%------------------------------------------------------------------------------
% File     : ITP068_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    : path.ax [Gau19]
%          : HL4068_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  524 ( 202 unt; 190 typ;   0 def)
%            Number of atoms       :  627 ( 379 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :  311 (  18   ~;  13   |; 120   &)
%                                         (  56 <=>; 104  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  164 (  95   >;  69   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  187 ( 187 usr;  16 con; 0-10 aty)
%            Number of variables   : 1865 (1540   !;  42   ?;1865   :)
%                                         ( 283  !>;   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_2Ellist_2Ellist,type,
    tyop_2Ellist_2Ellist: $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(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(tyop_2Epath_2Epath,type,
    tyop_2Epath_2Epath: ( $tType * $tType ) > $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_2Epair_2E_23_23_2E0,type,
    c_2Epair_2E_23_23_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_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)))) ).

tff(c_2Epair_2E_23_23_2E2,type,
    c_2Epair_2E_23_23_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_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,A_27d)) ) ).

tff(c_2Epair_2E_23_23_2E3,type,
    c_2Epair_2E_23_23_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_2Epair_2Eprod(A_27a,A_27b) ) > tyop_2Epair_2Eprod(A_27c,A_27d) ) ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

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_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > 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_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_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > 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_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).

tff(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ellist_2ELAPPEND_2E0,type,
    c_2Ellist_2ELAPPEND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELAPPEND_2E2,type,
    c_2Ellist_2ELAPPEND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Ellist_2Ellist(A_27a) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Ellist_2ELCONS_2E0,type,
    c_2Ellist_2ELCONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELCONS_2E2,type,
    c_2Ellist_2ELCONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(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_2Ellist_2ELFINITE_2E0,type,
    c_2Ellist_2ELFINITE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Ellist_2ELFINITE_2E1,type,
    c_2Ellist_2ELFINITE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Emin_2Ebool ) ).

tff(c_2Ellist_2ELMAP_2E0,type,
    c_2Ellist_2ELMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))) ).

tff(c_2Ellist_2ELMAP_2E1,type,
    c_2Ellist_2ELMAP_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)) ) ).

tff(c_2Ellist_2ELMAP_2E2,type,
    c_2Ellist_2ELMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Ellist_2Ellist(A_27b) ) ).

tff(c_2Ellist_2ELNIL_2E0,type,
    c_2Ellist_2ELNIL_2E0: 
      !>[A_27a: $tType] : tyop_2Ellist_2Ellist(A_27a) ).

tff(c_2Ellist_2ELNTH_2E0,type,
    c_2Ellist_2ELNTH_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a))) ).

tff(c_2Ellist_2ELNTH_2E2,type,
    c_2Ellist_2ELNTH_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Ellist_2ELTAKE_2E0,type,
    c_2Ellist_2ELTAKE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2Ellist_2ELTAKE_2E2,type,
    c_2Ellist_2ELTAKE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Ellist_2Ellist(A_27a) ) > tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2Ellist_2ELUNFOLD_2E0,type,
    c_2Ellist_2ELUNFOLD_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a))) ).

tff(c_2Ellist_2ELUNFOLD_2E2,type,
    c_2Ellist_2ELUNFOLD_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))) * A_27b ) > tyop_2Ellist_2Ellist(A_27a) ) ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: 
      !>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))) ).

tff(c_2Eoption_2EOPTION__MAP_2E2,type,
    c_2Eoption_2EOPTION__MAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Eoption_2Eoption(A_27a) ) > tyop_2Eoption_2Eoption(A_27b) ) ).

tff(c_2Epath_2EPL_2E0,type,
    c_2Epath_2EPL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Epath_2EPL_2E1,type,
    c_2Epath_2EPL_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) ).

tff(c_2Epath_2ESN_2E0,type,
    c_2Epath_2ESN_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool) ).

tff(c_2Epath_2ESN_2E1,type,
    c_2Epath_2ESN_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) > tyop_2Emin_2Ebool ) ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).

tff(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).

tff(c_2Eoption_2ETHE_2E1,type,
    c_2Eoption_2ETHE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Eoption_2Eoption(A_27a) > A_27a ) ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_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_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).

tff(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).

tff(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_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_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

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_2Epath_2Edrop_2E0,type,
    c_2Epath_2Edrop_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))) ).

tff(c_2Epath_2Edrop_2E2,type,
    c_2Epath_2Edrop_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Eel_2E0,type,
    c_2Epath_2Eel_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),A_27a)) ).

tff(c_2Epath_2Eel_2E2,type,
    c_2Epath_2Eel_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Epath_2Epath(A_27a,A_27b) ) > A_27a ) ).

tff(c_2Epath_2Eevery_2E0,type,
    c_2Epath_2Eevery_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Epath_2Eevery_2E2,type,
    c_2Epath_2Eevery_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Eexists_2E0,type,
    c_2Epath_2Eexists_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Epath_2Eexists_2E2,type,
    c_2Epath_2Eexists_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Efilter_2E0,type,
    c_2Epath_2Efilter_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))) ).

tff(c_2Epath_2Efilter_2E2,type,
    c_2Epath_2Efilter_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Efinite_2E0,type,
    c_2Epath_2Efinite_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool) ).

tff(c_2Epath_2Efinite_2E1,type,
    c_2Epath_2Efinite_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Efirst_2E0,type,
    c_2Epath_2Efirst_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),A_27a) ).

tff(c_2Epath_2Efirst_2E1,type,
    c_2Epath_2Efirst_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > A_27a ) ).

tff(c_2Epath_2EfirstP__at_2E0,type,
    c_2Epath_2EfirstP__at_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))) ).

tff(c_2Epath_2EfirstP__at_2E3,type,
    c_2Epath_2EfirstP__at_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Epath_2Epath(A_27a,A_27b) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Efirst__label_2E0,type,
    c_2Epath_2Efirst__label_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),A_27b) ).

tff(c_2Epath_2Efirst__label_2E1,type,
    c_2Epath_2Efirst__label_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > A_27b ) ).

tff(c_2Epath_2EfromPath_2E0,type,
    c_2Epath_2EfromPath_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))) ).

tff(c_2Epath_2EfromPath_2E1,type,
    c_2Epath_2EfromPath_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))) ) ).

