G @ X2 ) )
% 3.30/1.71 = ( N @ ( H2 @ X2 ) ) )
% 3.30/1.71 => ( ( comp @ B @ E @ C @ ( comp @ A @ E @ B @ F @ M ) @ G @ X2 )
% 3.30/1.71 = ( comp @ D @ E @ C @ ( comp @ A @ E @ D @ F @ N ) @ H2 @ X2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_120_comp__cong,axiom,
% 3.30/1.71 ! [C: $tType,B: $tType,D: $tType,A: $tType,E: $tType,F: B > A,G: C > B,X2: C,F4: D > A,G4: E > D,X5: E] :
% 3.30/1.71 ( ( ( F @ ( G @ X2 ) )
% 3.30/1.71 = ( F4 @ ( G4 @ X5 ) ) )
% 3.30/1.71 => ( ( comp @ B @ A @ C @ F @ G @ X2 )
% 3.30/1.71 = ( comp @ D @ A @ E @ F4 @ G4 @ X5 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_121_if__prs,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.71 => ( ( map_fun @ $o @ $o @ ( A > A > A ) @ ( B > B > B ) @ ( id @ $o ) @ ( map_fun @ B @ A @ ( A > A ) @ ( B > B ) @ Rep @ ( map_fun @ B @ A @ A @ B @ Rep @ Abs ) ) @ ( if @ A ) )
% 3.30/1.71 = ( if @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_122_o__prs_I2_J,axiom,
% 3.30/1.71 ! [F3: $tType,E: $tType,C: $tType,D: $tType,A: $tType,B: $tType,H: $tType,G2: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: C > C > $o,Abs22: C > D,Rep22: D > C,R32: E > E > $o,Abs32: E > F3,Rep32: F3 > E] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 3.30/1.71 => ( ( quotient3 @ C @ D @ R2 @ Abs22 @ Rep22 )
% 3.30/1.71 => ( ( quotient3 @ E @ F3 @ R32 @ Abs32 @ Rep32 )
% 3.30/1.71 => ( ( map_fun @ ( G2 > H ) @ ( G2 > H ) @ ( ( A > G2 ) > A > H ) @ ( ( B > G2 ) > B > H ) @ ( id @ ( G2 > H ) ) @ ( map_fun @ ( B > G2 ) @ ( A > G2 ) @ ( A > H ) @ ( B > H ) @ ( map_fun @ A @ B @ G2 @ G2 @ Abs12 @ ( id @ G2 ) ) @ ( map_fun @ B @ A @ H @ H @ Rep12 @ ( id @ H ) ) ) @ ( comp @ G2 @ H @ A ) )
% 3.30/1.71 = ( comp @ G2 @ H @ B ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_123_fun__ord__parametric,axiom,
% 3.30/1.71 ! [C: $tType,D: $tType,A: $tType,B: $tType,F3: $tType,E: $tType,C2: A > B > $o,A2: C > E > $o,B2: D > F3 > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ C2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( C > D > $o ) @ ( E > F3 > $o ) @ ( ( A > C ) > ( A > D ) > $o ) @ ( ( B > E ) > ( B > F3 ) > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ C @ E @ ( D > $o ) @ ( F3 > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ D @ F3 @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ ( A > C ) @ ( B > E ) @ ( ( A > D ) > $o ) @ ( ( B > F3 ) > $o ) @ ( bNF_rel_fun @ A @ B @ C @ E @ C2 @ A2 )
% 3.30/1.71 @ ( bNF_rel_fun @ ( A > D ) @ ( B > F3 ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ D @ F3 @ C2 @ B2 )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( partial_fun_ord @ C @ D @ A )
% 3.30/1.71 @ ( partial_fun_ord @ E @ F3 @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_124_id__apply,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( ( id @ A )
% 3.30/1.71 = ( ^ [X4: A] : X4 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_125_fun_Omap__id,axiom,
% 3.30/1.71 ! [A: $tType,D: $tType,T2: D > A] :
% 3.30/1.71 ( ( comp @ A @ A @ D @ ( id @ A ) @ T2 )
% 3.30/1.71 = T2 ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_126_comp__id,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,F: A > B] :
% 3.30/1.71 ( ( comp @ A @ B @ A @ F @ ( id @ A ) )
% 3.30/1.71 = F ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_127_id__comp,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,G: A > B] :
% 3.30/1.71 ( ( comp @ B @ B @ A @ ( id @ B ) @ G )
% 3.30/1.71 = G ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_128_fun_Omap__id0,axiom,
% 3.30/1.71 ! [A: $tType,D: $tType] :
% 3.30/1.71 ( ( comp @ A @ A @ D @ ( id @ A ) )
% 3.30/1.71 = ( id @ ( D > A ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_129_map__fun__id,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( map_fun @ A @ A @ B @ B @ ( id @ A ) @ ( id @ B ) )
% 3.30/1.71 = ( id @ ( A > B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_130_llist_Omap__id0,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( ( coinductive_lmap @ A @ A @ ( id @ A ) )
% 3.30/1.71 = ( id @ ( coinductive_llist @ A ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_131_eq__id__iff,axiom,
% 3.30/1.71 ! [A: $tType,F: A > A] :
% 3.30/1.71 ( ( ! [X4: A] :
% 3.30/1.71 ( ( F @ X4 )
% 3.30/1.71 = X4 ) )
% 3.30/1.71 = ( F
% 3.30/1.71 = ( id @ A ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_132_id__def,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( ( id @ A )
% 3.30/1.71 = ( ^ [X4: A] : X4 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_133_llist_Obi__total__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ R )
% 3.30/1.71 => ( bi_total @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_134_bi__total__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( bi_total @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ( ! [X4: A] :
% 3.30/1.71 ( ^ [P4: B > $o] :
% 3.30/1.71 ? [X6: B] : ( P4 @ X6 )
% 3.30/1.71 @ ( R4 @ X4 ) )
% 3.30/1.71 & ! [Y5: B] :
% 3.30/1.71 ? [X4: A] : ( R4 @ X4 @ Y5 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_135_bi__total__eq,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( bi_total @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_136_id__rsp,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > B > $o] : ( bNF_rel_fun @ A @ B @ A @ B @ R @ R @ ( id @ A ) @ ( id @ B ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_137_id__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] : ( bNF_rel_fun @ A @ B @ A @ B @ A2 @ A2 @ ( id @ A ) @ ( id @ B ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_138_pointfree__idE,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,F: B > A,G: A > B,X2: A] :
% 3.30/1.71 ( ( ( comp @ B @ A @ A @ F @ G )
% 3.30/1.71 = ( id @ A ) )
% 3.30/1.71 => ( ( F @ ( G @ X2 ) )
% 3.30/1.71 = X2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_139_comp__eq__id__dest,axiom,
% 3.30/1.71 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B3: A > C,C3: A > B,V: A] :
% 3.30/1.71 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.30/1.71 = ( comp @ B @ B @ A @ ( id @ B ) @ C3 ) )
% 3.30/1.71 => ( ( A3 @ ( B3 @ V ) )
% 3.30/1.71 = ( C3 @ V ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_140_llist_Omap__id,axiom,
% 3.30/1.71 ! [A: $tType,T2: coinductive_llist @ A] :
% 3.30/1.71 ( ( coinductive_lmap @ A @ A @ ( id @ A ) @ T2 )
% 3.30/1.71 = T2 ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_141_identity__quotient3,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( quotient3 @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ ( id @ A )
% 3.30/1.71 @ ( id @ A ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_142_abs__o__rep,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.71 => ( ( comp @ A @ B @ B @ Abs @ Rep )
% 3.30/1.71 = ( id @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_143_id__prs,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > A > $o,Abs: A > B,Rep: B > A] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R @ Abs @ Rep )
% 3.30/1.71 => ( ( map_fun @ B @ A @ A @ B @ Rep @ Abs @ ( id @ A ) )
% 3.30/1.71 = ( id @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_144_transfer__forall__transfer_I1_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( transfer_forall @ A )
% 3.30/1.71 @ ( transfer_forall @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_145_monotone__parametric,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ ( ( C > C > $o ) > ( A > C ) > $o ) @ ( ( D > D > $o ) > ( B > D ) > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ ( C > C > $o ) @ ( D > D > $o ) @ ( ( A > C ) > $o ) @ ( ( B > D ) > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ ( C > $o ) @ ( D > $o ) @ B2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( comple1396247847notone @ A @ C )
% 3.30/1.71 @ ( comple1396247847notone @ B @ D ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_146_swap__comp__involutory,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A3: A,B3: A] :
% 3.30/1.71 ( ( comp @ ( A > B ) @ ( A > B ) @ ( A > B ) @ ( swap @ A @ B @ A3 @ B3 ) @ ( swap @ A @ B @ A3 @ B3 ) )
% 3.30/1.71 = ( id @ ( A > B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_147_ex1__prs,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > A > $o,Absf: A > B,Repf: B > A,F: B > $o] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R @ Absf @ Repf )
% 3.30/1.71 => ( ( map_fun @ ( B > $o ) @ ( A > $o ) @ $o @ $o @ ( map_fun @ A @ B @ $o @ $o @ Absf @ ( id @ $o ) ) @ ( id @ $o ) @ ( bex1_rel @ A @ R ) @ F )
% 3.30/1.71 = ( ? [X4: B] :
% 3.30/1.71 ( ( F @ X4 )
% 3.30/1.71 & ! [Y5: B] :
% 3.30/1.71 ( ( F @ Y5 )
% 3.30/1.71 => ( Y5 = X4 ) ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_148_swap__apply_I3_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C3: B,A3: B,B3: B,F: B > A] :
% 3.30/1.71 ( ( C3 != A3 )
% 3.30/1.71 => ( ( C3 != B3 )
% 3.30/1.71 => ( ( swap @ B @ A @ A3 @ B3 @ F @ C3 )
% 3.30/1.71 = ( F @ C3 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_149_swap__apply_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A3: B,B3: B,F: B > A] :
% 3.30/1.71 ( ( swap @ B @ A @ A3 @ B3 @ F @ B3 )
% 3.30/1.71 = ( F @ A3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_150_swap__apply_I1_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A3: B,B3: B,F: B > A] :
% 3.30/1.71 ( ( swap @ B @ A @ A3 @ B3 @ F @ A3 )
% 3.30/1.71 = ( F @ B3 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_151_swap__self,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A3: A,F: A > B] :
% 3.30/1.71 ( ( swap @ A @ B @ A3 @ A3 @ F )
% 3.30/1.71 = F ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_152_swap__nilpotent,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A3: A,B3: A,F: A > B] :
% 3.30/1.71 ( ( swap @ A @ B @ A3 @ B3 @ ( swap @ A @ B @ A3 @ B3 @ F ) )
% 3.30/1.71 = F ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_153_swap__triple,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A3: A,C3: A,B3: A,F: A > B] :
% 3.30/1.71 ( ( A3 != C3 )
% 3.30/1.71 => ( ( B3 != C3 )
% 3.30/1.71 => ( ( swap @ A @ B @ A3 @ B3 @ ( swap @ A @ B @ B3 @ C3 @ ( swap @ A @ B @ A3 @ B3 @ F ) ) )
% 3.30/1.71 = ( swap @ A @ B @ A3 @ C3 @ F ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_154_swap__commute,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( swap @ A @ B )
% 3.30/1.71 = ( ^ [A5: A,B5: A] : ( swap @ A @ B @ B5 @ A5 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_155_comp__swap,axiom,
% 3.30/1.71 ! [B: $tType,C: $tType,A: $tType,F: C > B,A3: A,B3: A,G: A > C] :
% 3.30/1.71 ( ( comp @ C @ B @ A @ F @ ( swap @ A @ C @ A3 @ B3 @ G ) )
% 3.30/1.71 = ( swap @ A @ B @ A3 @ B3 @ ( comp @ C @ B @ A @ F @ G ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_156_transfer__forall__transfer_I4_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ rev_implies
% 3.30/1.71 @ ( transfer_forall @ A )
% 3.30/1.71 @ ( transfer_forall @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_157_transfer__forall__transfer_I5_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ rev_implies ) @ rev_implies @ ( transfer_forall @ A ) @ ( transfer_forall @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_158_Domainp__transfer,axiom,
% 3.30/1.71 ! [C: $tType,A: $tType,B: $tType,D: $tType,B2: A > B > $o,A2: C > D > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( C > A > $o ) @ ( D > B > $o ) @ ( C > $o ) @ ( D > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ( domainp @ C @ A )
% 3.30/1.71 @ ( domainp @ D @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_159_rev__implies__def,axiom,
% 3.30/1.71 ( rev_implies
% 3.30/1.71 = ( ^ [X4: $o,Y5: $o] :
% 3.30/1.71 ( Y5
% 3.30/1.71 => X4 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_160_Domainp__refl,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( domainp @ A @ B )
% 3.30/1.71 = ( domainp @ A @ B ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_161_Domainp__iff,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( domainp @ A @ B )
% 3.30/1.71 = ( ^ [T3: A > B > $o,X4: A] :
% 3.30/1.71 ( ^ [P4: B > $o] :
% 3.30/1.71 ? [X6: B] : ( P4 @ X6 )
% 3.30/1.71 @ ( T3 @ X4 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_162_llist_ODomainp__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( domainp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) )
% 3.30/1.71 = ( coindu543516966_llist @ A @ ( domainp @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_163_reflp__transfer_I5_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ rev_implies
% 3.30/1.71 @ ( reflp @ A )
% 3.30/1.71 @ ( reflp @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_164_reflp__transfer_I4_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ rev_implies ) ) @ rev_implies @ ( reflp @ A ) @ ( reflp @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_165_Ex1__parametric,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( ex1 @ A )
% 3.30/1.71 @ ( ex1 @ B ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_166_bi__unique__fun,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_unique @ C @ D @ B2 )
% 3.30/1.71 => ( bi_unique @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_167_fun_Orel__reflp,axiom,
% 3.30/1.71 ! [D: $tType,A: $tType,R: A > A > $o] :
% 3.30/1.71 ( ( reflp @ A @ R )
