ITP001 Axioms: ITP070_7.ax
%------------------------------------------------------------------------------
% File : ITP070_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : quotient_list.ax [Gau19]
% : HL4070_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 173 ( 63 unt; 65 typ; 0 def)
% Number of atoms : 192 ( 87 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 87 ( 3 ~; 3 |; 14 &)
% ( 15 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 59 ( 32 >; 27 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 62 ( 62 usr; 6 con; 0-7 aty)
% Number of variables : 581 ( 502 !; 1 ?; 581 :)
% ( 78 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Equotient_2E_2D_2D_3E_2E0,type,
c_2Equotient_2E_2D_2D_3E_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)))) ).
tff(c_2Equotient_2E_2D_2D_3E_2E2,type,
c_2Equotient_2E_2D_2D_3E_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)) ) ).
tff(c_2Equotient_2E_2D_2D_3E_2E3,type,
c_2Equotient_2E_2D_2D_3E_2E3:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27c) * tyop_2Emin_2Efun(A_27b,A_27d) * tyop_2Emin_2Efun(A_27c,A_27b) ) > tyop_2Emin_2Efun(A_27a,A_27d) ) ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Equotient_2E_3D_3D_3D_3E_2E0,type,
c_2Equotient_2E_3D_3D_3D_3E_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))) ).
tff(c_2Equotient_2E_3D_3D_3D_3E_2E2,type,
c_2Equotient_2E_3D_3D_3D_3E_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)) ) ).
tff(c_2Equotient_2E_3D_3D_3D_3E_2E4,type,
c_2Equotient_2E_3D_3D_3D_3E_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Equotient_2EEQUIV_2E0,type,
c_2Equotient_2EEQUIV_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Equotient_2EEQUIV_2E1,type,
c_2Equotient_2EEQUIV_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EEXISTS_2E0,type,
c_2Elist_2EEXISTS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2EEXISTS_2E2,type,
c_2Elist_2EEXISTS_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Elist_2EFILTER_2E0,type,
c_2Elist_2EFILTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EFILTER_2E2,type,
c_2Elist_2EFILTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EFLAT_2E0,type,
c_2Elist_2EFLAT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EFLAT_2E1,type,
c_2Elist_2EFLAT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Elist_2EFOLDR_2E0,type,
c_2Elist_2EFOLDR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDR_2E3,type,
c_2Elist_2EFOLDR_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Elist_2ELIST__REL_2E0,type,
c_2Elist_2ELIST__REL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))) ).
tff(c_2Elist_2ELIST__REL_2E1,type,
c_2Elist_2ELIST__REL_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)) ) ).
tff(c_2Elist_2ELIST__REL_2E3,type,
c_2Elist_2ELIST__REL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) * tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27b) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E1,type,
c_2Elist_2EMAP_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)) ) ).
tff(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Elist_2ENULL_2E0,type,
c_2Elist_2ENULL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2ENULL_2E1,type,
c_2Elist_2ENULL_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Equotient_2EQUOTIENT_2E0,type,
c_2Equotient_2EQUOTIENT_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))) ).
tff(c_2Equotient_2EQUOTIENT_2E3,type,
c_2Equotient_2EQUOTIENT_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EREVERSE_2E0,type,
c_2Elist_2EREVERSE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Elist_2EREVERSE_2E1,type,
c_2Elist_2EREVERSE_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Ebool,A_27b,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Equotient_2E_2D_2D_3E_2E0(A_27a,tyop_2Emin_2Ebool,A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Equotient_2E_2D_2D_3E_2E3(A_27a,A_27d,A_27c,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Equotient_2E_2D_2D_3E_2E0(A_27a,A_27d,A_27c,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27c_29_20mono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c))] : ( c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Efun(A_27d,A_27c),A_27c,tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Equotient_2E_2D_2D_3E_2E0(A_27a,tyop_2Emin_2Efun(A_27d,A_27c),A_27c,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27d_2CA_27d_29_20mono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27d),tyop_2Emin_2Efun(A_27b,A_27b)),X2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d))] : ( c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Efun(A_27d,A_27d),A_27c,tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27d),tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27d),tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0(A_27a,tyop_2Emin_2Efun(A_27d,A_27d),A_27c,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Equotient_2E_2D_2D_3E_2E2(A_27b,A_27c,A_27d,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(A_27b,A_27a))),c_2Equotient_2E_2D_2D_3E_2E0(A_27b,A_27c,A_27d,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] : ( c_2Equotient_2E_2D_2D_3E_2E2(A_27b,A_27d,A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27d),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27d),tyop_2Emin_2Efun(A_27b,A_27b))),c_2Equotient_2E_2D_2D_3E_2E0(A_27b,A_27d,A_27d,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Ebool)),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))] : ( c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Equotient_2E_3D_3D_3D_3E_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] : ( c_2Equotient_2E_3D_3D_3D_3E_2E2(A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Ebool))),c_2Equotient_2E_3D_3D_3D_3E_2E0(A_27b,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EAPPEND_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EAPPEND_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ECONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Equotient_2EEQUIV_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Equotient_2EEQUIV_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEVERY_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEVERY_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EEVERY_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEXISTS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EEXISTS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEXISTS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EEXISTS_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFILTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFILTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EFILTER_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFILTER_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EFILTER_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2EFLAT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Elist_2EFLAT_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EFLAT_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EFLAT_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(A_27b),c_2Elist_2EFLAT_2E0(A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFOLDL_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),c_2Elist_2EFOLDL_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),X1_2E0: A_27c,X2_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Elist_2EFOLDL_2E3(A_27d,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),A_27c,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),A_27c),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),A_27c)),c_2Elist_2EFOLDL_2E0(A_27d,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDR_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d)),X1_2E0: A_27d,X2_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EFOLDR_2E3(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),A_27d,app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d)),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27d)),c_2Elist_2EFOLDR_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__REL_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Elist_2ELIST__REL_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27b_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(A_27b),X2_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELIST__REL_2E3(A_27b,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(A_27b,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),X2_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] : ( c_2Elist_2ELIST__REL_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool)),c_2Elist_2ELIST__REL_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] : ( c_2Elist_2EMAP_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27a,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Elist_2EMAP_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EMAP_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Elist_2EMAP_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EMAP_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27d)),c_2Elist_2EMAP_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EMAP_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27d)),c_2Elist_2EMAP_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27d_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Elist_2EMAP_2E2(A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27d,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b)),tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))),c_2Elist_2EMAP_2E0(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ENULL_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ENULL_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E0(A_27b),X0_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d,axiom,
! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27d),X2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] : ( c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(A_27b,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X2_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))] : ( c_2Equotient_2EQUOTIENT_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool)),c_2Equotient_2EQUOTIENT_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EREVERSE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EREVERSE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),c_2Elist_2EREVERSE_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Equotient__list_2ELIST__MAP__I,axiom,
! [A_27a: $tType] : ( c_2Elist_2EMAP_2E1(A_27a,A_27a,c_2Ecombin_2EI_2E0(A_27a)) = c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(A_27a)) ) ).
tff(thm_2Equotient__list_2ELIST__REL__EQ,axiom,
! [A_27a: $tType] : ( c_2Elist_2ELIST__REL_2E1(A_27a,A_27a,c_2Emin_2E_3D_2E0(A_27a)) = c_2Emin_2E_3D_2E0(tyop_2Elist_2Elist(A_27a)) ) ).
tff(thm_2Equotient__list_2ELIST__REL__REFL,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0),V2y_2E0))
<=> ( app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V1x_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V2y_2E0) ) )
=> ! [V3x_2E0: tyop_2Elist_2Elist(A_27a)] : p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3x_2E0,V3x_2E0)) ) ).
tff(thm_2Equotient__list_2ELIST__EQUIV,axiom,
! [A_27a: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] :
( p(c_2Equotient_2EEQUIV_2E1(A_27a,V0R_2E0))
=> p(c_2Equotient_2EEQUIV_2E1(tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__REL_2E1(A_27a,A_27a,V0R_2E0))) ) ).
tff(thm_2Equotient__list_2ELIST__REL__REL,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3r_2E0: tyop_2Elist_2Elist(A_27a),V4s_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3r_2E0,V4s_2E0))
<=> ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3r_2E0,V3r_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V4s_2E0,V4s_2E0))
& ( c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,V3r_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,V4s_2E0) ) ) ) ) ).
tff(thm_2Equotient__list_2ELIST__QUOTIENT,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> p(c_2Equotient_2EQUOTIENT_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),c_2Elist_2ELIST__REL_2E1(A_27a,A_27a,V0R_2E0),c_2Elist_2EMAP_2E1(A_27a,A_27b,V1abs_2E0),c_2Elist_2EMAP_2E1(A_27b,A_27a,V2rep_2E0))) ) ).