tff(c_2EfixedPoint_2Egfp_2E0,type,
    c_2EfixedPoint_2Egfp_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2EfixedPoint_2Egfp_2E1,type,
    c_2EfixedPoint_2Egfp_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epath_2Eis__stopped_2E0,type,
    c_2Epath_2Eis__stopped_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool) ).

tff(c_2Epath_2Eis__stopped_2E1,type,
    c_2Epath_2Eis__stopped_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Elabels_2E0,type,
    c_2Epath_2Elabels_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)) ).

tff(c_2Epath_2Elabels_2E1,type,
    c_2Epath_2Elabels_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Ellist_2Ellist(A_27b) ) ).

tff(c_2Epath_2Elast_2E0,type,
    c_2Epath_2Elast_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),A_27a) ).

tff(c_2Epath_2Elast_2E1,type,
    c_2Epath_2Elast_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > A_27a ) ).

tff(c_2Epath_2Elength_2E0,type,
    c_2Epath_2Elength_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)) ).

tff(c_2Epath_2Elength_2E1,type,
    c_2Epath_2Elength_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Eoption_2Eoption(tyop_2Enum_2Enum) ) ).

tff(c_2Epath_2Emem_2E0,type,
    c_2Epath_2Emem_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Epath_2Emem_2E2,type,
    c_2Epath_2Emem_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2EfixedPoint_2Emonotone_2E0,type,
    c_2EfixedPoint_2Emonotone_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2EfixedPoint_2Emonotone_2E1,type,
    c_2EfixedPoint_2Emonotone_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Enth__label_2E0,type,
    c_2Epath_2Enth__label_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27a),A_27a)) ).

tff(c_2Epath_2Enth__label_2E2,type,
    c_2Epath_2Enth__label_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Epath_2Epath(A_27b,A_27a) ) > A_27a ) ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Epath_2Eokpath_2E0,type,
    c_2Epath_2Eokpath_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)) ).

tff(c_2Epath_2Eokpath_2E1,type,
    c_2Epath_2Eokpath_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) > tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Epath_2Eokpath_2E2,type,
    c_2Epath_2Eokpath_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Eokpath__f_2E0,type,
    c_2Epath_2Eokpath__f_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Epath_2Eokpath__f_2E1,type,
    c_2Epath_2Eokpath__f_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)) ) ).

tff(c_2Epath_2Eokpath__f_2E2,type,
    c_2Epath_2Eokpath__f_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) * tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).

tff(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)) ).

tff(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) ) > A_27a ) ).

tff(c_2Epath_2Eparallel__comp_2E0,type,
    c_2Epath_2Eparallel__comp_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool))))) ).

tff(c_2Epath_2Eparallel__comp_2E2,type,
    c_2Epath_2Eparallel__comp_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))) * tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool))) ) ).

tff(c_2Epath_2Eparallel__comp_2E5,type,
    c_2Epath_2Eparallel__comp_2E5: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))) * tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))) * tyop_2Epair_2Eprod(A_27a,A_27d) * A_27b * tyop_2Epair_2Eprod(A_27c,A_27e) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Epconcat_2E0,type,
    c_2Epath_2Epconcat_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)))) ).

tff(c_2Epath_2Epconcat_2E3,type,
    c_2Epath_2Epconcat_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epath_2Epath(A_27a,A_27b) * A_27b * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Epcons_2E0,type,
    c_2Epath_2Epcons_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)))) ).

tff(c_2Epath_2Epcons_2E3,type,
    c_2Epath_2Epcons_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Epgenerate_2E0,type,
    c_2Epath_2Epgenerate_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))) ).

tff(c_2Epath_2Epgenerate_2E2,type,
    c_2Epath_2Epgenerate_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Eplink_2E0,type,
    c_2Epath_2Eplink_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))) ).

tff(c_2Epath_2Eplink_2E2,type,
    c_2Epath_2Eplink_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Epath_2Epath(A_27a,A_27b) * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Epmap_2E0,type,
    c_2Epath_2Epmap_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_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d)))) ).

tff(c_2Epath_2Epmap_2E3,type,
    c_2Epath_2Epmap_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_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27c,A_27d) ) ).

tff(c_2Epath_2Eseg_2E0,type,
    c_2Epath_2Eseg_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)))) ).

tff(c_2Epath_2Eseg_2E3,type,
    c_2Epath_2Eseg_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Enum_2Enum * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Estopped__at_2E0,type,
    c_2Epath_2Estopped__at_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27a,A_27b)) ).

tff(c_2Epath_2Estopped__at_2E1,type,
    c_2Epath_2Estopped__at_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Etail_2E0,type,
    c_2Epath_2Etail_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)) ).

tff(c_2Epath_2Etail_2E1,type,
    c_2Epath_2Etail_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epath_2Epath(A_27a,A_27b) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Etake_2E0,type,
    c_2Epath_2Etake_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))) ).

tff(c_2Epath_2Etake_2E2,type,
    c_2Epath_2Etake_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Epath_2Epath(A_27a,A_27b) ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Ellist_2EtoList_2E0,type,
    c_2Ellist_2EtoList_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Ellist_2EtoList_2E1,type,
    c_2Ellist_2EtoList_2E1: 
      !>[A_27a: $tType] : ( tyop_2Ellist_2Ellist(A_27a) > tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2Epath_2EtoPath_2E0,type,
    c_2Epath_2EtoPath_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epath_2Epath(A_27a,A_27b)) ).

tff(c_2Epath_2EtoPath_2E1,type,
    c_2Epath_2EtoPath_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

tff(c_2Epath_2Etrace__machine_2E0,type,
    c_2Epath_2Etrace__machine_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))) ).

tff(c_2Epath_2Etrace__machine_2E1,type,
    c_2Epath_2Etrace__machine_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))) ) ).

tff(c_2Epath_2Etrace__machine_2E4,type,
    c_2Epath_2Etrace__machine_2E4: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) * tyop_2Elist_2Elist(A_27a) * A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epath_2Eunfold_2E0,type,
    c_2Epath_2Eunfold_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27a,A_27b)))) ).

tff(c_2Epath_2Eunfold_2E3,type,
    c_2Epath_2Eunfold_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27a) * tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))) * A_27c ) > tyop_2Epath_2Epath(A_27a,A_27b) ) ).

