ITP001 Axioms: ITP070_7.ax


%------------------------------------------------------------------------------
% File     : ITP070_7 : TPTP v9.0.0. 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))) ) ) ) ).

%------------------------------------------------------------------------------