% 3.30/1.71 => ( reflp @ ( D > A )
% 3.30/1.71 @ ( bNF_rel_fun @ D @ D @ A @ A
% 3.30/1.71 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.71 @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_168_DEADID_Orel__reflp,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( reflp @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_169_bi__uniqueDl,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A2: A > B > $o,X2: A,Y2: B,Z2: A] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( A2 @ X2 @ Y2 )
% 3.30/1.71 => ( ( A2 @ Z2 @ Y2 )
% 3.30/1.71 => ( X2 = Z2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_170_bi__uniqueDr,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o,X2: A,Y2: B,Z2: B] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( A2 @ X2 @ Y2 )
% 3.30/1.71 => ( ( A2 @ X2 @ Z2 )
% 3.30/1.71 => ( Y2 = Z2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_171_bi__unique__eq,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( bi_unique @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_172_bi__unique__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( bi_unique @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ( ! [X4: A,Y5: B,Z3: B] :
% 3.30/1.71 ( ( R4 @ X4 @ Y5 )
% 3.30/1.71 => ( ( R4 @ X4 @ Z3 )
% 3.30/1.71 => ( Y5 = Z3 ) ) )
% 3.30/1.71 & ! [X4: A,Y5: A,Z3: B] :
% 3.30/1.71 ( ( R4 @ X4 @ Z3 )
% 3.30/1.71 => ( ( R4 @ Y5 @ Z3 )
% 3.30/1.71 => ( X4 = Y5 ) ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_173_llist_Orel__reflp,axiom,
% 3.30/1.71 ! [A: $tType,R: A > A > $o] :
% 3.30/1.71 ( ( reflp @ A @ R )
% 3.30/1.71 => ( reflp @ ( coinductive_llist @ A ) @ ( coindu1486289336t_all2 @ A @ A @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_174_llist_Obi__unique__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ R )
% 3.30/1.71 => ( bi_unique @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_175_bi__total__fun,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ C @ D @ B2 )
% 3.30/1.71 => ( bi_total @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_176_eq__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_177_bi__unique__alt__def2,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( bi_unique @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ R4
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R4
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_178_reflp__transfer_I1_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( reflp @ A )
% 3.30/1.71 @ ( reflp @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_179_fun__upd__transfer,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C ) @ ( B > D ) @ ( A > C > A > C ) @ ( B > D > B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) @ ( bNF_rel_fun @ A @ B @ ( C > A > C ) @ ( D > B > D ) @ A2 @ ( bNF_rel_fun @ C @ D @ ( A > C ) @ ( B > D ) @ B2 @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) @ ( fun_upd @ A @ C ) @ ( fun_upd @ B @ D ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_180_right__unique__parametric,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_unique @ C @ D @ B2 )
% 3.30/1.71 => ( ( bi_total @ C @ D @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( right_unique @ A @ C )
% 3.30/1.71 @ ( right_unique @ B @ D ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_181_left__unique__parametric,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ C @ D @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( left_unique @ A @ C )
% 3.30/1.71 @ ( left_unique @ B @ D ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_182_fun__upd__apply,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType] :
% 3.30/1.71 ( ( fun_upd @ B @ A )
% 3.30/1.71 = ( ^ [F2: B > A,X4: B,Y5: A,Z3: B] : ( if @ A @ ( Z3 = X4 ) @ Y5 @ ( F2 @ Z3 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_183_fun__upd__triv,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,F: A > B,X2: A] :
% 3.30/1.71 ( ( fun_upd @ A @ B @ F @ X2 @ ( F @ X2 ) )
% 3.30/1.71 = F ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_184_fun__upd__upd,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F: A > B,X2: A,Y2: B,Z2: B] :
% 3.30/1.71 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X2 @ Y2 ) @ X2 @ Z2 )
% 3.30/1.71 = ( fun_upd @ A @ B @ F @ X2 @ Z2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_185_bi__uniqueI,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( left_unique @ A @ B @ R )
% 3.30/1.71 => ( ( right_unique @ A @ B @ R )
% 3.30/1.71 => ( bi_unique @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_186_bi__unique__alt__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( bi_unique @ A @ B )
% 3.30/1.71 = ( ^ [A6: A > B > $o] :
% 3.30/1.71 ( ( left_unique @ A @ B @ A6 )
% 3.30/1.71 & ( right_unique @ A @ B @ A6 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_187_fun__upd__comp,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,F: C > B,G: A > C,X2: A,Y2: C] :
% 3.30/1.71 ( ( comp @ C @ B @ A @ F @ ( fun_upd @ A @ C @ G @ X2 @ Y2 ) )
% 3.30/1.71 = ( fun_upd @ A @ B @ ( comp @ C @ B @ A @ F @ G ) @ X2 @ ( F @ Y2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_188_fun__upd__idem__iff,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F: A > B,X2: A,Y2: B] :
% 3.30/1.71 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y2 )
% 3.30/1.71 = F )
% 3.30/1.71 = ( ( F @ X2 )
% 3.30/1.71 = Y2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_189_fun__upd__twist,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A3: A,C3: A,M2: A > B,B3: B,D3: B] :
% 3.30/1.71 ( ( A3 != C3 )
% 3.30/1.71 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ A3 @ B3 ) @ C3 @ D3 )
% 3.30/1.71 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ C3 @ D3 ) @ A3 @ B3 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_190_fun__upd__other,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,Z2: A,X2: A,F: A > B,Y2: B] :
% 3.30/1.71 ( ( Z2 != X2 )
% 3.30/1.71 => ( ( fun_upd @ A @ B @ F @ X2 @ Y2 @ Z2 )
% 3.30/1.71 = ( F @ Z2 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_191_fun__upd__same,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,F: B > A,X2: B,Y2: A] :
% 3.30/1.71 ( ( fun_upd @ B @ A @ F @ X2 @ Y2 @ X2 )
% 3.30/1.71 = Y2 ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_192_fun__upd__idem,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F: B > A,X2: B,Y2: A] :
% 3.30/1.71 ( ( ( F @ X2 )
% 3.30/1.71 = Y2 )
% 3.30/1.71 => ( ( fun_upd @ B @ A @ F @ X2 @ Y2 )
% 3.30/1.71 = F ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_193_fun__upd__eqD,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,F: A > B,X2: A,Y2: B,G: A > B,Z2: B] :
% 3.30/1.71 ( ( ( fun_upd @ A @ B @ F @ X2 @ Y2 )
% 3.30/1.71 = ( fun_upd @ A @ B @ G @ X2 @ Z2 ) )
% 3.30/1.71 => ( Y2 = Z2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_194_fun__upd__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( fun_upd @ A @ B )
% 3.30/1.71 = ( ^ [F2: A > B,A5: A,B5: B,X4: A] : ( if @ B @ ( X4 = A5 ) @ B5 @ ( F2 @ X4 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_195_right__unique__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( right_unique @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ! [X4: A,Y5: B,Z3: B] :
% 3.30/1.71 ( ( R4 @ X4 @ Y5 )
% 3.30/1.71 => ( ( R4 @ X4 @ Z3 )
% 3.30/1.71 => ( Y5 = Z3 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_196_right__unique__eq,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( right_unique @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_197_left__unique__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( left_unique @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ! [X4: A,Y5: A,Z3: B] :
% 3.30/1.71 ( ( R4 @ X4 @ Z3 )
% 3.30/1.71 => ( ( R4 @ Y5 @ Z3 )
% 3.30/1.71 => ( X4 = Y5 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_198_left__unique__eq,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( left_unique @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_199_right__uniqueI,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ! [X: A,Y: B,Z4: B] :
% 3.30/1.71 ( ( A2 @ X @ Y )
% 3.30/1.71 => ( ( A2 @ X @ Z4 )
% 3.30/1.71 => ( Y = Z4 ) ) )
% 3.30/1.71 => ( right_unique @ A @ B @ A2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_200_right__uniqueD,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o,X2: A,Y2: B,Z2: B] :
% 3.30/1.71 ( ( right_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( A2 @ X2 @ Y2 )
% 3.30/1.71 => ( ( A2 @ X2 @ Z2 )
% 3.30/1.71 => ( Y2 = Z2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_201_left__uniqueI,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ! [X: A,Y: A,Z4: B] :
% 3.30/1.71 ( ( A2 @ X @ Z4 )
% 3.30/1.71 => ( ( A2 @ Y @ Z4 )
% 3.30/1.71 => ( X = Y ) ) )
% 3.30/1.71 => ( left_unique @ A @ B @ A2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_202_left__uniqueD,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,A2: A > B > $o,X2: A,Z2: B,Y2: A] :
% 3.30/1.71 ( ( left_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( A2 @ X2 @ Z2 )
% 3.30/1.71 => ( ( A2 @ Y2 @ Z2 )
% 3.30/1.71 => ( X2 = Y2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_203_llist_Oright__unique__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( right_unique @ A @ B @ R )
% 3.30/1.71 => ( right_unique @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_204_llist_Oleft__unique__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( left_unique @ A @ B @ R )
% 3.30/1.71 => ( left_unique @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_205_swap__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( swap @ A @ B )
% 3.30/1.71 = ( ^ [A5: A,B5: A,F2: A > B] : ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F2 @ A5 @ ( F2 @ B5 ) ) @ B5 @ ( F2 @ A5 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_206_right__unique__alt__def2,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( right_unique @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ R4 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ R4 @ (=>) )
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_207_eq__imp__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( right_unique @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ (=>) )
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ ^ [Y3: B,Z: B] : ( Y3 = Z ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_208_left__unique__transfer,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( right_total @ C @ D @ B2 )
% 3.30/1.71 => ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ (=>)
% 3.30/1.71 @ ( left_unique @ A @ C )
% 3.30/1.71 @ ( left_unique @ B @ D ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_209_right__unique__transfer,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( right_total @ C @ D @ B2 )
% 3.30/1.71 => ( ( bi_unique @ C @ D @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ (=>)
% 3.30/1.71 @ ( right_unique @ A @ C )
% 3.30/1.71 @ ( right_unique @ B @ D ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_210_rtranclp__parametric,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ ( A > A > $o ) @ ( B > B > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( transitive_rtranclp @ A )
% 3.30/1.71 @ ( transitive_rtranclp @ B ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_211_right__total__fun,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( right_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( right_total @ C @ D @ B2 )
% 3.30/1.71 => ( right_total @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_212_functional__converse__relation,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( left_unique @ A @ B @ R )
% 3.30/1.71 => ( ( right_total @ A @ B @ R )
% 3.30/1.71 => ! [Y6: B] :
% 3.30/1.71 ? [X: A] :
% 3.30/1.71 ( ( R @ X @ Y6 )
% 3.30/1.71 & ! [Ya3: A] :
% 3.30/1.71 ( ( R @ Ya3 @ Y6 )
% 3.30/1.71 => ( Ya3 = X ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_213_right__totalE,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o,Y2: B] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ~ ! [X: A] :
% 3.30/1.71 ~ ( A2 @ X @ Y2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_214_right__totalI,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: B > A > $o] :
% 3.30/1.71 ( ! [Y: A] :
% 3.30/1.71 ? [X7: B] : ( A2 @ X7 @ Y )
% 3.30/1.71 => ( right_total @ B @ A @ A2 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_215_right__total__eq,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( right_total @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_216_right__total__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( right_total @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ! [Y5: B] :
% 3.30/1.71 ? [X4: A] : ( R4 @ X4 @ Y5 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_217_llist_Oright__total__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ R )
% 3.30/1.71 => ( right_total @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_218_right__unique__fun,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( right_unique @ C @ D @ B2 )
% 3.30/1.71 => ( right_unique @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_219_transfer__forall__transfer_I3_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ (=>) ) @ (=>) @ ( transfer_forall @ A ) @ ( transfer_forall @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_220_transfer__forall__transfer_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ (=>)