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_2Epair_2E_23_23_2E3_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_20mono_2EA_27c_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27d_2CA_27c_29_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_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),X2_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Epair_2E_23_23_2E3(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),app_2E2(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))))),c_2Epair_2E_23_23_2E0(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_23_23_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,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_27a,A_27c)] : ( c_2Epair_2E_23_23_2E2(A_27b,A_27a,A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c))),c_2Epair_2E_23_23_2E0(A_27b,A_27a,A_27d,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epair_2E_2C_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: A_27a,X1_2E0: A_27d] : ( c_2Epair_2E_2C_2E2(A_27a,A_27d,X0_2E0,X1_2E0) = app_2E2(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d),app_2E2(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Epair_2Eprod(A_27a,A_27d)),c_2Epair_2E_2C_2E0(A_27a,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Epair_2E_2C_2E0(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epair_2E_2C_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27e,axiom,
    ! [A_27c: $tType,A_27e: $tType,X0_2E0: A_27c,X1_2E0: A_27e] : ( c_2Epair_2E_2C_2E2(A_27c,A_27e,X0_2E0,X1_2E0) = app_2E2(A_27e,tyop_2Epair_2Eprod(A_27c,A_27e),app_2E2(A_27c,tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(A_27c,A_27e)),c_2Epair_2E_2C_2E0(A_27c,A_27e),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Epair_2Eprod(A_27b,A_27a)] : ( c_2Epair_2E_2C_2E2(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2E_2C_2E0(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,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_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_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(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(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Epath_2Epath(A_27a,A_27b)),X0_2E0),X1_2E0),X2_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_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2EEL_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),c_2Elist_2EEL_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Epair_2EFST_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),A_27a,c_2Epair_2EFST_2E0(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epath_2Epath(A_27a,A_27b),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epath_2Epath(A_27a,A_27b),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2Ctyop_2Epath_2Epath_28A_27a_2CA_27b_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epath_2Epath(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b),X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELAPPEND_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELAPPEND_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ellist_2ELAPPEND_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ellist_2ELAPPEND_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELCONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELCONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,A_27a),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ellist_2ELCONS_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ellist_2ELCONS_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_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_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ellist_2ELFINITE_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X1_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ellist_2ELMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELMAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2ELMAP_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27d_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c))] : ( c_2Ellist_2ELMAP_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),c_2Ellist_2ELMAP_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELNTH_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Ellist_2ELNTH_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27a)] : ( c_2Ellist_2ELTAKE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Ellist_2ELTAKE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2ELTAKE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),c_2Ellist_2ELTAKE_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),X1_2E0: A_27a] : ( c_2Ellist_2ELUNFOLD_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Ellist_2Ellist(A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELUNFOLD_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),X1_2E0: A_27c] : ( c_2Ellist_2ELUNFOLD_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ellist_2ELUNFOLD_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))] : ( c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Eoption_2EOPTION__MAP_2E0(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2EPL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epath_2EPL_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2EPL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2EPL_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epath_2EPL_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2ESN_2E1_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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Epath_2ESN_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Ebool,c_2Epath_2ESN_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epair_2ESND_2E0(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27b),X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Eoption_2ESOME_2E0(tyop_2Elist_2Elist(A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27c)] : ( c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Eoption_2ESOME_2E0(tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Eoption_2ETHE_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)] : ( c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Eoption_2ETHE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Ellist_2Ellist_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epath_2Epath(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Epath_2Epath_28A_27a_2CA_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epath_2Epath_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b))),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epath_2Epath_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27b,tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27b,tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))))] : ( c_2Epair_2EUNCURRY_2E1(A_27c,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2EUNCURRY_2E0(A_27c,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Epath_2Epath(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(A_27a),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(arityeq2_2Ec_2Epath_2Edrop_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),c_2Epath_2Edrop_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eel_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),A_27a),c_2Epath_2Eel_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eel_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Eel_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),A_27c,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),A_27c),c_2Epath_2Eel_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eevery_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eevery_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epath_2Eevery_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eevery_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Eevery_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Epath_2Eevery_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eexists_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eexists_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epath_2Eexists_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eexists_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Eexists_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Epath_2Eexists_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Efilter_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efilter_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),c_2Epath_2Efilter_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efinite_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efinite_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epath_2Efinite_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efinite_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Efinite_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Emin_2Ebool,c_2Epath_2Efinite_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efirst_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),A_27a,c_2Epath_2Efirst_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Efirst_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),A_27a,c_2Epath_2Efirst_2E0(A_27a,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27b,A_27c)] : ( c_2Epath_2Efirst_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27b,c_2Epath_2Efirst_2E0(A_27b,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27b)] : ( c_2Epath_2Efirst_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27b),A_27c,c_2Epath_2Efirst_2E0(A_27c,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Efirst_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),A_27c,c_2Epath_2Efirst_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a)] : ( c_2Epath_2Efirst_2E1(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Elist_2Elist(A_27a),c_2Epath_2Efirst_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] : ( c_2Epath_2Efirst_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epath_2Efirst_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X0_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2EfirstP__at_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),X2_2E0: tyop_2Enum_2Enum] : ( c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epath_2EfirstP__at_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst__label_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efirst__label_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),A_27b,c_2Epath_2Efirst__label_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Efirst__label_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Efirst__label_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27a),A_27a,c_2Epath_2Efirst__label_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2EfromPath_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EfromPath_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epath_2EfromPath_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2EfixedPoint_2Egfp_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2EfixedPoint_2Egfp_2E1(tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2EfixedPoint_2Egfp_2E0(tyop_2Epath_2Epath(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Eis__stopped_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eis__stopped_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epath_2Eis__stopped_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Eis__stopped_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Eis__stopped_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Emin_2Ebool,c_2Epath_2Eis__stopped_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elabels_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b),c_2Epath_2Elabels_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Elabels_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Ellist_2Ellist(A_27c),c_2Epath_2Elabels_2E0(A_27a,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27b,A_27c)] : ( c_2Epath_2Elabels_2E1(A_27b,A_27c,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Ellist_2Ellist(A_27c),c_2Epath_2Elabels_2E0(A_27b,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27b)] : ( c_2Epath_2Elabels_2E1(A_27c,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27b),tyop_2Ellist_2Ellist(A_27b),c_2Epath_2Elabels_2E0(A_27c,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a)] : ( c_2Epath_2Elabels_2E1(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a),c_2Epath_2Elabels_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elabels_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] : ( c_2Epath_2Elabels_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Ellist_2Ellist(A_27b),c_2Epath_2Elabels_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elast_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elast_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),A_27a,c_2Epath_2Elast_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elast_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Elast_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),A_27c,c_2Epath_2Elast_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elength_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Elength_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Elength_2E1(A_27a,A_27c,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Elength_2E0(A_27a,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27b,A_27d)] : ( c_2Epath_2Elength_2E1(A_27b,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27d),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Elength_2E0(A_27b,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Elength_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