tff(thm_2Equotient__list_2ECONS__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3t_2E0: tyop_2Elist_2Elist(A_27b),V4h_2E0: A_27b] : ( c_2Elist_2ECONS_2E2(A_27b,V4h_2E0,V3t_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27b,A_27a,V2rep_2E0,V4h_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3t_2E0))) ) ) ).
tff(thm_2Equotient__list_2ECONS__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3t1_2E0: tyop_2Elist_2Elist(A_27a),V4t2_2E0: tyop_2Elist_2Elist(A_27a),V5h1_2E0: A_27a,V6h2_2E0: A_27a] :
( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0,V5h1_2E0),V6h2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3t1_2E0,V4t2_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,c_2Elist_2ECONS_2E2(A_27a,V5h1_2E0,V3t1_2E0),c_2Elist_2ECONS_2E2(A_27a,V6h2_2E0,V4t2_2E0))) ) ) ).
tff(thm_2Equotient__list_2ENIL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ( c_2Elist_2ENIL_2E0(A_27b) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,c_2Elist_2ENIL_2E0(A_27a)) ) ) ).
tff(thm_2Equotient__list_2ENIL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,c_2Elist_2ENIL_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a))) ) ).
tff(thm_2Equotient__list_2EMAP__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6l_2E0: tyop_2Elist_2Elist(A_27c),V7f_2E0: tyop_2Emin_2Efun(A_27c,A_27d)] : ( c_2Elist_2EMAP_2E2(A_27c,A_27d,V7f_2E0,V6l_2E0) = c_2Elist_2EMAP_2E2(A_27b,A_27d,V4abs2_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,A_27d,A_27c,A_27b,V1abs1_2E0,V5rep2_2E0,V7f_2E0),c_2Elist_2EMAP_2E2(A_27c,A_27a,V2rep1_2E0,V6l_2E0))) ) ) ) ).
tff(thm_2Equotient__list_2EMAP__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6l1_2E0: tyop_2Elist_2Elist(A_27a),V7l2_2E0: tyop_2Elist_2Elist(A_27a),V8f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V9f2_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,A_27b,V0R1_2E0,V3R2_2E0,V8f1_2E0,V9f2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R1_2E0,V6l1_2E0,V7l2_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27b,A_27b,V3R2_2E0,c_2Elist_2EMAP_2E2(A_27a,A_27b,V8f1_2E0,V6l1_2E0),c_2Elist_2EMAP_2E2(A_27a,A_27b,V9f2_2E0,V7l2_2E0))) ) ) ) ).
tff(thm_2Equotient__list_2ELENGTH__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ELENGTH_2E1(A_27b,V3l_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3l_2E0)) ) ) ).
tff(thm_2Equotient__list_2ELENGTH__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3l1_2E0,V4l2_2E0))
=> ( c_2Elist_2ELENGTH_2E1(A_27a,V3l1_2E0) = c_2Elist_2ELENGTH_2E1(A_27a,V4l2_2E0) ) ) ) ).
tff(thm_2Equotient__list_2EAPPEND__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27b),V4m_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EAPPEND_2E2(A_27b,V3l_2E0,V4m_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3l_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V4m_2E0))) ) ) ).
tff(thm_2Equotient__list_2EAPPEND__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a),V5m1_2E0: tyop_2Elist_2Elist(A_27a),V6m2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3l1_2E0,V4l2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V5m1_2E0,V6m2_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V3l1_2E0,V5m1_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V4l2_2E0,V6m2_2E0))) ) ) ).
tff(thm_2Equotient__list_2EFLAT__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27b))] : ( c_2Elist_2EFLAT_2E1(A_27b,V3l_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,c_2Elist_2EFLAT_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E1(A_27b,A_27a,V2rep_2E0),V3l_2E0))) ) ) ).
tff(thm_2Equotient__list_2EFLAT__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a)),V4l2_2E0: tyop_2Elist_2Elist(tyop_2Elist_2Elist(A_27a))] :
( p(c_2Elist_2ELIST__REL_2E3(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),c_2Elist_2ELIST__REL_2E1(A_27a,A_27a,V0R_2E0),V3l1_2E0,V4l2_2E0))
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,c_2Elist_2EFLAT_2E1(A_27a,V3l1_2E0),c_2Elist_2EFLAT_2E1(A_27a,V4l2_2E0))) ) ) ).