% 3.30/1.71 @ ( transfer_forall @ A )
% 3.30/1.71 @ ( transfer_forall @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_221_right__total__parametric,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ C @ D @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( right_total @ A @ C )
% 3.30/1.71 @ ( right_total @ B @ D ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_222_reflp__transfer_I2_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2 @ (=>) ) ) @ (=>) @ ( reflp @ A ) @ ( reflp @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_223_reflp__transfer_I3_J,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > A > $o ) @ ( B > B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ (=>)
% 3.30/1.71 @ ( reflp @ A )
% 3.30/1.71 @ ( reflp @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_224_Domainp__forall__transfer,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,A2: A > B > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > $o ) @ ( B > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( transfer_bforall @ A @ ( domainp @ A @ B @ A2 ) )
% 3.30/1.71 @ ( transfer_forall @ B ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_225_left__total__parametric,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,D: $tType,B: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ C @ D @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( A > C > $o ) @ ( B > D > $o ) @ $o @ $o
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( C > $o ) @ ( D > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ ( left_total @ A @ C )
% 3.30/1.71 @ ( left_total @ B @ D ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_226_left__total__fun,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( left_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( left_total @ C @ D @ B2 )
% 3.30/1.71 => ( left_total @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_227_functional__relation,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( right_unique @ A @ B @ R )
% 3.30/1.71 => ( ( left_total @ A @ B @ R )
% 3.30/1.71 => ! [X7: A] :
% 3.30/1.71 ? [Xa2: B] :
% 3.30/1.71 ( ( R @ X7 @ Xa2 )
% 3.30/1.71 & ! [Y6: B] :
% 3.30/1.71 ( ( R @ X7 @ Y6 )
% 3.30/1.71 => ( Y6 = Xa2 ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_228_left__unique__fun,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,D: $tType,C: $tType,A2: A > B > $o,B2: C > D > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( left_unique @ C @ D @ B2 )
% 3.30/1.71 => ( left_unique @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ A @ B @ C @ D @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_229_left__total__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( left_total @ A @ B )
% 3.30/1.71 = ( ^ [R4: A > B > $o] :
% 3.30/1.71 ! [X4: A] :
% 3.30/1.71 ( ^ [P4: B > $o] :
% 3.30/1.71 ? [X6: B] : ( P4 @ X6 )
% 3.30/1.71 @ ( R4 @ X4 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_230_left__total__eq,axiom,
% 3.30/1.71 ! [A: $tType] :
% 3.30/1.71 ( left_total @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_231_left__totalI,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ! [X: A] :
% 3.30/1.71 ? [X12: B] : ( R @ X @ X12 )
% 3.30/1.71 => ( left_total @ A @ B @ R ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_232_left__totalE,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ R )
% 3.30/1.71 => ! [X7: A] :
% 3.30/1.71 ? [X13: B] : ( R @ X7 @ X13 ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_233_llist_Oleft__total__rel,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ R )
% 3.30/1.71 => ( left_total @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coindu1486289336t_all2 @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_234_bi__totalI,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,R: A > B > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ R )
% 3.30/1.71 => ( ( right_total @ A @ B @ R )
% 3.30/1.71 => ( bi_total @ A @ B @ R ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_235_bi__total__alt__def,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType] :
% 3.30/1.71 ( ( bi_total @ A @ B )
% 3.30/1.71 = ( ^ [A6: A > B > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ A6 )
% 3.30/1.71 & ( right_total @ A @ B @ A6 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_236_lhd__lfilter,axiom,
% 3.30/1.71 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 3.30/1.71 ( ( coinductive_lhd @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 3.30/1.71 = ( coinductive_lhd @ A @ ( coindu218763757pWhile @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ Xs ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_237_relcompp__transfer,axiom,
% 3.30/1.71 ! [C: $tType,A: $tType,E: $tType,F3: $tType,B: $tType,D: $tType,B2: A > B > $o,A2: C > D > $o,C2: E > F3 > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ B2 )
% 3.30/1.71 => ( bNF_rel_fun @ ( C > A > $o ) @ ( D > B > $o ) @ ( ( A > E > $o ) > C > E > $o ) @ ( ( B > F3 > $o ) > D > F3 > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ ( A > $o ) @ ( B > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ $o @ $o @ B2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ ( A > E > $o ) @ ( B > F3 > $o ) @ ( C > E > $o ) @ ( D > F3 > $o )
% 3.30/1.71 @ ( bNF_rel_fun @ A @ B @ ( E > $o ) @ ( F3 > $o ) @ B2
% 3.30/1.71 @ ( bNF_rel_fun @ E @ F3 @ $o @ $o @ C2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) )
% 3.30/1.71 @ ( bNF_rel_fun @ C @ D @ ( E > $o ) @ ( F3 > $o ) @ A2
% 3.30/1.71 @ ( bNF_rel_fun @ E @ F3 @ $o @ $o @ C2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z ) ) ) )
% 3.30/1.71 @ ( relcompp @ C @ A @ E )
% 3.30/1.71 @ ( relcompp @ D @ B @ F3 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_238_pcr__Domainp__par__left__total,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,B2: A > B > $o,P: A > $o,A2: C > A > $o,P2: C > $o] :
% 3.30/1.71 ( ( ( domainp @ A @ B @ B2 )
% 3.30/1.71 = P )
% 3.30/1.71 => ( ( left_total @ C @ A @ A2 )
% 3.30/1.71 => ( ( bNF_rel_fun @ C @ A @ $o @ $o @ A2
% 3.30/1.71 @ ^ [Y3: $o,Z: $o] : ( Y3 = Z )
% 3.30/1.71 @ P2
% 3.30/1.71 @ P )
% 3.30/1.71 => ( ( domainp @ C @ B @ ( relcompp @ C @ A @ B @ A2 @ B2 ) )
% 3.30/1.71 = P2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_239_right__unique__OO,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 3.30/1.71 ( ( right_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( right_unique @ B @ C @ B2 )
% 3.30/1.71 => ( right_unique @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_240_right__total__OO,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 3.30/1.71 ( ( right_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( right_total @ B @ C @ B2 )
% 3.30/1.71 => ( right_total @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_241_pcr__Domainp__total,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,B2: A > B > $o,A2: C > A > $o,P: C > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ B2 )
% 3.30/1.71 => ( ( ( domainp @ C @ A @ A2 )
% 3.30/1.71 = P )
% 3.30/1.71 => ( ( domainp @ C @ B @ ( relcompp @ C @ A @ B @ A2 @ B2 ) )
% 3.30/1.71 = P ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_242_left__total__OO,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 3.30/1.71 ( ( left_total @ A @ B @ R )
% 3.30/1.71 => ( ( left_total @ B @ C @ S )
% 3.30/1.71 => ( left_total @ A @ C @ ( relcompp @ A @ B @ C @ R @ S ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_243_bi__unique__OO,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 3.30/1.71 ( ( bi_unique @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_unique @ B @ C @ B2 )
% 3.30/1.71 => ( bi_unique @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_244_bi__total__OO,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,A2: A > B > $o,B2: B > C > $o] :
% 3.30/1.71 ( ( bi_total @ A @ B @ A2 )
% 3.30/1.71 => ( ( bi_total @ B @ C @ B2 )
% 3.30/1.71 => ( bi_total @ A @ C @ ( relcompp @ A @ B @ C @ A2 @ B2 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_245_lhd__LCons,axiom,
% 3.30/1.71 ! [A: $tType,X21: A,X222: coinductive_llist @ A] :
% 3.30/1.71 ( ( coinductive_lhd @ A @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 3.30/1.71 = X21 ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_246_lhd__iterates,axiom,
% 3.30/1.71 ! [A: $tType,F: A > A,X2: A] :
% 3.30/1.71 ( ( coinductive_lhd @ A @ ( coinductive_iterates @ A @ F @ X2 ) )
% 3.30/1.71 = X2 ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_247_unfold__llist_Osimps_I3_J,axiom,
% 3.30/1.71 ! [B: $tType,A: $tType,P3: A > $o,A3: A,G21: A > B,G22: A > A] :
% 3.30/1.71 ( ~ ( P3 @ A3 )
% 3.30/1.71 => ( ( coinductive_lhd @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A3 ) )
% 3.30/1.71 = ( G21 @ A3 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_248_llist_Ocorec__sel_I1_J,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,P3: C > $o,A3: C,G21: C > A,Q22: C > $o,G221: C > ( coinductive_llist @ A ),G222: C > C] :
% 3.30/1.71 ( ~ ( P3 @ A3 )
% 3.30/1.71 => ( ( coinductive_lhd @ A @ ( coindu1259883913_llist @ C @ A @ P3 @ G21 @ Q22 @ G221 @ G222 @ A3 ) )
% 3.30/1.71 = ( G21 @ A3 ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_249_eq__comp__r,axiom,
% 3.30/1.71 ! [A: $tType,R: A > A > $o] :
% 3.30/1.71 ( ( relcompp @ A @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ ( relcompp @ A @ A @ A @ R
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z ) ) )
% 3.30/1.71 = R ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_250_llist_Orel__compp,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 3.30/1.71 ( ( coindu1486289336t_all2 @ A @ C @ ( relcompp @ A @ B @ C @ R @ S ) )
% 3.30/1.71 = ( relcompp @ ( coinductive_llist @ A ) @ ( coinductive_llist @ B ) @ ( coinductive_llist @ C ) @ ( coindu1486289336t_all2 @ A @ B @ R ) @ ( coindu1486289336t_all2 @ B @ C @ S ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_251_OOO__eq__quotient3,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,Abs22: B > C,Rep22: C > B] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 3.30/1.71 => ( ( quotient3 @ B @ C
% 3.30/1.71 @ ^ [Y3: B,Z: B] : ( Y3 = Z )
% 3.30/1.71 @ Abs22
% 3.30/1.71 @ Rep22 )
% 3.30/1.71 => ( quotient3 @ A @ C
% 3.30/1.71 @ ( relcompp @ A @ A @ A @ R1
% 3.30/1.71 @ ( relcompp @ A @ A @ A
% 3.30/1.71 @ ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.30/1.71 @ R1 ) )
% 3.30/1.71 @ ( comp @ B @ C @ A @ Abs22 @ Abs12 )
% 3.30/1.71 @ ( comp @ B @ A @ C @ Rep12 @ Rep22 ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_252_OOO__quotient3,axiom,
% 3.30/1.71 ! [A: $tType,B: $tType,C: $tType,R1: A > A > $o,Abs12: A > B,Rep12: B > A,R2: B > B > $o,Abs22: B > C,Rep22: C > B,R23: A > A > $o] :
% 3.30/1.71 ( ( quotient3 @ A @ B @ R1 @ Abs12 @ Rep12 )
% 3.30/1.71 => ( ( quotient3 @ B @ C @ R2 @ Abs22 @ Rep22 )
% 3.30/1.71 => ( ! [X: A,Y: A] :
% 3.30/1.71 ( ( R23 @ X @ Y )
% 3.30/1.71 => ( ( R1 @ X @ X )
% 3.30/1.71 => ( ( R1 @ Y @ Y )
% 3.30/1.71 => ( R2 @ ( Abs12 @ X ) @ ( Abs12 @ Y ) ) ) ) )
% 3.30/1.71 => ( ! [X: B,Y: B] :
% 3.30/1.71 ( ( R2 @ X @ Y )
% 3.30/1.71 => ( R23 @ ( Rep12 @ X ) @ ( Rep12 @ Y ) ) )
% 3.30/1.71 => ( quotient3 @ A @ C @ ( relcompp @ A @ A @ A @ R1 @ ( relcompp @ A @ A @ A @ R23 @ R1 ) ) @ ( comp @ B @ C @ A @ Abs22 @ Abs12 ) @ ( comp @ B @ A @ C @ Rep12 @ Rep22 ) ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_253_left__unique__OO,axiom,
% 3.30/1.71 ! [A: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 3.30/1.71 ( ( left_unique @ A @ B @ R )
% 3.30/1.71 => ( ( left_unique @ B @ C @ S )
% 3.30/1.71 => ( left_unique @ A @ C @ ( relcompp @ A @ B @ C @ R @ S ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_254_fun_Orel__compp,axiom,
% 3.30/1.71 ! [A: $tType,D: $tType,C: $tType,B: $tType,R: A > B > $o,S: B > C > $o] :
% 3.30/1.71 ( ( bNF_rel_fun @ D @ D @ A @ C
% 3.30/1.71 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.71 @ ( relcompp @ A @ B @ C @ R @ S ) )
% 3.30/1.71 = ( relcompp @ ( D > A ) @ ( D > B ) @ ( D > C )
% 3.30/1.71 @ ( bNF_rel_fun @ D @ D @ A @ B
% 3.30/1.71 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.71 @ R )
% 3.30/1.71 @ ( bNF_rel_fun @ D @ D @ B @ C
% 3.30/1.71 @ ^ [Y3: D,Z: D] : ( Y3 = Z )
% 3.30/1.71 @ S ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(fact_255_neg__fun__distr2,axiom,
% 3.30/1.71 ! [F3: $tType,E: $tType,A: $tType,B: $tType,D: $tType,C: $tType,R7: A > B > $o,S5: C > D > $o,R: E > A > $o,S: F3 > C > $o] :
% 3.30/1.71 ( ( right_unique @ A @ B @ R7 )
% 3.30/1.71 => ( ( left_total @ A @ B @ R7 )
% 3.30/1.71 => ( ( left_unique @ C @ D @ S5 )
% 3.30/1.71 => ( ( right_total @ C @ D @ S5 )
% 3.30/1.71 => ( ord_less_eq @ ( ( E > F3 ) > ( B > D ) > $o ) @ ( bNF_rel_fun @ E @ B @ F3 @ D @ ( relcompp @ E @ A @ B @ R @ R7 ) @ ( relcompp @ F3 @ C @ D @ S @ S5 ) ) @ ( relcompp @ ( E > F3 ) @ ( A > C ) @ ( B > D ) @ ( bNF_rel_fun @ E @ A @ F3 @ C @ R @ S ) @ ( bNF_rel_fun @ A @ B @ C @ D @ R7 @ S5 ) ) ) ) ) ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(help_If_3_1_T,axiom,
% 3.30/1.71 ! [P: $o] :
% 3.30/1.71 ( ( P = $true )
% 3.30/1.71 | ( P = $false ) ) ).