Elength_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Elength_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Emem_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Emem_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epath_2Emem_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Emem_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Emem_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Emin_2Ebool),c_2Epath_2Emem_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2EfixedPoint_2Emonotone_2E1_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2EfixedPoint_2Emonotone_2E1(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2EfixedPoint_2Emonotone_2E0(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Enth__label_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Enth__label_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),A_27b),c_2Epath_2Enth__label_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Enth__label_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Enth__label_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27a),A_27a),c_2Epath_2Enth__label_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Enth__label_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27d,A_27c)] : ( c_2Epath_2Enth__label_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27d,A_27c),A_27c,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27d,A_27c),A_27c),c_2Epath_2Enth__label_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,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_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Ecombin_2Eo_2E0(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] : ( c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27b,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),c_2Ecombin_2Eo_2E0(tyop_2Enum_2Enum,A_27b,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Eokpath_2E1_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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Epath_2Eokpath_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eokpath_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Eokpath_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(A_27b,A_27c)] : ( c_2Epath_2Eokpath_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(A_27c,A_27b)] : ( c_2Epath_2Eokpath_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27b),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a)] : ( c_2Epath_2Eokpath_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)] : ( c_2Epath_2Eokpath_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool))),X1_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] : ( c_2Epath_2Eokpath_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Ebool),c_2Epath_2Eokpath_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Eokpath__f_2E1_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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Epath_2Eokpath__f_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epath_2Eokpath__f_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eokpath__f_2E2_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,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epath_2Eokpath__f_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epath_2Eokpath__f_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X1_2E0: tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),X1_2E0: tyop_2Epath_2Epath(A_27b,A_27c),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Epath_2Epath(A_27b,A_27c))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0: tyop_2Epath_2Epath(A_27b,A_27c),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c))] : ( c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Epath_2Epath(A_27b,A_27c))),c_2Eoption_2Eoption__CASE_2E0(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c))),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c))),tyop_2Epath_2Epath(A_27b,A_27c)),c_2Epair_2Epair__CASE_2E0(tyop_2Epath_2Epath(A_27b,A_27c),A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c))),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Epair_2Eprod(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c))),tyop_2Epath_2Epath(A_27b,A_27c)),c_2Epair_2Epair__CASE_2E0(tyop_2Epath_2Epath(A_27b,A_27c),A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))),tyop_2Epath_2Epath(A_27b,A_27c)),c_2Epair_2Epair__CASE_2E0(tyop_2Epath_2Epath(A_27b,A_27c),A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eparallel__comp_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)))] : ( c_2Epath_2Eparallel__comp_2E2(A_27a,A_27b,A_27a,A_27c,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)))),c_2Epath_2Eparallel__comp_2E0(A_27a,A_27b,A_27a,A_27c,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq5_2Ec_2Epath_2Eparallel__comp_2E5_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),X2_2E0: tyop_2Epair_2Eprod(A_27a,A_27d),X3_2E0: A_27b,X4_2E0: tyop_2Epair_2Eprod(A_27c,A_27e)] : ( c_2Epath_2Eparallel__comp_2E5(A_27a,A_27b,A_27c,A_27d,A_27e,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27d),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27e),tyop_2Emin_2Ebool)))),c_2Epath_2Eparallel__comp_2E0(A_27a,A_27b,A_27c,A_27d,A_27e),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eparallel__comp_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] : ( c_2Epath_2Eparallel__comp_2E2(A_27a,A_27c,A_27a,A_27b,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Epath_2Eparallel__comp_2E0(A_27a,A_27c,A_27a,A_27b,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epconcat_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b),X1_2E0: A_27b,X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epconcat_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epath_2Epconcat_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epconcat_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epath_2Epath(A_27c,A_27d),X1_2E0: A_27d,X2_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Epconcat_2E3(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27c,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27c,A_27d)),app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27c,A_27d))),c_2Epath_2Epconcat_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b,X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epcons_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epath_2Epcons_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: A_27a,X1_2E0: A_27c,X2_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Epcons_2E3(A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Epath_2Epath(A_27a,A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Epath_2Epath(A_27a,A_27c)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Epath_2Epath(A_27a,A_27c))),c_2Epath_2Epcons_2E0(A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: A_27a,X1_2E0: A_27d,X2_2E0: tyop_2Epath_2Epath(A_27a,A_27d)] : ( c_2Epath_2Epcons_2E3(A_27a,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27d),tyop_2Epath_2Epath(A_27a,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27d),tyop_2Epath_2Epath(A_27a,A_27d)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27d),tyop_2Epath_2Epath(A_27a,A_27d))),c_2Epath_2Epcons_2E0(A_27a,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27b,X1_2E0: A_27c,X2_2E0: tyop_2Epath_2Epath(A_27b,A_27c)] : ( c_2Epath_2Epcons_2E3(A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27b,A_27c),tyop_2Epath_2Epath(A_27b,A_27c))),c_2Epath_2Epcons_2E0(A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epcons_2E3_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: A_27c,X1_2E0: A_27d,X2_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Epcons_2E3(A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27c,A_27d),app_2E2(A_27d,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27c,A_27d)),app_2E2(A_27c,tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27c,A_27d))),c_2Epath_2Epcons_2E0(A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Epgenerate_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Epath_2Epgenerate_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),c_2Epath_2Epgenerate_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Eplink_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b),X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eplink_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),c_2Epath_2Eplink_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27b),X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epath_2Epmap_2E0(A_27a,A_27b,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27c,A_27b,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27d),app_2E2(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27d))),c_2Epath_2Epmap_2E0(A_27a,A_27c,A_27b,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27c),X2_2E0: tyop_2Epath_2Epath(A_27a,A_27d)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27d,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27d),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27d),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27d),tyop_2Epath_2Epath(A_27b,A_27c))),c_2Epath_2Epmap_2E0(A_27a,A_27d,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,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_27b,A_27d),X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27c,A_27d,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d),app_2E2(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27c,A_27d))),c_2Epath_2Epmap_2E0(A_27a,A_27b,A_27c,A_27d),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27d,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27d,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27d,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27d,A_27c))),c_2Epath_2Epmap_2E0(A_27a,A_27b,A_27d,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Epmap_2E3(A_27c,A_27d,A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27c,A_27d),tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epath_2Epmap_2E0(A_27c,A_27d,A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27c),X2_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)] : ( c_2Epath_2Epmap_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Epath_2Epath(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27c,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Epath_2Epath(A_27a,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Epath_2Epath(A_27a,A_27c))),c_2Epath_2Epmap_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Epmap_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X1_2E0: tyop_2Emin_2Efun(A_27c,A_27c),X2_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)] : ( c_2Epath_2Epmap_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27c,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27c),tyop_2Emin_2Efun(tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Epath_2Epath(A_27b,A_27c))),c_2Epath_2Epmap_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Eseg_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eseg_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epath_2Eseg_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Estopped__at_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Epath_2Estopped__at_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Epath_2Epath(A_27a,A_27b),c_2Epath_2Estopped__at_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Estopped__at_2E1_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: $tType,A_27d: $tType,X0_2E0: A_27a] : ( c_2Epath_2Estopped__at_2E1(A_27a,A_27d,X0_2E0) = app_2E2(A_27a,tyop_2Epath_2Epath(A_27a,A_27d),c_2Epath_2Estopped__at_2E0(A_27a,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Estopped__at_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27b] : ( c_2Epath_2Estopped__at_2E1(A_27b,A_27c,X0_2E0) = app_2E2(A_27b,tyop_2Epath_2Epath(A_27b,A_27c),c_2Epath_2Estopped__at_2E0(A_27b,A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Etail_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etail_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),c_2Epath_2Etail_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Etail_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Etail_2E1(A_27b,A_27a,X0_2E0) = app_2E2(tyop_2Epath_2Epath(A_27b,A_27a),tyop_2Epath_2Epath(A_27b,A_27a),c_2Epath_2Etail_2E0(A_27b,A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epath_2Etake_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etake_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b)),c_2Epath_2Etake_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(A_27b)] : ( c_2Ellist_2EtoList_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2EtoList_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))] : ( c_2Ellist_2EtoList_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0) = app_2E2(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Ellist_2EtoList_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2EtoPath_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Epath_2EtoPath_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epath_2Epath(A_27a,A_27b),c_2Epath_2EtoPath_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2EtoPath_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)))] : ( c_2Epath_2EtoPath_2E1(A_27c,A_27d,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c))),tyop_2Epath_2Epath(A_27c,A_27d),c_2Epath_2EtoPath_2E0(A_27c,A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epath_2Etrace__machine_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epath_2Etrace__machine_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Epath_2Etrace__machine_2E0(A_27a),X0_2E0) ) ).