tff(thm_2Equotient__list_2EREVERSE__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EREVERSE_2E1(A_27b,V3l_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,c_2Elist_2EREVERSE_2E1(A_27a,c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3l_2E0))) ) ) ).
tff(thm_2Equotient__list_2EREVERSE__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3l1_2E0,V4l2_2E0))
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,c_2Elist_2EREVERSE_2E1(A_27a,V3l1_2E0),c_2Elist_2EREVERSE_2E1(A_27a,V4l2_2E0))) ) ) ).
tff(thm_2Equotient__list_2EFILTER__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EFILTER_2E2(A_27b,V3P_2E0,V4l_2E0) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V1abs_2E0,c_2Elist_2EFILTER_2E2(A_27a,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Ebool,A_27b,tyop_2Emin_2Ebool,V1abs_2E0,c_2Ecombin_2EI_2E0(tyop_2Emin_2Ebool),V3P_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V4l_2E0))) ) ) ).
tff(thm_2Equotient__list_2EFILTER__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5l1_2E0: tyop_2Elist_2Elist(A_27a),V6l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Ebool,V0R_2E0,c_2Emin_2E_3D_2E0(tyop_2Emin_2Ebool),V3P1_2E0,V4P2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V5l1_2E0,V6l2_2E0)) )
=> p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,c_2Elist_2EFILTER_2E2(A_27a,V3P1_2E0,V5l1_2E0),c_2Elist_2EFILTER_2E2(A_27a,V4P2_2E0,V6l2_2E0))) ) ) ).
tff(thm_2Equotient__list_2ENULL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ENULL_2E1(A_27b,V3l_2E0) = c_2Elist_2ENULL_2E1(A_27a,c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3l_2E0)) ) ) ).
tff(thm_2Equotient__list_2ENULL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3l1_2E0,V4l2_2E0))
=> ( c_2Elist_2ENULL_2E1(A_27a,V3l1_2E0) = c_2Elist_2ENULL_2E1(A_27a,V4l2_2E0) ) ) ) ).
tff(thm_2Equotient__list_2EALL__EL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27b),V4P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEVERY_2E2(A_27b,V4P_2E0,V3l_2E0) = c_2Elist_2EEVERY_2E2(A_27a,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Ebool,A_27b,tyop_2Emin_2Ebool,V1abs_2E0,c_2Ecombin_2EI_2E0(tyop_2Emin_2Ebool),V4P_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3l_2E0)) ) ) ).
tff(thm_2Equotient__list_2EALL__EL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a),V5P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Ebool,V0R_2E0,c_2Emin_2E_3D_2E0(tyop_2Emin_2Ebool),V5P1_2E0,V6P2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3l1_2E0,V4l2_2E0)) )
=> ( c_2Elist_2EEVERY_2E2(A_27a,V5P1_2E0,V3l1_2E0) = c_2Elist_2EEVERY_2E2(A_27a,V6P2_2E0,V4l2_2E0) ) ) ) ).
tff(thm_2Equotient__list_2ESOME__EL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l_2E0: tyop_2Elist_2Elist(A_27b),V4P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Elist_2EEXISTS_2E2(A_27b,V4P_2E0,V3l_2E0) = c_2Elist_2EEXISTS_2E2(A_27a,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Ebool,A_27b,tyop_2Emin_2Ebool,V1abs_2E0,c_2Ecombin_2EI_2E0(tyop_2Emin_2Ebool),V4P_2E0),c_2Elist_2EMAP_2E2(A_27b,A_27a,V2rep_2E0,V3l_2E0)) ) ) ).
tff(thm_2Equotient__list_2ESOME__EL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2rep_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27b,V0R_2E0,V1abs_2E0,V2rep_2E0))
=> ! [V3l1_2E0: tyop_2Elist_2Elist(A_27a),V4l2_2E0: tyop_2Elist_2Elist(A_27a),V5P1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V6P2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Ebool,V0R_2E0,c_2Emin_2E_3D_2E0(tyop_2Emin_2Ebool),V5P1_2E0,V6P2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R_2E0,V3l1_2E0,V4l2_2E0)) )
=> ( c_2Elist_2EEXISTS_2E2(A_27a,V5P1_2E0,V3l1_2E0) = c_2Elist_2EEXISTS_2E2(A_27a,V6P2_2E0,V4l2_2E0) ) ) ) ).