% 3.30/1.71
% 3.30/1.71 thf(help_If_2_1_T,axiom,
% 3.30/1.71 ! [A: $tType,X2: A,Y2: A] :
% 3.30/1.71 ( ( if @ A @ $false @ X2 @ Y2 )
% 3.30/1.71 = Y2 ) ).
% 3.30/1.71
% 3.30/1.71 thf(help_If_1_1_T,axiom,
% 3.30/1.71 ! [A: $tType,X2: A,Y2: A] :
% 3.30/1.71 ( ( if @ A @ $true @ X2 @ Y2 )
% 3.30/1.71 = X2 ) ).
% 3.30/1.71
% 3.30/1.71 thf(conj_0,conjecture,
% 3.30/1.71 bNF_rel_fun @ ( coinductive_llist @ a ) @ ( coinductive_llist @ b ) @ ( coinductive_llist @ a ) @ ( coinductive_llist @ b ) @ ( coindu1486289336t_all2 @ a @ b @ a2 ) @ ( coindu1486289336t_all2 @ a @ b @ a2 ) @ ( lMirro427583474mirror @ a ) @ ( lMirro427583474mirror @ b ) ).
% 3.30/1.71 ------------------------
% 3.30/1.75 % (25347)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_25247 for (2999ds/4Mi)
% 3.30/1.75 % (25352)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/18Mi)
% 3.30/1.75 % (25351)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_25247 for (2999ds/275Mi)
% 3.30/1.75 % (25349)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/2Mi)
% 3.30/1.75 % (25348)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_25247 for (2999ds/27Mi)
% 3.30/1.75 % (25350)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_25247 for (2999ds/2Mi)
% 3.30/1.75 % (25346)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/183Mi)
% 3.30/1.75 % (25349)Instruction limit reached!
% 3.30/1.75 % (25349)------------------------------
% 3.30/1.75 % (25349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.75 % (25349)Termination reason: Unknown
% 3.30/1.75 % (25349)Termination phase: shuffling
% 3.30/1.75
% 3.30/1.75 % (25349)Memory used [KB]: 1535
% 3.30/1.75 % (25349)Time elapsed: 0.003 s
% 3.30/1.75 % (25349)Instructions burned: 2 (million)
% 3.30/1.75 % (25349)------------------------------
% 3.30/1.75 % (25349)------------------------------
% 3.30/1.75 % (25350)Instruction limit reached!
% 3.30/1.75 % (25350)------------------------------
% 3.30/1.75 % (25350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.75 % (25350)Termination reason: Unknown
% 3.30/1.75 % (25350)Termination phase: shuffling
% 3.30/1.75
% 3.30/1.75 % (25350)Memory used [KB]: 1535
% 3.30/1.75 % (25350)Time elapsed: 0.003 s
% 3.30/1.75 % (25350)Instructions burned: 2 (million)
% 3.30/1.75 % (25350)------------------------------
% 3.30/1.75 % (25350)------------------------------
% 3.30/1.75 % (25347)Instruction limit reached!
% 3.30/1.75 % (25347)------------------------------
% 3.30/1.75 % (25347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.75 % (25347)Termination reason: Unknown
% 3.30/1.75 % (25347)Termination phase: shuffling
% 3.30/1.75
% 3.30/1.75 % (25347)Memory used [KB]: 1663
% 3.30/1.75 % (25347)Time elapsed: 0.004 s
% 3.30/1.75 % (25347)Instructions burned: 4 (million)
% 3.30/1.75 % (25347)------------------------------
% 3.30/1.75 % (25347)------------------------------
% 3.30/1.76 % (25352)Instruction limit reached!
% 3.30/1.76 % (25352)------------------------------
% 3.30/1.76 % (25352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.76 % (25352)Termination reason: Unknown
% 3.30/1.76 % (25352)Termination phase: shuffling
% 3.30/1.76
% 3.30/1.76 % (25352)Memory used [KB]: 1918
% 3.30/1.76 % (25352)Time elapsed: 0.011 s
% 3.30/1.76 % (25352)Instructions burned: 19 (million)
% 3.30/1.76 % (25352)------------------------------
% 3.30/1.76 % (25352)------------------------------
% 3.30/1.76 % (25348)Instruction limit reached!
% 3.30/1.76 % (25348)------------------------------
% 3.30/1.76 % (25348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.76 % (25348)Termination reason: Unknown
% 3.30/1.76 % (25348)Termination phase: shuffling
% 3.30/1.76
% 3.30/1.76 % (25348)Memory used [KB]: 2046
% 3.30/1.76 % (25348)Time elapsed: 0.016 s
% 3.30/1.76 % (25348)Instructions burned: 29 (million)
% 3.30/1.76 % (25348)------------------------------
% 3.30/1.76 % (25348)------------------------------
% 3.30/1.77 % (25353)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/3Mi)
% 3.30/1.77 % (25354)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_25247 for (2999ds/37Mi)
% 3.30/1.77 % (25355)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_25247 for (2999ds/15Mi)
% 3.30/1.77 % (25353)Instruction limit reached!
% 3.30/1.77 % (25353)------------------------------
% 3.30/1.77 % (25353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.77 % (25353)Termination reason: Unknown
% 3.30/1.77 % (25353)Termination phase: shuffling
% 3.30/1.77
% 3.30/1.77 % (25353)Memory used [KB]: 1535
% 3.30/1.77 % (25353)Time elapsed: 0.003 s
% 3.30/1.77 % (25353)Instructions burned: 3 (million)
% 3.30/1.77 % (25353)------------------------------
% 3.30/1.77 % (25353)------------------------------
% 3.30/1.78 % (25355)Instruction limit reached!
% 3.30/1.78 % (25355)------------------------------
% 3.30/1.78 % (25355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.78 % (25355)Termination reason: Unknown
% 3.30/1.78 % (25355)Termination phase: shuffling
% 3.30/1.78
% 3.30/1.78 % (25355)Memory used [KB]: 1791
% 3.30/1.78 % (25355)Time elapsed: 0.009 s
% 3.30/1.78 % (25355)Instructions burned: 15 (million)
% 3.30/1.78 % (25355)------------------------------
% 3.30/1.78 % (25355)------------------------------
% 3.30/1.78 % (25356)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_25247 for (2999ds/3Mi)
% 3.30/1.78 % (25356)Instruction limit reached!
% 3.30/1.78 % (25356)------------------------------
% 3.30/1.78 % (25356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.78 % (25356)Termination reason: Unknown
% 3.30/1.78 % (25356)Termination phase: shuffling
% 3.30/1.78
% 3.30/1.78 % (25356)Memory used [KB]: 1535
% 3.30/1.78 % (25356)Time elapsed: 0.003 s
% 3.30/1.78 % (25356)Instructions burned: 3 (million)
% 3.30/1.78 % (25356)------------------------------
% 3.30/1.78 % (25356)------------------------------
% 3.30/1.78 % (25357)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_25247 for (2999ds/1041Mi)
% 3.30/1.78 % (25354)Instruction limit reached!
% 3.30/1.78 % (25354)------------------------------
% 3.30/1.78 % (25354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.78 % (25354)Termination reason: Unknown
% 3.30/1.78 % (25358)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/7Mi)
% 3.30/1.78 % (25354)Termination phase: shuffling
% 3.30/1.78
% 3.30/1.78 % (25354)Memory used [KB]: 2302
% 3.30/1.78 % (25354)Time elapsed: 0.019 s
% 3.30/1.78 % (25354)Instructions burned: 37 (million)
% 3.30/1.79 % (25354)------------------------------
% 3.30/1.79 % (25354)------------------------------
% 3.30/1.79 % (25358)Instruction limit reached!
% 3.30/1.79 % (25358)------------------------------
% 3.30/1.79 % (25358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.79 % (25358)Termination reason: Unknown
% 3.30/1.79 % (25358)Termination phase: shuffling
% 3.30/1.79
% 3.30/1.79 % (25358)Memory used [KB]: 1663
% 3.30/1.79 % (25358)Time elapsed: 0.005 s
% 3.30/1.79 % (25358)Instructions burned: 7 (million)
% 3.30/1.79 % (25358)------------------------------
% 3.30/1.79 % (25358)------------------------------
% 3.30/1.79 % (25359)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/16Mi)
% 3.30/1.79 % (25360)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_25247 for (2999ds/3Mi)
% 3.30/1.79 % (25360)Instruction limit reached!
% 3.30/1.79 % (25360)------------------------------
% 3.30/1.79 % (25360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.30/1.79 % (25360)Termination reason: Unknown
% 3.30/1.79 % (25360)Termination phase: shuffling
% 3.30/1.79
% 3.30/1.79 % (25360)Memory used [KB]: 1535
% 3.30/1.79 % (25360)Time elapsed: 0.003 s
% 3.30/1.79 % (25360)Instructions burned: 3 (million)
% 3.30/1.79 % (25360)------------------------------
% 3.30/1.79 % (25360)------------------------------
% 3.36/1.80 % (25359)Instruction limit reached!
% 3.36/1.80 % (25359)------------------------------
% 3.36/1.80 % (25359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.80 % (25359)Termination reason: Unknown
% 3.36/1.80 % (25359)Termination phase: shuffling
% 3.36/1.80
% 3.36/1.80 % (25359)Memory used [KB]: 1791
% 3.36/1.80 % (25359)Time elapsed: 0.010 s
% 3.36/1.80 % (25359)Instructions burned: 18 (million)
% 3.36/1.80 % (25359)------------------------------
% 3.36/1.80 % (25359)------------------------------
% 3.36/1.80 % (25361)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_25247 for (2999ds/3Mi)
% 3.36/1.80 % (25361)Instruction limit reached!
% 3.36/1.80 % (25361)------------------------------
% 3.36/1.80 % (25361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.80 % (25361)Termination reason: Unknown
% 3.36/1.80 % (25361)Termination phase: shuffling
% 3.36/1.80
% 3.36/1.80 % (25361)Memory used [KB]: 1535
% 3.36/1.80 % (25361)Time elapsed: 0.003 s
% 3.36/1.80 % (25361)Instructions burned: 3 (million)
% 3.36/1.80 % (25361)------------------------------
% 3.36/1.80 % (25361)------------------------------
% 3.36/1.80 % (25362)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/7Mi)
% 3.36/1.81 % (25362)Instruction limit reached!
% 3.36/1.81 % (25362)------------------------------
% 3.36/1.81 % (25362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.81 % (25362)Termination reason: Unknown
% 3.36/1.81 % (25362)Termination phase: shuffling
% 3.36/1.81
% 3.36/1.81 % (25362)Memory used [KB]: 1663
% 3.36/1.81 % (25362)Time elapsed: 0.005 s
% 3.36/1.81 % (25362)Instructions burned: 7 (million)
% 3.36/1.81 % (25362)------------------------------
% 3.36/1.81 % (25362)------------------------------
% 3.36/1.81 % (25363)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/3Mi)
% 3.36/1.81 % (25363)Instruction limit reached!
% 3.36/1.81 % (25363)------------------------------
% 3.36/1.81 % (25363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.81 % (25363)Termination reason: Unknown
% 3.36/1.81 % (25363)Termination phase: shuffling
% 3.36/1.81
% 3.36/1.81 % (25363)Memory used [KB]: 1663
% 3.36/1.81 % (25363)Time elapsed: 0.003 s
% 3.36/1.81 % (25363)Instructions burned: 3 (million)
% 3.36/1.81 % (25363)------------------------------
% 3.36/1.81 % (25363)------------------------------
% 3.36/1.82 % (25364)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/4Mi)
% 3.36/1.82 % (25365)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/18Mi)
% 3.36/1.82 % (25364)Instruction limit reached!
% 3.36/1.82 % (25364)------------------------------
% 3.36/1.82 % (25364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.82 % (25364)Termination reason: Unknown
% 3.36/1.82 % (25364)Termination phase: shuffling
% 3.36/1.82
% 3.36/1.82 % (25364)Memory used [KB]: 1663
% 3.36/1.82 % (25364)Time elapsed: 0.004 s
% 3.36/1.82 % (25364)Instructions burned: 5 (million)
% 3.36/1.82 % (25364)------------------------------
% 3.36/1.82 % (25364)------------------------------
% 3.36/1.82 % (25366)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/710Mi)
% 3.36/1.83 % (25365)Instruction limit reached!
% 3.36/1.83 % (25365)------------------------------
% 3.36/1.83 % (25365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.83 % (25365)Termination reason: Unknown
% 3.36/1.83 % (25365)Termination phase: shuffling
% 3.36/1.83
% 3.36/1.83 % (25365)Memory used [KB]: 1918
% 3.36/1.83 % (25365)Time elapsed: 0.011 s
% 3.36/1.83 % (25365)Instructions burned: 19 (million)
% 3.36/1.83 % (25365)------------------------------
% 3.36/1.83 % (25365)------------------------------
% 3.36/1.83 % (25367)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25247 for (2999ds/6Mi)
% 3.36/1.83 % (25367)Instruction limit reached!