tff(arityeq4_2Ec_2Epath_2Etrace__machine_2E4_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(A_27a),X2_2E0: A_27a,X3_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Epath_2Etrace__machine_2E4(A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),c_2Epath_2Etrace__machine_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Eunfold_2E3_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),X2_2E0: A_27a] : ( c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27a,tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))),c_2Epath_2Eunfold_2E0(A_27b,A_27c,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epath_2Eunfold_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X2_2E0: A_27c] : ( c_2Epath_2Eunfold_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27c,tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27a,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epath_2Eunfold_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_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_2Epath_2Epath__TY__DEF,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Ebool)] :
      ( ! [V1x_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Ebool,F0_2E0,V1x_2E0) = c_2Ebool_2ET_2E0 )
     => ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Epath_2Epath(A_27a,A_27b),F0_2E0,V0rep_2E0)) ) ).

tff(thm_2Epath_2Epath__absrep__bijections,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0a_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EtoPath_2E1(A_27a,A_27b,c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0a_2E0)) = V0a_2E0 )
      & ! [V1r_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
          ( p(c_2Ebool_2ET_2E0)
        <=> ( c_2Epath_2EfromPath_2E1(A_27a,A_27b,c_2Epath_2EtoPath_2E1(A_27a,A_27b,V1r_2E0)) = V1r_2E0 ) ) ) ).

tff(thm_2Epath_2Efirst__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p_2E0) = c_2Epair_2EFST_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0p_2E0)) ) ).

tff(thm_2Epath_2Estopped__at__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a] : ( c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0) = c_2Epath_2EtoPath_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),V0x_2E0,c_2Ellist_2ELNIL_2E0(tyop_2Epair_2Eprod(A_27b,A_27a)))) ) ).

tff(thm_2Epath_2Epcons__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: A_27b,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2p_2E0) = c_2Epath_2EtoPath_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),V0x_2E0,c_2Ellist_2ELCONS_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V1r_2E0,c_2Epath_2Efirst_2E1(A_27a,A_27b,V2p_2E0)),c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V2p_2E0))))) ) ).

tff(thm_2Epath_2Efinite__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0sigma_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efinite_2E1(A_27a,A_27b,V0sigma_2E0) = c_2Ellist_2ELFINITE_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0sigma_2E0))) ) ).

tff(thm_2Epath_2Elast__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Elast_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = V0x_2E0 )
      & ! [V1x_2E0: A_27a,V2r_2E0: A_27b,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elast_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V1x_2E0,V2r_2E0,V3p_2E0)) = c_2Epath_2Elast_2E1(A_27a,A_27b,V3p_2E0) ) ) ).

tff(thm_2Epath_2Epmap__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1g_2E0,V2p_2E0) = c_2Epath_2EtoPath_2E1(A_27c,A_27d,c_2Epair_2E_23_23_2E3(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),A_27c,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27d,A_27c)),V0f_2E0,c_2Ellist_2ELMAP_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(A_27d,A_27c),c_2Epair_2E_23_23_2E2(A_27b,A_27a,A_27d,A_27c,V1g_2E0,V0f_2E0)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V2p_2E0))) ) ).

tff(thm_2Epath_2Etail__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: A_27b,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etail_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2p_2E0)) = V2p_2E0 ) ).

tff(thm_2Epath_2Efirst__label__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: A_27b,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efirst__label_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2p_2E0)) = V1r_2E0 ) ).

tff(thm_2Epath_2Elength__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elength_2E1(A_27a,A_27b,V0p_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Elist_2ELENGTH_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Eoption_2ETHE_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Ellist_2EtoList_2E1(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0p_2E0))))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ).