tff(thm_2Equotient__list_2EFOLDL__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6l_2E0: tyop_2Elist_2Elist(A_27d),V7f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),V8e_2E0: A_27c] : ( c_2Elist_2EFOLDL_2E3(A_27d,A_27c,V7f_2E0,V8e_2E0,V6l_2E0) = app_2E2(A_27a,A_27c,V1abs1_2E0,c_2Elist_2EFOLDL_2E3(A_27b,A_27a,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Efun(A_27d,A_27c),A_27c,tyop_2Emin_2Efun(A_27b,A_27a),V1abs1_2E0,c_2Equotient_2E_2D_2D_3E_2E2(A_27b,A_27c,A_27d,A_27a,V4abs2_2E0,V2rep1_2E0),V7f_2E0),app_2E2(A_27c,A_27a,V2rep1_2E0,V8e_2E0),c_2Elist_2EMAP_2E2(A_27d,A_27b,V5rep2_2E0,V6l_2E0))) ) ) ) ).
tff(thm_2Equotient__list_2EFOLDL__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6l1_2E0: tyop_2Elist_2Elist(A_27b),V7l2_2E0: tyop_2Elist_2Elist(A_27b),V8f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V9f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),V10e1_2E0: A_27a,V11e2_2E0: A_27a] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),V0R1_2E0,c_2Equotient_2E_3D_3D_3D_3E_2E2(A_27b,A_27a,V3R2_2E0,V0R1_2E0),V8f1_2E0,V9f2_2E0))
& p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R1_2E0,V10e1_2E0),V11e2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27b,A_27b,V3R2_2E0,V6l1_2E0,V7l2_2E0)) )
=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R1_2E0,c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V8f1_2E0,V10e1_2E0,V6l1_2E0)),c_2Elist_2EFOLDL_2E3(A_27b,A_27a,V9f2_2E0,V11e2_2E0,V7l2_2E0))) ) ) ) ).
tff(thm_2Equotient__list_2EFOLDR__PRS,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6l_2E0: tyop_2Elist_2Elist(A_27c),V7f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27d)),V8e_2E0: A_27d] : ( c_2Elist_2EFOLDR_2E3(A_27c,A_27d,V7f_2E0,V8e_2E0,V6l_2E0) = app_2E2(A_27b,A_27d,V4abs2_2E0,c_2Elist_2EFOLDR_2E3(A_27a,A_27b,c_2Equotient_2E_2D_2D_3E_2E3(A_27a,tyop_2Emin_2Efun(A_27d,A_27d),A_27c,tyop_2Emin_2Efun(A_27b,A_27b),V1abs1_2E0,c_2Equotient_2E_2D_2D_3E_2E2(A_27b,A_27d,A_27d,A_27b,V4abs2_2E0,V5rep2_2E0),V7f_2E0),app_2E2(A_27d,A_27b,V5rep2_2E0,V8e_2E0),c_2Elist_2EMAP_2E2(A_27c,A_27a,V2rep1_2E0,V6l_2E0))) ) ) ) ).
tff(thm_2Equotient__list_2EFOLDR__RSP,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0R1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1abs1_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2rep1_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27a,A_27c,V0R1_2E0,V1abs1_2E0,V2rep1_2E0))
=> ! [V3R2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4abs2_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V5rep2_2E0: tyop_2Emin_2Efun(A_27d,A_27b)] :
( p(c_2Equotient_2EQUOTIENT_2E3(A_27b,A_27d,V3R2_2E0,V4abs2_2E0,V5rep2_2E0))
=> ! [V6l1_2E0: tyop_2Elist_2Elist(A_27a),V7l2_2E0: tyop_2Elist_2Elist(A_27a),V8f1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V9f2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V10e1_2E0: A_27b,V11e2_2E0: A_27b] :
( ( p(c_2Equotient_2E_3D_3D_3D_3E_2E4(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0R1_2E0,c_2Equotient_2E_3D_3D_3D_3E_2E2(A_27b,A_27b,V3R2_2E0,V3R2_2E0),V8f1_2E0,V9f2_2E0))
& p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R2_2E0,V10e1_2E0),V11e2_2E0))
& p(c_2Elist_2ELIST__REL_2E3(A_27a,A_27a,V0R1_2E0,V6l1_2E0,V7l2_2E0)) )
=> p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3R2_2E0,c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V8f1_2E0,V10e1_2E0,V6l1_2E0)),c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V9f2_2E0,V11e2_2E0,V7l2_2E0))) ) ) ) ).
%------------------------------------------------------------------------------