ITP001 Axioms: ITP070^5.ax
%------------------------------------------------------------------------------
% File : ITP070^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : quotient_list^2.ax [Gau20]
% : HL4070^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 32 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 1120 ( 15 equ; 0 cnn)
% Maximal formula atoms : 67 ( 35 avg)
% Number of connectives : 2154 ( 0 ~; 0 |; 12 &;1911 @)
% ( 8 <=>; 223 =>; 0 <=; 0 <~>)
% Maximal formula depth : 45 ( 24 avg;1911 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 28 usr; 28 con; 0-2 aty)
% Number of variables : 247 ( 0 ^ 247 !; 0 ?; 247 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(conj_thm_2Equotient__list_2ELIST__MAP__I,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27a ) @ ( c_2Ecombin_2EI @ A_27a ) )
= ( c_2Ecombin_2EI @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).
thf(conj_thm_2Equotient__list_2ELIST__REL__EQ,axiom,
! [A_27a: del] :
( ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ ( c_2Emin_2E_3D @ A_27a ) )
= ( c_2Emin_2E_3D @ ( ty_2Elist_2Elist @ A_27a ) ) ) ).
thf(conj_thm_2Equotient__list_2ELIST__REL__REFL,axiom,
! [A_27a: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ( ! [V1x: $i] :
( ( mem @ V1x @ A_27a )
=> ! [V2y: $i] :
( ( mem @ V2y @ A_27a )
=> ( ( p @ ( ap @ ( ap @ V0R @ V1x ) @ V2y ) )
<=> ( ( ap @ V0R @ V1x )
= ( ap @ V0R @ V2y ) ) ) ) )
=> ! [V3x: $i] :
( ( mem @ V3x @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3x ) @ V3x ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ELIST__EQUIV,axiom,
! [A_27a: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ( ( p @ ( ap @ ( c_2Equotient_2EEQUIV @ A_27a ) @ V0R ) )
=> ( p @ ( ap @ ( c_2Equotient_2EEQUIV @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ELIST__REL__REL,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3r: $i] :
( ( mem @ V3r @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4s: $i] :
( ( mem @ V4s @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3r ) @ V4s ) )
<=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3r ) @ V3r ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V4s ) @ V4s ) )
& ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ V3r )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ V4s ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ELIST__QUOTIENT,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27b ) ) @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) ) @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) ) @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ECONS__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3t: $i] :
( ( mem @ V3t @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4h: $i] :
( ( mem @ V4h @ A_27b )
=> ( ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27b ) @ V4h ) @ V3t )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ ( ap @ V2rep @ V4h ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3t ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ECONS__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3t1: $i] :
( ( mem @ V3t1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4t2: $i] :
( ( mem @ V4t2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5h1: $i] :
( ( mem @ V5h1 @ A_27a )
=> ! [V6h2: $i] :
( ( mem @ V6h2 @ A_27a )
=> ( ( ( p @ ( ap @ ( ap @ V0R @ V5h1 ) @ V6h2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3t1 ) @ V4t2 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V5h1 ) @ V3t1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2ECONS @ A_27a ) @ V6h2 ) @ V4t2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ENIL__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ( ( c_2Elist_2ENIL @ A_27b )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ENIL__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ ( c_2Elist_2ENIL @ A_27a ) ) @ ( c_2Elist_2ENIL @ A_27a ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EMAP__PRS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs1: $i] :
( ( mem @ V1abs1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2rep1: $i] :
( ( mem @ V2rep1 @ ( arr @ A_27c @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27c ) @ V0R1 ) @ V1abs1 ) @ V2rep1 ) )
=> ! [V3R2: $i] :
( ( mem @ V3R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
=> ! [V4abs2: $i] :
( ( mem @ V4abs2 @ ( arr @ A_27b @ A_27d ) )
=> ! [V5rep2: $i] :
( ( mem @ V5rep2 @ ( arr @ A_27d @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27b @ A_27d ) @ V3R2 ) @ V4abs2 ) @ V5rep2 ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Elist_2Elist @ A_27c ) )
=> ! [V7f: $i] :