tff(thm_2Epath_2Eel__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),V2p_2E0) = c_2Epath_2Eel_2E2(A_27a,A_27b,V1n_2E0,c_2Epath_2Etail_2E1(A_27a,A_27b,V2p_2E0)) ) ) ).

tff(thm_2Epath_2Enth__label__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = c_2Epath_2Efirst__label_2E1(A_27b,A_27a,V0p_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),V2p_2E0) = c_2Epath_2Enth__label_2E2(A_27a,A_27b,V1n_2E0,c_2Epath_2Etail_2E1(A_27b,A_27a,V2p_2E0)) ) ) ).

tff(thm_2Epath_2Epconcat__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1lab_2E0: A_27b,V2p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epconcat_2E3(A_27a,A_27b,V0p1_2E0,V1lab_2E0,V2p2_2E0) = c_2Epath_2EtoPath_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p1_2E0),c_2Ellist_2ELAPPEND_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0p1_2E0)),c_2Ellist_2ELCONS_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epair_2E_2C_2E2(A_27b,A_27a,V1lab_2E0,c_2Epath_2Efirst_2E1(A_27a,A_27b,V2p2_2E0)),c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V2p2_2E0)))))) ) ).

tff(thm_2Epath_2EPL__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0p_2E0),V1i_2E0))
        <=> ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0))
           => p(c_2Eprim__rec_2E_3C_2E2(V1i_2E0,c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Epath_2Elength_2E1(A_27a,A_27b,V0p_2E0)))) ) )
     => ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0p_2E0),V1i_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1i_2E0,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0,V0p_2E0),V1i_2E0)) )
       => ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0p_2E0)) ) ) ) ).

tff(thm_2Epath_2EfirstP__at__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V0P_2E0,V1p_2E0,V2i_2E0))
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Eel_2E2(A_27a,A_27b,V2i_2E0,V1p_2E0)))
        & ! [V3j_2E0: tyop_2Enum_2Enum] :
            ( p(c_2Eprim__rec_2E_3C_2E2(V3j_2E0,V2i_2E0))
           => ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Eel_2E2(A_27a,A_27b,V3j_2E0,V1p_2E0))) ) ) ) ).

tff(thm_2Epath_2Eexists__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eexists_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
    <=> ? [V2i_2E0: tyop_2Enum_2Enum] : p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V0P_2E0,V1p_2E0,V2i_2E0)) ) ).

tff(thm_2Epath_2Eevery__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eevery_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
    <=> ~ p(c_2Epath_2Eexists_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1p_2E0)) ) ).

tff(thm_2Epath_2Emem__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: A_27a,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Emem_2E2(A_27a,A_27b,V0s_2E0,V1p_2E0))
    <=> ? [V2i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
          & ( V0s_2E0 = c_2Epath_2Eel_2E2(A_27a,A_27b,V2i_2E0,V1p_2E0) ) ) ) ).

tff(thm_2Epath_2Edrop__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = V0p_2E0 )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),V2p_2E0) = c_2Epath_2Edrop_2E2(A_27a,A_27b,V1n_2E0,c_2Epath_2Etail_2E1(A_27a,A_27b,V2p_2E0)) ) ) ).

tff(thm_2Epath_2Etake__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p_2E0)) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Enum_2ESUC_2E1(V1n_2E0),V2p_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,c_2Epath_2Efirst_2E1(A_27a,A_27b,V2p_2E0),c_2Epath_2Efirst__label_2E1(A_27a,A_27b,V2p_2E0),c_2Epath_2Etake_2E2(A_27a,A_27b,V1n_2E0,c_2Epath_2Etail_2E1(A_27a,A_27b,V2p_2E0))) ) ) ).

tff(thm_2Epath_2Eseg__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eseg_2E3(A_27a,A_27b,V0i_2E0,V1j_2E0,V2p_2E0) = c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(V1j_2E0,V0i_2E0),c_2Epath_2Edrop_2E2(A_27a,A_27b,V0i_2E0,V2p_2E0)) ) ).

tff(thm_2Epath_2Elabels__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Elabels_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Ellist_2ELNIL_2E0(A_27b) )
      & ! [V1x_2E0: A_27a,V2r_2E0: A_27b,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elabels_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V1x_2E0,V2r_2E0,V3p_2E0)) = c_2Ellist_2ELCONS_2E2(A_27b,V2r_2E0,c_2Epath_2Elabels_2E1(A_27a,A_27b,V3p_2E0)) ) ) ).

tff(thm_2Epath_2Eis__stopped__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eis__stopped_2E1(A_27a,A_27b,V0p_2E0))
    <=> ? [V1x_2E0: A_27a] : ( V0p_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0) ) ) ).

tff(thm_2Epath_2Efilter__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V1x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0))
         => ( c_2Epath_2Efilter_2E2(A_27a,A_27b,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0)) = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0) ) )
      & ! [V2x_2E0: A_27a,V3r_2E0: A_27b,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efilter_2E2(A_27a,A_27b,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,V4p_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Epath_2Epath(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0),c_2Ebool_2ECOND_2E3(tyop_2Epath_2Epath(A_27a,A_27b),c_2Epath_2Eexists_2E2(A_27a,A_27b,V0P_2E0,V4p_2E0),c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,c_2Epath_2Efilter_2E2(A_27a,A_27b,V0P_2E0,V4p_2E0)),c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0)),c_2Epath_2Efilter_2E2(A_27a,A_27b,V0P_2E0,V4p_2E0)) ) ) ).

tff(thm_2Epath_2Epgenerate__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,A_27a,V0f_2E0,c_2Enum_2E0_2E0),app_2E2(tyop_2Enum_2Enum,A_27b,V1g_2E0,c_2Enum_2E0_2E0),c_2Epath_2Epgenerate_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27a,tyop_2Enum_2Enum,V0f_2E0,c_2Enum_2ESUC_2E0),c_2Ecombin_2Eo_2E2(tyop_2Enum_2Enum,A_27b,tyop_2Enum_2Enum,V1g_2E0,c_2Enum_2ESUC_2E0))) ) ).