% 3.36/1.83 % (25367)------------------------------
% 3.36/1.83 % (25367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.83 % (25367)Termination reason: Unknown
% 3.36/1.83 % (25367)Termination phase: shuffling
% 3.36/1.83
% 3.36/1.83 % (25367)Memory used [KB]: 1663
% 3.36/1.83 % (25367)Time elapsed: 0.005 s
% 3.36/1.83 % (25367)Instructions burned: 7 (million)
% 3.36/1.83 % (25367)------------------------------
% 3.36/1.83 % (25367)------------------------------
% 3.36/1.83 % (25368)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/902Mi)
% 3.36/1.84 % (25346)Instruction limit reached!
% 3.36/1.84 % (25346)------------------------------
% 3.36/1.84 % (25346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.84 % (25346)Termination reason: Unknown
% 3.36/1.84 % (25346)Termination phase: Property scanning
% 3.36/1.84
% 3.36/1.84 % (25346)Memory used [KB]: 3070
% 3.36/1.84 % (25346)Time elapsed: 0.088 s
% 3.36/1.84 % (25346)Instructions burned: 185 (million)
% 3.36/1.84 % (25346)------------------------------
% 3.36/1.84 % (25346)------------------------------
% 3.36/1.84 % (25369)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/21Mi)
% 3.36/1.85 % (25370)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/5Mi)
% 3.36/1.85 % (25370)Instruction limit reached!
% 3.36/1.85 % (25370)------------------------------
% 3.36/1.85 % (25370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.85 % (25370)Termination reason: Unknown
% 3.36/1.85 % (25370)Termination phase: shuffling
% 3.36/1.85
% 3.36/1.85 % (25370)Memory used [KB]: 1663
% 3.36/1.85 % (25370)Time elapsed: 0.004 s
% 3.36/1.85 % (25370)Instructions burned: 5 (million)
% 3.36/1.85 % (25370)------------------------------
% 3.36/1.85 % (25370)------------------------------
% 3.36/1.85 % (25371)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/6Mi)
% 3.36/1.85 % (25369)Instruction limit reached!
% 3.36/1.85 % (25369)------------------------------
% 3.36/1.85 % (25369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.85 % (25369)Termination reason: Unknown
% 3.36/1.85 % (25369)Termination phase: shuffling
% 3.36/1.85
% 3.36/1.85 % (25369)Memory used [KB]: 1918
% 3.36/1.85 % (25369)Time elapsed: 0.012 s
% 3.36/1.85 % (25369)Instructions burned: 21 (million)
% 3.36/1.85 % (25369)------------------------------
% 3.36/1.85 % (25369)------------------------------
% 3.36/1.86 % (25371)Instruction limit reached!
% 3.36/1.86 % (25371)------------------------------
% 3.36/1.86 % (25371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.86 % (25371)Termination reason: Unknown
% 3.36/1.86 % (25371)Termination phase: shuffling
% 3.36/1.86
% 3.36/1.86 % (25371)Memory used [KB]: 1791
% 3.36/1.86 % (25371)Time elapsed: 0.005 s
% 3.36/1.86 % (25371)Instructions burned: 7 (million)
% 3.36/1.86 % (25371)------------------------------
% 3.36/1.86 % (25371)------------------------------
% 3.36/1.87 % (25372)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/377Mi)
% 3.36/1.87 % (25373)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/779Mi)
% 3.36/1.87 % (25374)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/19Mi)
% 3.36/1.88 % (25374)Instruction limit reached!
% 3.36/1.88 % (25374)------------------------------
% 3.36/1.88 % (25374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (25374)Termination reason: Unknown
% 3.36/1.88 % (25374)Termination phase: shuffling
% 3.36/1.88
% 3.36/1.88 % (25374)Memory used [KB]: 2046
% 3.36/1.88 % (25374)Time elapsed: 0.011 s
% 3.36/1.88 % (25374)Instructions burned: 20 (million)
% 3.36/1.88 % (25374)------------------------------
% 3.36/1.88 % (25374)------------------------------
% 3.36/1.88 % (25351)Instruction limit reached!
% 3.36/1.88 % (25351)------------------------------
% 3.36/1.88 % (25351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.88 % (25351)Termination reason: Unknown
% 3.36/1.88 % (25351)Termination phase: Saturation
% 3.36/1.88
% 3.36/1.88 % (25351)Memory used [KB]: 7803
% 3.36/1.88 % (25351)Time elapsed: 0.134 s
% 3.36/1.88 % (25351)Instructions burned: 276 (million)
% 3.36/1.88 % (25351)------------------------------
% 3.36/1.88 % (25351)------------------------------
% 3.36/1.90 % (25375)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/879Mi)
% 3.36/1.90 % (25376)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25247 for (2998ds/17Mi)
% 3.36/1.91 % (25376)Instruction limit reached!
% 3.36/1.91 % (25376)------------------------------
% 3.36/1.91 % (25376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.91 % (25376)Termination reason: Unknown
% 3.36/1.91 % (25376)Termination phase: shuffling
% 3.36/1.91
% 3.36/1.91 % (25376)Memory used [KB]: 1918
% 3.36/1.91 % (25376)Time elapsed: 0.010 s
% 3.36/1.91 % (25376)Instructions burned: 17 (million)
% 3.36/1.91 % (25376)------------------------------
% 3.36/1.91 % (25376)------------------------------
% 3.36/1.92 % (25377)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25247 for (2997ds/3Mi)
% 3.36/1.93 % (25377)Instruction limit reached!
% 3.36/1.93 % (25377)------------------------------
% 3.36/1.93 % (25377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.93 % (25377)Termination reason: Unknown
% 3.36/1.93 % (25377)Termination phase: shuffling
% 3.36/1.93
% 3.36/1.93 % (25377)Memory used [KB]: 1535
% 3.36/1.93 % (25377)Time elapsed: 0.003 s
% 3.36/1.93 % (25377)Instructions burned: 3 (million)
% 3.36/1.93 % (25377)------------------------------
% 3.36/1.93 % (25377)------------------------------
% 3.36/1.94 % (25378)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25247 for (2997ds/30Mi)
% 3.36/1.96 % (25378)Instruction limit reached!
% 3.36/1.96 % (25378)------------------------------
% 3.36/1.96 % (25378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.36/1.96 % (25378)Termination reason: Unknown
% 3.36/1.96 % (25378)Termination phase: shuffling
% 3.36/1.96
% 3.36/1.96 % (25378)Memory used [KB]: 2046
% 3.36/1.96 % (25378)Time elapsed: 0.017 s
% 3.36/1.96 % (25378)Instructions burned: 31 (million)
% 3.36/1.96 % (25378)------------------------------
% 3.36/1.96 % (25378)------------------------------
% 3.36/1.97 % (25379)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_25247 for (2997ds/127Mi)
% 5.34/2.03 % (25379)Instruction limit reached!
% 5.34/2.03 % (25379)------------------------------
% 5.34/2.03 % (25379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.34/2.03 % (25379)Termination reason: Unknown
% 5.34/2.03 % (25379)Termination phase: Function definition elimination
% 5.34/2.03
% 5.34/2.03 % (25379)Memory used [KB]: 2942
% 5.34/2.03 % (25379)Time elapsed: 0.062 s
% 5.34/2.03 % (25379)Instructions burned: 128 (million)
% 5.34/2.03 % (25379)------------------------------
% 5.34/2.03 % (25379)------------------------------
% 5.34/2.04 % (25372)Instruction limit reached!
% 5.34/2.04 % (25372)------------------------------
% 5.34/2.04 % (25372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.34/2.04 % (25372)Termination reason: Unknown
% 5.34/2.04 % (25372)Termination phase: Saturation
% 5.34/2.04
% 5.34/2.04 % (25372)Memory used [KB]: 8059
% 5.34/2.04 % (25372)Time elapsed: 0.174 s
% 5.34/2.04 % (25372)Instructions burned: 378 (million)
% 5.34/2.04 % (25372)------------------------------
% 5.34/2.04 % (25372)------------------------------
% 5.34/2.05 % (25380)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_25247 for (2996ds/100Mi)
% 5.34/2.06 % (25381)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_25247 for (2996ds/3Mi)
% 5.34/2.06 % (25381)Instruction limit reached!
% 5.34/2.06 % (25381)------------------------------
% 5.34/2.06 % (25381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.34/2.06 % (25381)Termination reason: Unknown
% 5.34/2.06 % (25381)Termination phase: shuffling
% 5.34/2.06
% 5.34/2.06 % (25381)Memory used [KB]: 1663
% 5.34/2.06 % (25381)Time elapsed: 0.003 s
% 5.34/2.06 % (25381)Instructions burned: 3 (million)
% 5.34/2.06 % (25381)------------------------------
% 5.34/2.06 % (25381)------------------------------
% 5.34/2.07 % (25382)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_25247 for (2996ds/20Mi)
% 5.34/2.08 % (25382)Instruction limit reached!
% 5.34/2.08 % (25382)------------------------------
% 5.34/2.08 % (25382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.34/2.08 % (25382)Termination reason: Unknown
% 5.34/2.08 % (25382)Termination phase: shuffling
% 5.34/2.08
% 5.34/2.08 % (25382)Memory used [KB]: 1918
% 5.34/2.08 % (25382)Time elapsed: 0.012 s
% 5.34/2.08 % (25382)Instructions burned: 21 (million)
% 5.34/2.08 % (25382)------------------------------
% 5.34/2.08 % (25382)------------------------------
% 5.34/2.10 % (25380)Instruction limit reached!
% 5.34/2.10 % (25380)------------------------------
% 5.34/2.10 % (25380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.34/2.10 % (25380)Termination reason: Unknown
% 5.34/2.10 % (25380)Termination phase: Preprocessing 1
% 5.34/2.10
% 5.34/2.10 % (25380)Memory used [KB]: 2814
% 5.34/2.10 % (25380)Time elapsed: 0.048 s
% 5.34/2.10 % (25380)Instructions burned: 101 (million)
% 5.34/2.10 % (25380)------------------------------
% 5.34/2.10 % (25380)------------------------------
% 5.34/2.10 % (25383)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_25247 for (2996ds/86Mi)
% 5.34/2.11 % (25384)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_25247 for (2996ds/107Mi)
% 6.01/2.14 % (25383)Instruction limit reached!
% 6.01/2.14 % (25383)------------------------------
% 6.01/2.14 % (25383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.14 % (25383)Termination reason: Unknown
% 6.01/2.14 % (25383)Termination phase: Preprocessing 3
% 6.01/2.14
% 6.01/2.14 % (25383)Memory used [KB]: 2814
% 6.01/2.14 % (25383)Time elapsed: 0.044 s
% 6.01/2.14 % (25383)Instructions burned: 87 (million)
% 6.01/2.14 % (25383)------------------------------
% 6.01/2.14 % (25383)------------------------------
% 6.01/2.15 % (25366)Instruction limit reached!
% 6.01/2.15 % (25366)------------------------------
% 6.01/2.15 % (25366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.15 % (25366)Termination reason: Unknown
% 6.01/2.15 % (25366)Termination phase: Saturation
% 6.01/2.15
% 6.01/2.15 % (25366)Memory used [KB]: 9722
% 6.01/2.15 % (25366)Time elapsed: 0.330 s
% 6.01/2.15 % (25366)Instructions burned: 710 (million)
% 6.01/2.15 % (25366)------------------------------
% 6.01/2.15 % (25366)------------------------------
% 6.01/2.16 % (25385)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_25247 for (2995ds/39Mi)
% 6.01/2.16 % (25384)Instruction limit reached!
% 6.01/2.16 % (25384)------------------------------
% 6.01/2.16 % (25384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.16 % (25384)Termination reason: Unknown
% 6.01/2.16 % (25384)Termination phase: Property scanning
% 6.01/2.16
% 6.01/2.16 % (25384)Memory used [KB]: 2942
% 6.01/2.16 % (25384)Time elapsed: 0.052 s
% 6.01/2.16 % (25384)Instructions burned: 107 (million)
% 6.01/2.16 % (25384)------------------------------
% 6.01/2.16 % (25384)------------------------------
% 6.01/2.17 % (25386)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_25247 for (2995ds/448Mi)
% 6.01/2.18 % (25385)Instruction limit reached!
% 6.01/2.18 % (25385)------------------------------
% 6.01/2.18 % (25385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.18 % (25385)Termination reason: Unknown
% 6.01/2.18 % (25385)Termination phase: shuffling
% 6.01/2.18
% 6.01/2.18 % (25385)Memory used [KB]: 2302
% 6.01/2.18 % (25385)Time elapsed: 0.020 s
% 6.01/2.18 % (25385)Instructions burned: 39 (million)
% 6.01/2.18 % (25385)------------------------------
% 6.01/2.18 % (25385)------------------------------
% 6.01/2.18 % (25387)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_25247 for (2995ds/46Mi)
% 6.01/2.19 % (25388)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_25247 for (2995ds/98Mi)
% 6.48/2.20 % (25387)Instruction limit reached!