( ( mem @ V7f @ ( arr @ A_27c @ A_27d ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27c @ A_27d ) @ V7f ) @ V6l )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27d ) @ V4abs2 ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27a @ A_27d @ A_27c @ A_27b ) @ V1abs1 ) @ V5rep2 ) @ V7f ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27c @ A_27a ) @ V2rep1 ) @ V6l ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EMAP__RSP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs1: $i] :
( ( mem @ V1abs1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2rep1: $i] :
( ( mem @ V2rep1 @ ( arr @ A_27c @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27c ) @ V0R1 ) @ V1abs1 ) @ V2rep1 ) )
=> ! [V3R2: $i] :
( ( mem @ V3R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
=> ! [V4abs2: $i] :
( ( mem @ V4abs2 @ ( arr @ A_27b @ A_27d ) )
=> ! [V5rep2: $i] :
( ( mem @ V5rep2 @ ( arr @ A_27d @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27b @ A_27d ) @ V3R2 ) @ V4abs2 ) @ V5rep2 ) )
=> ! [V6l1: $i] :
( ( mem @ V6l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V7l2: $i] :
( ( mem @ V7l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V8f1: $i] :
( ( mem @ V8f1 @ ( arr @ A_27a @ A_27b ) )
=> ! [V9f2: $i] :
( ( mem @ V9f2 @ ( arr @ A_27a @ A_27b ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27a @ A_27b ) @ V0R1 ) @ V3R2 ) @ V8f1 ) @ V9f2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R1 ) @ V6l1 ) @ V7l2 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27b @ A_27b ) @ V3R2 ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V8f1 ) @ V6l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V9f2 ) @ V7l2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ELENGTH__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27b ) @ V3l ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ELENGTH__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3l1 ) @ V4l2 ) )
=> ( ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V3l1 ) )
= ( surj__ty_2Enum_2Enum @ ( ap @ ( c_2Elist_2ELENGTH @ A_27a ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EAPPEND__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4m: $i] :
( ( mem @ V4m @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27b ) @ V3l ) @ V4m )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3l ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V4m ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EAPPEND__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5m1: $i] :
( ( mem @ V5m1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V6m2: $i] :
( ( mem @ V6m2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3l1 ) @ V4l2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V5m1 ) @ V6m2 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V3l1 ) @ V5m1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EAPPEND @ A_27a ) @ V4l2 ) @ V6m2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFLAT__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27b ) ) )
=> ( ( ap @ ( c_2Elist_2EFLAT @ A_27b ) @ V3l )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ ( ty_2Elist_2Elist @ A_27b ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFLAT__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ ( ty_2Elist_2Elist @ A_27a ) ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ ( ty_2Elist_2Elist @ A_27a ) @ ( ty_2Elist_2Elist @ A_27a ) ) @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) ) @ V3l1 ) @ V4l2 ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V3l1 ) ) @ ( ap @ ( c_2Elist_2EFLAT @ A_27a ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EREVERSE__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( c_2Elist_2EREVERSE @ A_27b ) @ V3l )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EREVERSE__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3l1 ) @ V4l2 ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V3l1 ) ) @ ( ap @ ( c_2Elist_2EREVERSE @ A_27a ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFILTER__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3P: $i] :
( ( mem @ V3P @ ( arr @ A_27b @ bool ) )
=> ! [V4l: $i] :
( ( mem @ V4l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27b ) @ V3P ) @ V4l )
= ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27a @ A_27b ) @ V1abs ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27a @ bool @ A_27b @ bool ) @ V1abs ) @ ( c_2Ecombin_2EI @ bool ) ) @ V3P ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V4l ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFILTER__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3P1: $i] :
( ( mem @ V3P1 @ ( arr @ A_27a @ bool ) )
=> ! [V4P2: $i] :
( ( mem @ V4P2 @ ( arr @ A_27a @ bool ) )
=> ! [V5l1: $i] :