tff(thm_2Epath_2Eokpath__f__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))] :
      ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V3x_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1X_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F3_2E0,V0R_2E0),V3x_2E0),V4r_2E0),V5p_2E0),V1X_2E0))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,V3x_2E0),V4r_2E0),c_2Epath_2Efirst_2E1(A_27a,A_27b,V5p_2E0)))
            & p(c_2Ebool_2EIN_2E2(tyop_2Epath_2Epath(A_27a,A_27b),V5p_2E0,V1X_2E0)) ) )
     => ( ! [V3x_2E0: A_27a,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1X_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))))),F2_2E0,V3x_2E0),V0R_2E0),V1X_2E0),V4r_2E0),V5p_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_2E0,V4r_2E0,V5p_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F3_2E0,V0R_2E0),V3x_2E0),V4r_2E0),V5p_2E0),V1X_2E0)) )
       => ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1X_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))),F1_2E0,V0R_2E0),V1X_2E0),V3x_2E0) = c_2Epair_2EUNCURRY_2E1(A_27b,tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))))),F2_2E0,V3x_2E0),V0R_2E0),V1X_2E0)) )
         => ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),F0_2E0,V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Epred__set_2EUNIV_2E0(A_27a))) )
           => ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1X_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epath_2Eokpath__f_2E2(A_27a,A_27b,V0R_2E0,V1X_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Epath_2Epath(A_27a,A_27b),c_2Epred__set_2EGSPEC_2E1(tyop_2Epath_2Epath(A_27a,A_27b),A_27a,F0_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b))),c_2Epair_2EUNCURRY_2E1(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Epath_2Epath(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)))),F1_2E0,V0R_2E0),V1X_2E0)))) ) ) ) ) ) ).

tff(thm_2Epath_2Eokpath__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Epath_2Eokpath_2E1(A_27a,A_27b,V0R_2E0) = c_2EfixedPoint_2Egfp_2E1(tyop_2Epath_2Epath(A_27a,A_27b),c_2Epath_2Eokpath__f_2E1(A_27a,A_27b,V0R_2E0)) ) ).

tff(thm_2Epath_2Eplink__def,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eplink_2E2(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0),V1p_2E0) = V1p_2E0 )
      & ! [V2x_2E0: A_27a,V3r_2E0: A_27b,V4p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V5p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eplink_2E2(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,V4p1_2E0),V5p2_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,c_2Epath_2Eplink_2E2(A_27a,A_27b,V4p1_2E0,V5p2_2E0)) ) ) ).

tff(thm_2Epath_2ESN__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,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),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0),V1x_2E0),V2y_2E0))
        <=> ? [V3l_2E0: A_27b] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,V2y_2E0),V3l_2E0),V1x_2E0)) )
     => ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : ( c_2Epath_2ESN_2E1(A_27a,A_27b,V0R_2E0) = c_2Erelation_2EWF_2E1(A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0,V0R_2E0)) ) ) ).

tff(thm_2Epath_2Eunfold__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))))))] :
      ( ! [V0proj_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V4next__s_2E0: A_27c,V5lbl_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),F1_2E0,V0proj_2E0),V4next__s_2E0),V5lbl_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a),V4next__s_2E0,c_2Epair_2E_2C_2E2(A_27b,A_27a,V5lbl_2E0,app_2E2(A_27c,A_27a,V0proj_2E0,V4next__s_2E0))) )
     => ( ! [V0proj_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V3s_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))))),F0_2E0,V0proj_2E0),V1f_2E0),V3s_2E0) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epair_2EUNCURRY_2E1(A_27c,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),F1_2E0,V0proj_2E0)),app_2E2(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),V1f_2E0,V3s_2E0)) )
       => ! [V0proj_2E0: tyop_2Emin_2Efun(A_27c,A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V2s_2E0: A_27c] : ( c_2Epath_2Eunfold_2E3(A_27a,A_27b,A_27c,V0proj_2E0,V1f_2E0,V2s_2E0) = c_2Epath_2EtoPath_2E1(A_27a,A_27b,c_2Epair_2E_2C_2E2(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(A_27c,A_27a,V0proj_2E0,V2s_2E0),c_2Ellist_2ELUNFOLD_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(A_27b,A_27a))))),F0_2E0,V0proj_2E0),V1f_2E0),V2s_2E0))) ) ) ) ).

tff(thm_2Epath_2Etrace__machine__def,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1s_2E0: tyop_2Elist_2Elist(A_27a),V2l_2E0: A_27a,V3s_27_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Epath_2Etrace__machine_2E4(A_27a,V0P_2E0,V1s_2E0,V2l_2E0,V3s_27_2E0))
    <=> ( p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,V1s_2E0,c_2Elist_2ECONS_2E2(A_27a,V2l_2E0,c_2Elist_2ENIL_2E0(A_27a)))))
        & ( V3s_27_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V1s_2E0,c_2Elist_2ECONS_2E2(A_27a,V2l_2E0,c_2Elist_2ENIL_2E0(A_27a))) ) ) ) ).

tff(thm_2Epath_2Eparallel__comp__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,V0m1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V1m2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool))),V2s1_2E0: A_27a,V3s2_2E0: A_27d,V4l_2E0: A_27b,V5s1_27_2E0: A_27c,V6s2_27_2E0: A_27e] :
      ( p(c_2Epath_2Eparallel__comp_2E5(A_27a,A_27b,A_27c,A_27d,A_27e,V0m1_2E0,V1m2_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27d,V2s1_2E0,V3s2_2E0),V4l_2E0,c_2Epair_2E_2C_2E2(A_27c,A_27e,V5s1_27_2E0,V6s2_27_2E0)))
    <=> ( p(app_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V0m1_2E0,V2s1_2E0),V4l_2E0),V5s1_27_2E0))
        & p(app_2E2(A_27e,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool),app_2E2(A_27d,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Ebool)),V1m2_2E0,V3s2_2E0),V4l_2E0),V6s2_27_2E0)) ) ) ).

tff(thm_2Epath_2Epath__rep__bijections__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0a_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EtoPath_2E1(A_27a,A_27b,c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0a_2E0)) = V0a_2E0 )
      & ! [V1r_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( c_2Epath_2EfromPath_2E1(A_27a,A_27b,c_2Epath_2EtoPath_2E1(A_27a,A_27b,V1r_2E0)) = V1r_2E0 ) ) ).

tff(thm_2Epath_2EtoPath__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a))),V1r_27_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
      ( ( c_2Epath_2EtoPath_2E1(A_27a,A_27b,V0r_2E0) = c_2Epath_2EtoPath_2E1(A_27a,A_27b,V1r_27_2E0) )
    <=> ( V0r_2E0 = V1r_27_2E0 ) ) ).