% 6.48/2.20 % (25387)------------------------------
% 6.48/2.20 % (25387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.20 % (25387)Termination reason: Unknown
% 6.48/2.20 % (25387)Termination phase: shuffling
% 6.48/2.20
% 6.48/2.20 % (25387)Memory used [KB]: 2302
% 6.48/2.20 % (25387)Time elapsed: 0.024 s
% 6.48/2.20 % (25387)Instructions burned: 46 (million)
% 6.48/2.20 % (25387)------------------------------
% 6.48/2.20 % (25387)------------------------------
% 6.48/2.22 % (25389)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_25247 for (2995ds/507Mi)
% 6.48/2.23 % (25373)Instruction limit reached!
% 6.48/2.23 % (25373)------------------------------
% 6.48/2.23 % (25373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.23 % (25373)Termination reason: Unknown
% 6.48/2.23 % (25373)Termination phase: Saturation
% 6.48/2.23
% 6.48/2.23 % (25373)Memory used [KB]: 10106
% 6.48/2.23 % (25373)Time elapsed: 0.383 s
% 6.48/2.23 % (25373)Instructions burned: 779 (million)
% 6.48/2.23 % (25373)------------------------------
% 6.48/2.23 % (25373)------------------------------
% 6.48/2.24 % (25388)Instruction limit reached!
% 6.48/2.24 % (25388)------------------------------
% 6.48/2.24 % (25388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.24 % (25388)Termination reason: Unknown
% 6.48/2.24 % (25388)Termination phase: Preprocessing 1
% 6.48/2.24
% 6.48/2.24 % (25388)Memory used [KB]: 2814
% 6.48/2.24 % (25388)Time elapsed: 0.047 s
% 6.48/2.24 % (25388)Instructions burned: 99 (million)
% 6.48/2.24 % (25388)------------------------------
% 6.48/2.24 % (25388)------------------------------
% 6.48/2.25 % (25390)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/149Mi)
% 6.48/2.25 % (25368)Instruction limit reached!
% 6.48/2.25 % (25368)------------------------------
% 6.48/2.25 % (25368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.25 % (25368)Termination reason: Unknown
% 6.48/2.25 % (25368)Termination phase: Saturation
% 6.48/2.25
% 6.48/2.25 % (25368)Memory used [KB]: 9083
% 6.48/2.25 % (25368)Time elapsed: 0.420 s
% 6.48/2.25 % (25368)Instructions burned: 903 (million)
% 6.48/2.25 % (25368)------------------------------
% 6.48/2.25 % (25368)------------------------------
% 6.48/2.25 % (25391)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/39Mi)
% 6.48/2.27 % (25392)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/6Mi)
% 6.48/2.27 % (25392)Instruction limit reached!
% 6.48/2.27 % (25392)------------------------------
% 6.48/2.27 % (25392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.27 % (25392)Termination reason: Unknown
% 6.48/2.27 % (25392)Termination phase: shuffling
% 6.48/2.27
% 6.48/2.27 % (25392)Memory used [KB]: 1791
% 6.48/2.27 % (25392)Time elapsed: 0.005 s
% 6.48/2.27 % (25392)Instructions burned: 7 (million)
% 6.48/2.27 % (25392)------------------------------
% 6.48/2.27 % (25392)------------------------------
% 6.48/2.27 % (25391)Instruction limit reached!
% 6.48/2.27 % (25391)------------------------------
% 6.48/2.27 % (25391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.27 % (25391)Termination reason: Unknown
% 6.48/2.27 % (25391)Termination phase: shuffling
% 6.48/2.27
% 6.48/2.27 % (25391)Memory used [KB]: 2174
% 6.48/2.27 % (25391)Time elapsed: 0.021 s
% 6.48/2.27 % (25391)Instructions burned: 40 (million)
% 6.48/2.27 % (25391)------------------------------
% 6.48/2.27 % (25391)------------------------------
% 6.48/2.28 % (25357)Instruction limit reached!
% 6.48/2.28 % (25357)------------------------------
% 6.48/2.28 % (25357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.28 % (25357)Termination reason: Unknown
% 6.48/2.28 % (25357)Termination phase: Saturation
% 6.48/2.28
% 6.48/2.28 % (25357)Memory used [KB]: 10234
% 6.48/2.28 % (25357)Time elapsed: 0.497 s
% 6.48/2.28 % (25357)Instructions burned: 1042 (million)
% 6.48/2.28 % (25357)------------------------------
% 6.48/2.28 % (25357)------------------------------
% 6.48/2.29 % (25375)Instruction limit reached!
% 6.48/2.29 % (25375)------------------------------
% 6.48/2.29 % (25375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.48/2.29 % (25375)Termination reason: Unknown
% 6.48/2.29 % (25375)Termination phase: Saturation
% 6.48/2.29
% 6.48/2.29 % (25375)Memory used [KB]: 8955
% 6.48/2.29 % (25375)Time elapsed: 0.411 s
% 6.48/2.29 % (25375)Instructions burned: 881 (million)
% 6.48/2.29 % (25375)------------------------------
% 6.48/2.29 % (25375)------------------------------
% 6.48/2.29 % (25393)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/1087Mi)
% 6.48/2.29 % (25394)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/47Mi)
% 6.48/2.29 % (25395)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/44Mi)
% 6.93/2.30 % (25396)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_25247 for (2994ds/432Mi)
% 6.93/2.31 % (25394)Instruction limit reached!
% 6.93/2.31 % (25394)------------------------------
% 6.93/2.31 % (25394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.31 % (25394)Termination reason: Unknown
% 6.93/2.31 % (25394)Termination phase: shuffling
% 6.93/2.31
% 6.93/2.31 % (25394)Memory used [KB]: 2302
% 6.93/2.31 % (25394)Time elapsed: 0.025 s
% 6.93/2.31 % (25394)Instructions burned: 48 (million)
% 6.93/2.31 % (25394)------------------------------
% 6.93/2.31 % (25394)------------------------------
% 6.93/2.31 % (25395)Instruction limit reached!
% 6.93/2.31 % (25395)------------------------------
% 6.93/2.31 % (25395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.31 % (25395)Termination reason: Unknown
% 6.93/2.31 % (25395)Termination phase: shuffling
% 6.93/2.31
% 6.93/2.31 % (25395)Memory used [KB]: 2430
% 6.93/2.31 % (25395)Time elapsed: 0.023 s
% 6.93/2.31 % (25395)Instructions burned: 45 (million)
% 6.93/2.31 % (25395)------------------------------
% 6.93/2.31 % (25395)------------------------------
% 6.93/2.32 % (25390)Instruction limit reached!
% 6.93/2.32 % (25390)------------------------------
% 6.93/2.32 % (25390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.32 % (25390)Termination reason: Unknown
% 6.93/2.32 % (25390)Termination phase: Property scanning
% 6.93/2.32
% 6.93/2.32 % (25390)Memory used [KB]: 3070
% 6.93/2.32 % (25390)Time elapsed: 0.072 s
% 6.93/2.32 % (25390)Instructions burned: 150 (million)
% 6.93/2.32 % (25390)------------------------------
% 6.93/2.32 % (25390)------------------------------
% 6.93/2.33 % (25397)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/62Mi)
% 6.93/2.33 % (25398)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/31Mi)
% 6.93/2.33 % (25399)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/96Mi)
% 6.93/2.35 % (25398)Instruction limit reached!
% 6.93/2.35 % (25398)------------------------------
% 6.93/2.35 % (25398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.35 % (25398)Termination reason: Unknown
% 6.93/2.35 % (25398)Termination phase: shuffling
% 6.93/2.35
% 6.93/2.35 % (25398)Memory used [KB]: 2046
% 6.93/2.35 % (25398)Time elapsed: 0.017 s
% 6.93/2.35 % (25398)Instructions burned: 31 (million)
% 6.93/2.35 % (25398)------------------------------
% 6.93/2.35 % (25398)------------------------------
% 6.93/2.36 % (25397)Instruction limit reached!
% 6.93/2.36 % (25397)------------------------------
% 6.93/2.36 % (25397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.36 % (25397)Termination reason: Unknown
% 6.93/2.36 % (25397)Termination phase: Property scanning
% 6.93/2.36
% 6.93/2.36 % (25397)Memory used [KB]: 2814
% 6.93/2.36 % (25397)Time elapsed: 0.031 s
% 6.93/2.36 % (25397)Instructions burned: 63 (million)
% 6.93/2.36 % (25397)------------------------------
% 6.93/2.36 % (25397)------------------------------
% 6.93/2.36 % (25400)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/453Mi)
% 6.93/2.38 % (25401)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/71Mi)
% 6.93/2.38 % (25386)Instruction limit reached!
% 6.93/2.38 % (25386)------------------------------
% 6.93/2.38 % (25386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.38 % (25386)Termination reason: Unknown
% 6.93/2.38 % (25386)Termination phase: Saturation
% 6.93/2.38
% 6.93/2.38 % (25386)Memory used [KB]: 9594
% 6.93/2.38 % (25386)Time elapsed: 0.209 s
% 6.93/2.38 % (25386)Instructions burned: 449 (million)
% 6.93/2.38 % (25386)------------------------------
% 6.93/2.38 % (25386)------------------------------
% 6.93/2.38 % (25399)Instruction limit reached!
% 6.93/2.38 % (25399)------------------------------
% 6.93/2.38 % (25399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.93/2.38 % (25399)Termination reason: Unknown
% 6.93/2.38 % (25399)Termination phase: Preprocessing 3
% 6.93/2.38
% 6.93/2.38 % (25399)Memory used [KB]: 2814
% 6.93/2.38 % (25399)Time elapsed: 0.048 s
% 6.93/2.38 % (25399)Instructions burned: 98 (million)
% 6.93/2.38 % (25399)------------------------------
% 6.93/2.38 % (25399)------------------------------
% 6.93/2.39 % (25402)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/83Mi)
% 7.45/2.40 % (25403)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/11Mi)
% 7.45/2.40 % (25403)Instruction limit reached!
% 7.45/2.40 % (25403)------------------------------
% 7.45/2.40 % (25403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.40 % (25403)Termination reason: Unknown
% 7.45/2.40 % (25403)Termination phase: shuffling
% 7.45/2.40
% 7.45/2.40 % (25403)Memory used [KB]: 1791
% 7.45/2.40 % (25403)Time elapsed: 0.007 s
% 7.45/2.40 % (25403)Instructions burned: 12 (million)
% 7.45/2.40 % (25403)------------------------------
% 7.45/2.40 % (25403)------------------------------
% 7.45/2.41 % (25401)Instruction limit reached!
% 7.45/2.41 % (25401)------------------------------
% 7.45/2.41 % (25401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.41 % (25401)Termination reason: Unknown
% 7.45/2.41 % (25401)Termination phase: Property scanning
% 7.45/2.41
% 7.45/2.41 % (25401)Memory used [KB]: 2814
% 7.45/2.41 % (25401)Time elapsed: 0.037 s
% 7.45/2.41 % (25401)Instructions burned: 72 (million)
% 7.45/2.41 % (25401)------------------------------
% 7.45/2.41 % (25401)------------------------------
% 7.45/2.42 % (25404)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/41Mi)
% 7.45/2.43 % (25405)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25247 for (2993ds/6Mi)
% 7.45/2.43 % (25405)Instruction limit reached!
% 7.45/2.43 % (25405)------------------------------
% 7.45/2.43 % (25405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.43 % (25405)Termination reason: Unknown
% 7.45/2.43 % (25405)Termination phase: shuffling
% 7.45/2.43
% 7.45/2.43 % (25405)Memory used [KB]: 1663
% 7.45/2.43 % (25405)Time elapsed: 0.005 s
% 7.45/2.43 % (25405)Instructions burned: 7 (million)
% 7.45/2.43 % (25405)------------------------------
% 7.45/2.43 % (25405)------------------------------
% 7.45/2.43 % (25402)Instruction limit reached!
% 7.45/2.43 % (25402)------------------------------
% 7.45/2.43 % (25402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.43 % (25402)Termination reason: Unknown
% 7.45/2.43 % (25402)Termination phase: SInE selection
% 7.45/2.43
% 7.45/2.43 % (25402)Memory used [KB]: 2430
% 7.45/2.43 % (25402)Time elapsed: 0.041 s
% 7.45/2.43 % (25402)Instructions burned: 83 (million)
% 7.45/2.43 % (25402)------------------------------
% 7.45/2.43 % (25402)------------------------------
% 7.45/2.44 % (25404)Instruction limit reached!
% 7.45/2.44 % (25404)------------------------------
% 7.45/2.44 % (25404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.44 % (25404)Termination reason: Unknown
% 7.45/2.44 % (25404)Termination phase: shuffling
% 7.45/2.44
% 7.45/2.44 % (25404)Memory used [KB]: 2302
% 7.45/2.44 % (25404)Time elapsed: 0.021 s
% 7.45/2.44 % (25404)Instructions burned: 42 (million)
% 7.45/2.44 % (25404)------------------------------
% 7.45/2.44 % (25404)------------------------------
% 7.45/2.45 % (25406)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/150Mi)
% 7.45/2.45 % (25407)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/343Mi)
% 7.45/2.45 % (25408)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/109Mi)
% 7.45/2.46 % (25389)Instruction limit reached!