( ( mem @ V5l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V6l2: $i] :
( ( mem @ V6l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27a @ bool ) @ V0R ) @ ( c_2Emin_2E_3D @ bool ) ) @ V3P1 ) @ V4P2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V5l1 ) @ V6l2 ) ) )
=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V3P1 ) @ V5l1 ) ) @ ( ap @ ( ap @ ( c_2Elist_2EFILTER @ A_27a ) @ V4P2 ) @ V6l2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ENULL__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ( ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27b ) @ V3l ) )
<=> ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3l ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ENULL__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3l1 ) @ V4l2 ) )
=> ( ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V3l1 ) )
<=> ( p @ ( ap @ ( c_2Elist_2ENULL @ A_27a ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EALL__EL__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4P: $i] :
( ( mem @ V4P @ ( arr @ A_27b @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27b ) @ V4P ) @ V3l ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27a @ bool @ A_27b @ bool ) @ V1abs ) @ ( c_2Ecombin_2EI @ bool ) ) @ V4P ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3l ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EALL__EL__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5P1: $i] :
( ( mem @ V5P1 @ ( arr @ A_27a @ bool ) )
=> ! [V6P2: $i] :
( ( mem @ V6P2 @ ( arr @ A_27a @ bool ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27a @ bool ) @ V0R ) @ ( c_2Emin_2E_3D @ bool ) ) @ V5P1 ) @ V6P2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3l1 ) @ V4l2 ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V5P1 ) @ V3l1 ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEVERY @ A_27a ) @ V6P2 ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ESOME__EL__PRS,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l: $i] :
( ( mem @ V3l @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V4P: $i] :
( ( mem @ V4P @ ( arr @ A_27b @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27b ) @ V4P ) @ V3l ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27a @ bool @ A_27b @ bool ) @ V1abs ) @ ( c_2Ecombin_2EI @ bool ) ) @ V4P ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27b @ A_27a ) @ V2rep ) @ V3l ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2ESOME__EL__RSP,axiom,
! [A_27a: del,A_27b: del,V0R: $i] :
( ( mem @ V0R @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs: $i] :
( ( mem @ V1abs @ ( arr @ A_27a @ A_27b ) )
=> ! [V2rep: $i] :
( ( mem @ V2rep @ ( arr @ A_27b @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27b ) @ V0R ) @ V1abs ) @ V2rep ) )
=> ! [V3l1: $i] :
( ( mem @ V3l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V4l2: $i] :
( ( mem @ V4l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V5P1: $i] :
( ( mem @ V5P1 @ ( arr @ A_27a @ bool ) )
=> ! [V6P2: $i] :
( ( mem @ V6P2 @ ( arr @ A_27a @ bool ) )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27a @ bool ) @ V0R ) @ ( c_2Emin_2E_3D @ bool ) ) @ V5P1 ) @ V6P2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R ) @ V3l1 ) @ V4l2 ) ) )
=> ( ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V5P1 ) @ V3l1 ) )
<=> ( p @ ( ap @ ( ap @ ( c_2Elist_2EEXISTS @ A_27a ) @ V6P2 ) @ V4l2 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFOLDL__PRS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs1: $i] :
( ( mem @ V1abs1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2rep1: $i] :
( ( mem @ V2rep1 @ ( arr @ A_27c @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27c ) @ V0R1 ) @ V1abs1 ) @ V2rep1 ) )
=> ! [V3R2: $i] :
( ( mem @ V3R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
=> ! [V4abs2: $i] :
( ( mem @ V4abs2 @ ( arr @ A_27b @ A_27d ) )
=> ! [V5rep2: $i] :
( ( mem @ V5rep2 @ ( arr @ A_27d @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27b @ A_27d ) @ V3R2 ) @ V4abs2 ) @ V5rep2 ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Elist_2Elist @ A_27d ) )
=> ! [V7f: $i] :
( ( mem @ V7f @ ( arr @ A_27c @ ( arr @ A_27d @ A_27c ) ) )
=> ! [V8e: $i] :
( ( mem @ V8e @ A_27c )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27d @ A_27c ) @ V7f ) @ V8e ) @ V6l )
= ( ap @ V1abs1 @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27a @ ( arr @ A_27d @ A_27c ) @ A_27c @ ( arr @ A_27b @ A_27a ) ) @ V1abs1 ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27b @ A_27c @ A_27d @ A_27a ) @ V4abs2 ) @ V2rep1 ) ) @ V7f ) ) @ ( ap @ V2rep1 @ V8e ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27d @ A_27b ) @ V5rep2 ) @ V6l ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFOLDL__RSP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs1: $i] :
( ( mem @ V1abs1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2rep1: $i] :
( ( mem @ V2rep1 @ ( arr @ A_27c @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27c ) @ V0R1 ) @ V1abs1 ) @ V2rep1 ) )
=> ! [V3R2: $i] :
( ( mem @ V3R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
=> ! [V4abs2: $i] :
( ( mem @ V4abs2 @ ( arr @ A_27b @ A_27d ) )
=> ! [V5rep2: $i] :
( ( mem @ V5rep2 @ ( arr @ A_27d @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27b @ A_27d ) @ V3R2 ) @ V4abs2 ) @ V5rep2 ) )
=> ! [V6l1: $i] :
( ( mem @ V6l1 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V7l2: $i] :
( ( mem @ V7l2 @ ( ty_2Elist_2Elist @ A_27b ) )
=> ! [V8f1: $i] :
( ( mem @ V8f1 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V9f2: $i] :
( ( mem @ V9f2 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27a ) ) )
=> ! [V10e1: $i] :
( ( mem @ V10e1 @ A_27a )
=> ! [V11e2: $i] :
( ( mem @ V11e2 @ A_27a )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27a @ ( arr @ A_27b @ A_27a ) ) @ V0R1 ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27b @ A_27a ) @ V3R2 ) @ V0R1 ) ) @ V8f1 ) @ V9f2 ) )
& ( p @ ( ap @ ( ap @ V0R1 @ V10e1 ) @ V11e2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27b @ A_27b ) @ V3R2 ) @ V6l1 ) @ V7l2 ) ) )
=> ( p @ ( ap @ ( ap @ V0R1 @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V8f1 ) @ V10e1 ) @ V6l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDL @ A_27b @ A_27a ) @ V9f2 ) @ V11e2 ) @ V7l2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFOLDR__PRS,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs1: $i] :
( ( mem @ V1abs1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2rep1: $i] :
( ( mem @ V2rep1 @ ( arr @ A_27c @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27c ) @ V0R1 ) @ V1abs1 ) @ V2rep1 ) )
=> ! [V3R2: $i] :
( ( mem @ V3R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
=> ! [V4abs2: $i] :
( ( mem @ V4abs2 @ ( arr @ A_27b @ A_27d ) )
=> ! [V5rep2: $i] :
( ( mem @ V5rep2 @ ( arr @ A_27d @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27b @ A_27d ) @ V3R2 ) @ V4abs2 ) @ V5rep2 ) )
=> ! [V6l: $i] :
( ( mem @ V6l @ ( ty_2Elist_2Elist @ A_27c ) )
=> ! [V7f: $i] :
( ( mem @ V7f @ ( arr @ A_27c @ ( arr @ A_27d @ A_27d ) ) )
=> ! [V8e: $i] :
( ( mem @ V8e @ A_27d )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27c @ A_27d ) @ V7f ) @ V8e ) @ V6l )
= ( ap @ V4abs2 @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27a @ ( arr @ A_27d @ A_27d ) @ A_27c @ ( arr @ A_27b @ A_27b ) ) @ V1abs1 ) @ ( ap @ ( ap @ ( c_2Equotient_2E_2D_2D_3E @ A_27b @ A_27d @ A_27d @ A_27b ) @ V4abs2 ) @ V5rep2 ) ) @ V7f ) ) @ ( ap @ V5rep2 @ V8e ) ) @ ( ap @ ( ap @ ( c_2Elist_2EMAP @ A_27c @ A_27a ) @ V2rep1 ) @ V6l ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2Equotient__list_2EFOLDR__RSP,axiom,
! [A_27a: del,A_27b: del,A_27c: del,A_27d: del,V0R1: $i] :
( ( mem @ V0R1 @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) )
=> ! [V1abs1: $i] :
( ( mem @ V1abs1 @ ( arr @ A_27a @ A_27c ) )
=> ! [V2rep1: $i] :
( ( mem @ V2rep1 @ ( arr @ A_27c @ A_27a ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27a @ A_27c ) @ V0R1 ) @ V1abs1 ) @ V2rep1 ) )
=> ! [V3R2: $i] :
( ( mem @ V3R2 @ ( arr @ A_27b @ ( arr @ A_27b @ bool ) ) )
=> ! [V4abs2: $i] :
( ( mem @ V4abs2 @ ( arr @ A_27b @ A_27d ) )
=> ! [V5rep2: $i] :
( ( mem @ V5rep2 @ ( arr @ A_27d @ A_27b ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2EQUOTIENT @ A_27b @ A_27d ) @ V3R2 ) @ V4abs2 ) @ V5rep2 ) )
=> ! [V6l1: $i] :
( ( mem @ V6l1 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V7l2: $i] :
( ( mem @ V7l2 @ ( ty_2Elist_2Elist @ A_27a ) )
=> ! [V8f1: $i] :
( ( mem @ V8f1 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V9f2: $i] :
( ( mem @ V9f2 @ ( arr @ A_27a @ ( arr @ A_27b @ A_27b ) ) )
=> ! [V10e1: $i] :
( ( mem @ V10e1 @ A_27b )
=> ! [V11e2: $i] :
( ( mem @ V11e2 @ A_27b )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27a @ ( arr @ A_27b @ A_27b ) ) @ V0R1 ) @ ( ap @ ( ap @ ( c_2Equotient_2E_3D_3D_3D_3E @ A_27b @ A_27b ) @ V3R2 ) @ V3R2 ) ) @ V8f1 ) @ V9f2 ) )
& ( p @ ( ap @ ( ap @ V3R2 @ V10e1 ) @ V11e2 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2ELIST__REL @ A_27a @ A_27a ) @ V0R1 ) @ V6l1 ) @ V7l2 ) ) )
=> ( p @ ( ap @ ( ap @ V3R2 @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V8f1 ) @ V10e1 ) @ V6l1 ) ) @ ( ap @ ( ap @ ( ap @ ( c_2Elist_2EFOLDR @ A_27a @ A_27b ) @ V9f2 ) @ V11e2 ) @ V7l2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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