% 7.45/2.46 % (25389)------------------------------
% 7.45/2.46 % (25389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.46 % (25389)Termination reason: Unknown
% 7.45/2.46 % (25389)Termination phase: Saturation
% 7.45/2.46
% 7.45/2.46 % (25389)Memory used [KB]: 10362
% 7.45/2.46 % (25389)Time elapsed: 0.240 s
% 7.45/2.46 % (25389)Instructions burned: 508 (million)
% 7.45/2.46 % (25389)------------------------------
% 7.45/2.46 % (25389)------------------------------
% 7.45/2.47 % (25409)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/253Mi)
% 7.89/2.51 % (25408)Instruction limit reached!
% 7.89/2.51 % (25408)------------------------------
% 7.89/2.51 % (25408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.51 % (25408)Termination reason: Unknown
% 7.89/2.51 % (25408)Termination phase: Preprocessing 3
% 7.89/2.51
% 7.89/2.51 % (25408)Memory used [KB]: 2814
% 7.89/2.51 % (25408)Time elapsed: 0.053 s
% 7.89/2.51 % (25408)Instructions burned: 109 (million)
% 7.89/2.51 % (25408)------------------------------
% 7.89/2.51 % (25408)------------------------------
% 7.89/2.51 % (25396)Instruction limit reached!
% 7.89/2.51 % (25396)------------------------------
% 7.89/2.51 % (25396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.51 % (25396)Termination reason: Unknown
% 7.89/2.51 % (25396)Termination phase: Saturation
% 7.89/2.51
% 7.89/2.51 % (25396)Memory used [KB]: 4733
% 7.89/2.51 % (25396)Time elapsed: 0.209 s
% 7.89/2.51 % (25396)Instructions burned: 433 (million)
% 7.89/2.51 % (25396)------------------------------
% 7.89/2.51 % (25396)------------------------------
% 7.89/2.52 % (25406)Instruction limit reached!
% 7.89/2.52 % (25406)------------------------------
% 7.89/2.52 % (25406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.52 % (25406)Termination reason: Unknown
% 7.89/2.52 % (25406)Termination phase: Function definition elimination
% 7.89/2.52
% 7.89/2.52 % (25406)Memory used [KB]: 3198
% 7.89/2.52 % (25406)Time elapsed: 0.072 s
% 7.89/2.52 % (25406)Instructions burned: 150 (million)
% 7.89/2.52 % (25406)------------------------------
% 7.89/2.52 % (25406)------------------------------
% 7.89/2.52 % (25411)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/140Mi)
% 7.89/2.53 % (25412)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/614Mi)
% 7.89/2.53 % (25413)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_25247 for (2992ds/202Mi)
% 7.89/2.57 % (25400)Instruction limit reached!
% 7.89/2.57 % (25400)------------------------------
% 7.89/2.57 % (25400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.57 % (25400)Termination reason: Unknown
% 7.89/2.57 % (25400)Termination phase: Saturation
% 7.89/2.57
% 7.89/2.57 % (25400)Memory used [KB]: 9210
% 7.89/2.57 % (25400)Time elapsed: 0.210 s
% 7.89/2.57 % (25400)Instructions burned: 453 (million)
% 7.89/2.57 % (25400)------------------------------
% 7.89/2.57 % (25400)------------------------------
% 7.89/2.59 % (25414)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_25247 for (2991ds/339Mi)
% 7.89/2.59 % (25411)Instruction limit reached!
% 7.89/2.59 % (25411)------------------------------
% 7.89/2.59 % (25411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.59 % (25411)Termination reason: Unknown
% 7.89/2.59 % (25411)Termination phase: Saturation
% 7.89/2.59
% 7.89/2.59 % (25411)Memory used [KB]: 7675
% 7.89/2.59 % (25411)Time elapsed: 0.091 s
% 7.89/2.59 % (25411)Instructions burned: 140 (million)
% 7.89/2.59 % (25411)------------------------------
% 7.89/2.59 % (25411)------------------------------
% 7.89/2.59 % (25409)Instruction limit reached!
% 7.89/2.59 % (25409)------------------------------
% 7.89/2.59 % (25409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.59 % (25409)Termination reason: Unknown
% 7.89/2.59 % (25409)Termination phase: Saturation
% 7.89/2.59
% 7.89/2.59 % (25409)Memory used [KB]: 8315
% 7.89/2.59 % (25409)Time elapsed: 0.122 s
% 7.89/2.59 % (25409)Instructions burned: 253 (million)
% 7.89/2.59 % (25409)------------------------------
% 7.89/2.59 % (25409)------------------------------
% 8.72/2.61 % (25415)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_25247 for (2991ds/283Mi)
% 8.72/2.61 % (25416)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_25247 for (2991ds/134Mi)
% 8.72/2.61 % (25407)Instruction limit reached!
% 8.72/2.61 % (25407)------------------------------
% 8.72/2.61 % (25407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.72/2.61 % (25407)Termination reason: Unknown
% 8.72/2.61 % (25407)Termination phase: Saturation
% 8.72/2.61
% 8.72/2.61 % (25407)Memory used [KB]: 8571
% 8.72/2.61 % (25407)Time elapsed: 0.166 s
% 8.72/2.61 % (25407)Instructions burned: 344 (million)
% 8.72/2.61 % (25407)------------------------------
% 8.72/2.61 % (25407)------------------------------
% 8.72/2.63 % (25413)Instruction limit reached!
% 8.72/2.63 % (25413)------------------------------
% 8.72/2.63 % (25413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.72/2.63 % (25413)Termination reason: Unknown
% 8.72/2.63 % (25413)Termination phase: Saturation
% 8.72/2.63
% 8.72/2.63 % (25413)Memory used [KB]: 8443
% 8.72/2.63 % (25413)Time elapsed: 0.117 s
% 8.72/2.63 % (25413)Instructions burned: 203 (million)
% 8.72/2.63 % (25413)------------------------------
% 8.72/2.63 % (25413)------------------------------
% 8.72/2.63 % (25417)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_25247 for (2990ds/298Mi)
% 8.72/2.64 % (25418)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_25247 for (2990ds/192Mi)
% 8.72/2.67 % (25416)Instruction limit reached!
% 8.72/2.67 % (25416)------------------------------
% 8.72/2.67 % (25416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.72/2.67 % (25416)Termination reason: Unknown
% 8.72/2.67 % (25416)Termination phase: Function definition elimination
% 8.72/2.67
% 8.72/2.67 % (25416)Memory used [KB]: 2942
% 8.72/2.67 % (25416)Time elapsed: 0.065 s
% 8.72/2.67 % (25416)Instructions burned: 135 (million)
% 8.72/2.67 % (25416)------------------------------
% 8.72/2.67 % (25416)------------------------------
% 8.72/2.69 % (25419)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_25247 for (2990ds/258Mi)
% 9.08/2.73 % (25418)Instruction limit reached!
% 9.08/2.73 % (25418)------------------------------
% 9.08/2.73 % (25418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.73 % (25418)Termination reason: Unknown
% 9.08/2.73 % (25418)Termination phase: Saturation
% 9.08/2.73
% 9.08/2.73 % (25418)Memory used [KB]: 3198
% 9.08/2.73 % (25418)Time elapsed: 0.091 s
% 9.08/2.73 % (25418)Instructions burned: 193 (million)
% 9.08/2.73 % (25418)------------------------------
% 9.08/2.73 % (25418)------------------------------
% 9.08/2.74 % (25415)Instruction limit reached!
% 9.08/2.74 % (25415)------------------------------
% 9.08/2.74 % (25415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.74 % (25415)Termination reason: Unknown
% 9.08/2.74 % (25415)Termination phase: Saturation
% 9.08/2.74
% 9.08/2.74 % (25415)Memory used [KB]: 8059
% 9.08/2.74 % (25415)Time elapsed: 0.134 s
% 9.08/2.74 % (25415)Instructions burned: 284 (million)
% 9.08/2.74 % (25415)------------------------------
% 9.08/2.74 % (25415)------------------------------
% 9.08/2.74 % (25414)Instruction limit reached!
% 9.08/2.74 % (25414)------------------------------
% 9.08/2.74 % (25414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.74 % (25414)Termination reason: Unknown
% 9.08/2.74 % (25414)Termination phase: Saturation
% 9.08/2.74
% 9.08/2.74 % (25414)Memory used [KB]: 7675
% 9.08/2.74 % (25414)Time elapsed: 0.156 s
% 9.08/2.74 % (25414)Instructions burned: 339 (million)
% 9.08/2.74 % (25414)------------------------------
% 9.08/2.74 % (25414)------------------------------
% 9.08/2.75 % (25420)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_25247 for (2989ds/90Mi)
% 9.08/2.76 % (25421)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_25247 for (2989ds/231Mi)
% 9.08/2.76 % (25422)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_25247 for (2989ds/458Mi)
% 9.08/2.77 % (25417)Instruction limit reached!
% 9.08/2.77 % (25417)------------------------------
% 9.08/2.77 % (25417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.77 % (25417)Termination reason: Unknown
% 9.08/2.77 % (25417)Termination phase: Saturation
% 9.08/2.77
% 9.08/2.77 % (25417)Memory used [KB]: 8827
% 9.08/2.77 % (25417)Time elapsed: 0.138 s
% 9.08/2.77 % (25417)Instructions burned: 300 (million)
% 9.08/2.77 % (25417)------------------------------
% 9.08/2.77 % (25417)------------------------------
% 9.08/2.77 % (25419)First to succeed.
% 9.08/2.77 % (25419)Refutation found. Thanks to Tanya!
% 9.08/2.77 % SZS status Theorem for DTF2THF_25247
% 9.08/2.77 % SZS output start Proof for DTF2THF_25247
% 9.08/2.77 thf(type_def_6, type, coinductive_llist: ($tType) > $tType).
% 9.08/2.77 thf(type_def_7, type, itself: ($tType) > $tType).
% 9.08/2.77 thf(type_def_8, type, a: $tType).
% 9.08/2.77 thf(type_def_9, type, b: $tType).
% 9.08/2.77 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 9.08/2.77 thf(func_def_1, type, itself: ($tType) > $tType).
% 9.08/2.77 thf(func_def_2, type, b: $tType).
% 9.08/2.77 thf(func_def_3, type, a: $tType).
% 9.08/2.77 thf(func_def_4, type, bNF_rel_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1 > $o) > (X2 > X3 > $o) > (X0 > X2) > (X1 > X3) > $o)).
% 9.08/2.77 thf(func_def_5, type, coinductive_iterates: !>[X0: $tType]:((X0 > X0) > X0 > coinductive_llist @ X0)).
% 9.08/2.77 thf(func_def_6, type, coindu218763757pWhile: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 9.08/2.77 thf(func_def_7, type, coinductive_lfilter: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 9.08/2.77 thf(func_def_8, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 9.08/2.77 thf(func_def_9, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0)).
% 9.08/2.77 thf(func_def_10, type, coindu1259883913_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coinductive_llist @ X1) > (X0 > X0) > X0 > coinductive_llist @ X1)).
% 9.08/2.77 thf(func_def_11, type, coinductive_lhd: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 9.08/2.77 thf(func_def_12, type, coindu1486289336t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coinductive_llist @ X0 > coinductive_llist @ X1 > $o)).
% 9.08/2.77 thf(func_def_13, type, coinductive_lmap: !>[X0: $tType, X1: $tType]:((X0 > X1) > coinductive_llist @ X0 > coinductive_llist @ X1)).
% 9.08/2.77 thf(func_def_14, type, coindu543516966_llist: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 9.08/2.77 thf(func_def_15, type, coinductive_lmember: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > $o)).
% 9.08/2.77 thf(func_def_16, type, coindu501562517eWhile: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 9.08/2.77 thf(func_def_17, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1)).
% 9.08/2.77 thf(func_def_18, type, comple1396247847notone: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X1 > $o) > (X0 > X1) > $o)).
% 9.08/2.77 thf(func_def_19, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 9.08/2.77 thf(func_def_20, type, fun_upd: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1 > X0 > X1)).
% 9.08/2.77 thf(func_def_21, type, id: !>[X0: $tType]:(X0 > X0)).
% 9.08/2.77 thf(func_def_22, type, map_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > X1) > (X2 > X3) > (X1 > X2) > X0 > X3)).
% 9.08/2.77 thf(func_def_23, type, swap: !>[X0: $tType, X1: $tType]:(X0 > X0 > (X0 > X1) > X0 > X1)).
% 9.08/2.77 thf(func_def_24, type, ex1: !>[X0: $tType]:((X0 > $o) > $o)).
% 9.08/2.77 thf(func_def_25, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 9.08/2.77 thf(func_def_26, type, lMirro427583474mirror: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 9.08/2.77 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 9.08/2.77 thf(func_def_28, type, partial_fun_ord: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X2 > X0) > (X2 > X1) > $o)).
% 9.08/2.77 thf(func_def_29, type, type: !>[X0: $tType]:(itself @ X0)).
% 9.08/2.77 thf(func_def_30, type, bex1_rel: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > $o) > $o)).
% 9.08/2.77 thf(func_def_31, type, quotient3: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X0 > X1) > (X1 > X0) > $o)).
% 9.08/2.77 thf(func_def_32, type, domainp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0 > $o)).
% 9.08/2.77 thf(func_def_33, type, reflp: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 9.08/2.77 thf(func_def_34, type, relcompp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > $o) > (X1 > X2 > $o) > X0 > X2 > $o)).
% 9.08/2.77 thf(func_def_35, type, bi_total: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > $o)).
% 9.08/2.77 thf(func_def_36, type, bi_unique: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > $o)).
% 9.08/2.77 thf(func_def_37, type, left_total: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > $o)).
% 9.08/2.77 thf(func_def_38, type, left_unique: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > $o)).
% 9.08/2.77 thf(func_def_39, type, rev_implies: $o > $o > $o).
% 9.08/2.77 thf(func_def_40, type, right_total: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > $o)).
% 9.08/2.77 thf(func_def_41, type, right_unique: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > $o)).
% 9.08/2.77 thf(func_def_42, type, transfer_bforall: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 9.08/2.77 thf(func_def_43, type, transfer_forall: !>[X0: $tType]:((X0 > $o) > $o)).
% 9.08/2.77 thf(func_def_44, type, transitive_rtranclp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > X0 > $o)).
% 9.08/2.77 thf(func_def_45, type, a2: a > b > $o).
% 9.08/2.77 thf(func_def_62, type, sK0: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_63, type, sK1: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_64, type, sK2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_65, type, sK3: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_66, type, sK4: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_67, type, sK5: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_68, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 9.08/2.77 thf(func_def_69, type, sK7: !>[X0: $tType]:((X0 > X0) > (X0 > coinductive_llist @ X0) > X0)).
% 9.08/2.77 thf(func_def_70, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 9.08/2.77 thf(func_def_71, type, sK9: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_72, type, sK10: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_73, type, sK11: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_74, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_75, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 9.08/2.77 thf(func_def_76, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X3 > X2) > (X0 > X1) > (X1 > X2 > $o) > (X0 > X3 > $o) > X0)).
% 9.08/2.77 thf(func_def_77, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X3 > X2) > (X0 > X1) > (X1 > X2 > $o) > (X0 > X3 > $o) > X3)).
% 9.08/2.77 thf(func_def_78, type, sK16: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_79, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_80, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X0)).
% 9.08/2.77 thf(func_def_81, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X1)).
% 9.08/2.77 thf(func_def_83, type, ph21: !>[X0: $tType]:(X0)).
% 9.08/2.77 thf(f832,plain,(
% 9.08/2.77 $false),
% 9.08/2.77 inference(subsumption_resolution,[status(thm)],[f824,f793])).
% 9.08/2.77 thf(f793,plain,(
% 9.08/2.77 ($true != (coindu1486289336t_all2 @ a @ b @ a2 @ (lMirro427583474mirror @ a @ (sK14 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2))) @ (lMirro427583474mirror @ b @ (sK15 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)))))),
% 9.08/2.77 inference(trivial_inequality_removal,[status(thm)],[f782])).
% 9.08/2.77 thf(f782,plain,(
% 9.08/2.77 ($true != $true) | ($true != (coindu1486289336t_all2 @ a @ b @ a2 @ (lMirro427583474mirror @ a @ (sK14 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2))) @ (lMirro427583474mirror @ b @ (sK15 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)))))),
% 9.08/2.77 inference(superposition,[status(thm)],[f722,f755])).
% 9.08/2.77 thf(f755,plain,(
% 9.08/2.77 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X0 > X1,X7 : X3 > X2,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o] : (($true = (bNF_rel_fun @ X0 @ X3 @ X1 @ X2 @ X4 @ X5 @ X6 @ X7)) | ($true != (X5 @ (X6 @ (sK14 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4)) @ (X7 @ (sK15 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4))))) )),
% 9.08/2.77 inference(cnf_transformation,[status(thm)],[f713])).
% 9.08/2.77 thf(f713,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o,X6 : X0 > X1,X7 : X3 > X2] : (($true = (bNF_rel_fun @ X0 @ X3 @ X1 @ X2 @ X4 @ X5 @ X6 @ X7)) | (($true = (X4 @ (sK14 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4) @ (sK15 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4))) & ($true != (X5 @ (X6 @ (sK14 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4)) @ (X7 @ (sK15 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4))))))),
% 9.08/2.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f678,f712])).
% 9.08/2.77 thf(f712,plain,(
% 9.08/2.77 ! [X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o,X6 : X0 > X1,X7 : X3 > X2] : (? [X8 : X0,X9 : X3] : (((X4 @ X8 @ X9) = $true) & ($true != (X5 @ (X6 @ X8) @ (X7 @ X9)))) => (($true = (X4 @ (sK14 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4) @ (sK15 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4))) & ($true != (X5 @ (X6 @ (sK14 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4)) @ (X7 @ (sK15 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4))))))),
% 9.08/2.77 introduced(definition,[],[choice_axiom])).
% 9.08/2.77 thf(f678,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o,X6 : X0 > X1,X7 : X3 > X2] : (($true = (bNF_rel_fun @ X0 @ X3 @ X1 @ X2 @ X4 @ X5 @ X6 @ X7)) | ? [X8 : X0,X9 : X3] : (((X4 @ X8 @ X9) = $true) & ($true != (X5 @ (X6 @ X8) @ (X7 @ X9)))))),
% 9.08/2.77 inference(ennf_transformation,[status(thm)],[f530])).
% 9.08/2.77 thf(f530,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o,X6 : X0 > X1,X7 : X3 > X2] : (! [X8 : X0,X9 : X3] : (((X4 @ X8 @ X9) = $true) => ($true = (X5 @ (X6 @ X8) @ (X7 @ X9)))) => ($true = (bNF_rel_fun @ X0 @ X3 @ X1 @ X2 @ X4 @ X5 @ X6 @ X7)))),
% 9.08/2.77 inference(fool_elimination,[status(thm)],[f529])).
% 9.08/2.77 thf(f529,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o,X6 : X0 > X1,X7 : X3 > X2] : (! [X8 : X0,X9 : X3] : ((X4 @ X8 @ X9) => (X5 @ (X6 @ X8) @ (X7 @ X9))) => (bNF_rel_fun @ X0 @ X3 @ X1 @ X2 @ X4 @ X5 @ X6 @ X7))),
% 9.08/2.77 inference(rectify,[status(thm)],[f4])).
% 9.08/2.77 thf(f4,axiom,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X3 : $tType,X2 : $tType,X8 : X0 > X2 > $o,X9 : X1 > X3 > $o,X10 : X0 > X1,X11 : X2 > X3] : (! [X12 : X0,X13 : X2] : ((X8 @ X12 @ X13) => (X9 @ (X10 @ X12) @ (X11 @ X13))) => (bNF_rel_fun @ X0 @ X2 @ X1 @ X3 @ X8 @ X9 @ X10 @ X11))),
% 9.08/2.77 file('/export/starexec/sandbox2/tmp/tmp.7OvFDdixfL/DTF2THF_25247.p',fact_3_rel__funI)).
% 9.08/2.77 thf(f722,plain,(
% 9.08/2.77 ((bNF_rel_fun @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ a @ coinductive_llist @ b @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2) @ lMirro427583474mirror @ a @ lMirro427583474mirror @ b) != $true)),
% 9.08/2.77 inference(cnf_transformation,[status(thm)],[f657])).
% 9.08/2.77 thf(f657,plain,(
% 9.08/2.77 ((bNF_rel_fun @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ a @ coinductive_llist @ b @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2) @ lMirro427583474mirror @ a @ lMirro427583474mirror @ b) != $true)),
% 9.08/2.77 inference(flattening,[status(thm)],[f488])).
% 9.08/2.77 thf(f488,plain,(
% 9.08/2.77 ~((bNF_rel_fun @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ a @ coinductive_llist @ b @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2) @ lMirro427583474mirror @ a @ lMirro427583474mirror @ b) = $true)),
% 9.08/2.77 inference(fool_elimination,[status(thm)],[f487])).
% 9.08/2.77 thf(f487,plain,(
% 9.08/2.77 ~(bNF_rel_fun @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ a @ coinductive_llist @ b @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2) @ lMirro427583474mirror @ a @ lMirro427583474mirror @ b)),
% 9.08/2.77 inference(rectify,[status(thm)],[f261])).
% 9.08/2.77 thf(f261,negated_conjecture,(
% 9.08/2.77 ~(bNF_rel_fun @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ a @ coinductive_llist @ b @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2) @ lMirro427583474mirror @ a @ lMirro427583474mirror @ b)),
% 9.08/2.77 inference(negated_conjecture,[status(cth)],[f260])).
% 9.08/2.77 thf(f260,conjecture,(
% 9.08/2.77 (bNF_rel_fun @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ a @ coinductive_llist @ b @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2) @ lMirro427583474mirror @ a @ lMirro427583474mirror @ b)),
% 9.08/2.77 file('/export/starexec/sandbox2/tmp/tmp.7OvFDdixfL/DTF2THF_25247.p',conj_0)).
% 9.08/2.77 thf(f824,plain,(
% 9.08/2.77 ($true = (coindu1486289336t_all2 @ a @ b @ a2 @ (lMirro427583474mirror @ a @ (sK14 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2))) @ (lMirro427583474mirror @ b @ (sK15 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)))))),
% 9.08/2.77 inference(trivial_inequality_removal,[status(thm)],[f796])).
% 9.08/2.77 thf(f796,plain,(
% 9.08/2.77 ($true != $true) | ($true = (coindu1486289336t_all2 @ a @ b @ a2 @ (lMirro427583474mirror @ a @ (sK14 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2))) @ (lMirro427583474mirror @ b @ (sK15 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)))))),
% 9.08/2.77 inference(superposition,[status(thm)],[f726,f787])).
% 9.08/2.77 thf(f787,plain,(
% 9.08/2.77 ($true = (coindu1486289336t_all2 @ a @ b @ a2 @ (sK14 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)) @ (sK15 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2))))),
% 9.08/2.77 inference(trivial_inequality_removal,[status(thm)],[f783])).
% 9.08/2.77 thf(f783,plain,(
% 9.08/2.77 ($true = (coindu1486289336t_all2 @ a @ b @ a2 @ (sK14 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)) @ (sK15 @ coinductive_llist @ a @ coinductive_llist @ a @ coinductive_llist @ b @ coinductive_llist @ b @ lMirro427583474mirror @ b @ lMirro427583474mirror @ a @ (coindu1486289336t_all2 @ a @ b @ a2) @ (coindu1486289336t_all2 @ a @ b @ a2)))) | ($true != $true)),
% 9.08/2.77 inference(superposition,[status(thm)],[f722,f756])).
% 9.08/2.77 thf(f756,plain,(
% 9.08/2.77 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X0 > X1,X7 : X3 > X2,X4 : X0 > X3 > $o,X5 : X1 > X2 > $o] : (($true = (X4 @ (sK14 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4) @ (sK15 @ X0 @ X1 @ X2 @ X3 @ X7 @ X6 @ X5 @ X4))) | ($true = (bNF_rel_fun @ X0 @ X3 @ X1 @ X2 @ X4 @ X5 @ X6 @ X7))) )),
% 9.08/2.77 inference(cnf_transformation,[status(thm)],[f713])).
% 9.08/2.77 thf(f726,plain,(
% 9.08/2.77 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : (($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (lMirro427583474mirror @ X0 @ X3) @ (lMirro427583474mirror @ X1 @ X4)) = $true)) )),
% 9.08/2.77 inference(cnf_transformation,[status(thm)],[f673])).
% 9.08/2.77 thf(f673,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : (($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (lMirro427583474mirror @ X0 @ X3) @ (lMirro427583474mirror @ X1 @ X4)) = $true))),
% 9.08/2.77 inference(ennf_transformation,[status(thm)],[f538])).
% 9.08/2.77 thf(f538,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : (($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) => ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (lMirro427583474mirror @ X0 @ X3) @ (lMirro427583474mirror @ X1 @ X4)) = $true))),
% 9.08/2.77 inference(fool_elimination,[status(thm)],[f537])).
% 9.08/2.77 thf(f537,plain,(
% 9.08/2.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (lMirro427583474mirror @ X0 @ X3) @ (lMirro427583474mirror @ X1 @ X4)))),
% 9.08/2.77 inference(rectify,[status(thm)],[f3])).
% 9.08/2.77 thf(f3,axiom,(
% 9.08/2.77 ! [X0 : $tType,X2 : $tType,X5 : X0 > X2 > $o,X6 : coinductive_llist @ X0,X7 : coinductive_llist @ X2] : ((coindu1486289336t_all2 @ X0 @ X2 @ X5 @ X6 @ X7) => (coindu1486289336t_all2 @ X0 @ X2 @ X5 @ (lMirro427583474mirror @ X0 @ X6) @ (lMirro427583474mirror @ X2 @ X7)))),
% 9.08/2.77 file('/export/starexec/sandbox2/tmp/tmp.7OvFDdixfL/DTF2THF_25247.p',fact_2_llist__all2__lmirrorI)).
% 9.08/2.77 % SZS output end Proof for DTF2THF_25247
% 9.08/2.77 % (25419)------------------------------
% 9.08/2.77 % (25419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.77 % (25419)Termination reason: Refutation
% 9.08/2.77
% 9.08/2.77 % (25419)Memory used [KB]: 7675
% 9.08/2.77 % (25419)Time elapsed: 0.082 s
% 9.08/2.77 % (25419)Instructions burned: 165 (million)
% 9.08/2.77 % (25419)------------------------------
% 9.08/2.77 % (25419)------------------------------
% 9.08/2.77 % (25345)Success in time 1.067 s
%------------------------------------------------------------------------------