tff(thm_2Epath_2EfromPath__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1a_27_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0a_2E0) = c_2Epath_2EfromPath_2E1(A_27a,A_27b,V1a_27_2E0) )
    <=> ( V0a_2E0 = V1a_27_2E0 ) ) ).

tff(thm_2Epath_2EfromPath__onto,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0r_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] :
    ? [V1a_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( V0r_2E0 = c_2Epath_2EfromPath_2E1(A_27a,A_27b,V1a_2E0) ) ).

tff(thm_2Epath_2EtoPath__onto,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0a_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
    ? [V1r_2E0: tyop_2Epair_2Eprod(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)))] : ( V0a_2E0 = c_2Epath_2EtoPath_2E1(A_27a,A_27b,V1r_2E0) ) ).

tff(thm_2Epath_2Estopped__at__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a] :
      ( ( c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0) = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1y_2E0) )
    <=> ( V0x_2E0 = V1y_2E0 ) ) ).

tff(thm_2Epath_2Epcons__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: A_27b,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V3y_2E0: A_27a,V4s_2E0: A_27b,V5q_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2p_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,V3y_2E0,V4s_2E0,V5q_2E0) )
    <=> ( ( V0x_2E0 = V3y_2E0 )
        & ( V1r_2E0 = V4s_2E0 )
        & ( V2p_2E0 = V5q_2E0 ) ) ) ).

tff(thm_2Epath_2Estopped__at__not__pcons,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27a,V2r_2E0: A_27b,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0) != c_2Epath_2Epcons_2E3(A_27a,A_27b,V1y_2E0,V2r_2E0,V3p_2E0) )
      & ( c_2Epath_2Epcons_2E3(A_27a,A_27b,V1y_2E0,V2r_2E0,V3p_2E0) != c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0) ) ) ).

tff(thm_2Epath_2Epath__cases,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ? [V1x_2E0: A_27a] : ( V0p_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0) )
      | ? [V2x_2E0: A_27a,V3r_2E0: A_27b,V4q_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( V0p_2E0 = c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,V4q_2E0) ) ) ).

tff(thm_2Epath_2EFORALL__path,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ! [V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V1p_2E0))
    <=> ( ! [V2x_2E0: A_27a] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0)))
        & ! [V3x_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_2E0,V4r_2E0,V5p_2E0))) ) ) ).

tff(thm_2Epath_2EEXISTS__path,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ? [V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V1p_2E0))
    <=> ( ? [V2x_2E0: A_27a] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0)))
        | ? [V3x_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_2E0,V4r_2E0,V5p_2E0))) ) ) ).

tff(thm_2Epath_2Efirst__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Efirst_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = V0x_2E0 )
      & ! [V1x_2E0: A_27a,V2r_2E0: A_27b,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efirst_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V1x_2E0,V2r_2E0,V3p_2E0)) = V1x_2E0 ) ) ).

tff(thm_2Epath_2Efinite__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Ebool_2ET_2E0 )
      & ! [V1x_2E0: A_27a,V2r_2E0: A_27b,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V1x_2E0,V2r_2E0,V3p_2E0)) = c_2Epath_2Efinite_2E1(A_27a,A_27b,V3p_2E0) ) ) ).

tff(thm_2Epath_2Epath__bisimulation,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( V0p1_2E0 = V1p2_2E0 )
    <=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V2R_2E0,V0p1_2E0),V1p2_2E0))
          & ! [V3q1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V4q2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
              ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V2R_2E0,V3q1_2E0),V4q2_2E0))
             => ( ? [V5x_2E0: A_27a] :
                    ( ( V3q1_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V5x_2E0) )
                    & ( V4q2_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V5x_2E0) ) )
                | ? [V6x_2E0: A_27a,V7r_2E0: A_27b,V8q1_27_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V9q2_27_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
                    ( ( V3q1_2E0 = c_2Epath_2Epcons_2E3(A_27a,A_27b,V6x_2E0,V7r_2E0,V8q1_27_2E0) )
                    & ( V4q2_2E0 = c_2Epath_2Epcons_2E3(A_27a,A_27b,V6x_2E0,V7r_2E0,V9q2_27_2E0) )
                    & p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V2R_2E0,V8q1_27_2E0),V9q2_27_2E0)) ) ) ) ) ) ).

tff(thm_2Epath_2Efinite__path__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ( ! [V1x_2E0: A_27a] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0)))
        & ! [V2x_2E0: A_27a,V3r_2E0: A_27b,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
            ( ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V4p_2E0))
              & p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V4p_2E0)) )
           => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,V4p_2E0))) ) )
     => ! [V5q_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V5q_2E0))
         => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V5q_2E0)) ) ) ).

tff(thm_2Epath_2Epmap__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27d,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( c_2Epath_2Epmap_2E3(A_27a,A_27d,A_27b,A_27c,V1f_2E0,V0g_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27d,V2x_2E0)) = c_2Epath_2Estopped__at_2E1(A_27b,A_27c,app_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0)) )
      & ! [V3x_2E0: A_27a,V4r_2E0: A_27d,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27d)] : ( c_2Epath_2Epmap_2E3(A_27a,A_27d,A_27b,A_27c,V1f_2E0,V0g_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27d,V3x_2E0,V4r_2E0,V5p_2E0)) = c_2Epath_2Epcons_2E3(A_27b,A_27c,app_2E2(A_27a,A_27b,V1f_2E0,V3x_2E0),app_2E2(A_27d,A_27c,V0g_2E0,V4r_2E0),c_2Epath_2Epmap_2E3(A_27a,A_27d,A_27b,A_27c,V1f_2E0,V0g_2E0,V5p_2E0)) ) ) ).

tff(thm_2Epath_2Efirst__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efirst_2E1(A_27c,A_27d,c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27c,A_27d,V1f_2E0,V0g_2E0,V2p_2E0)) = app_2E2(A_27a,A_27c,V1f_2E0,c_2Epath_2Efirst_2E1(A_27a,A_27b,V2p_2E0)) ) ).

tff(thm_2Epath_2Elast__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V2p_2E0))
     => ( c_2Epath_2Elast_2E1(A_27c,A_27d,c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27c,A_27d,V1f_2E0,V0g_2E0,V2p_2E0)) = app_2E2(A_27a,A_27c,V1f_2E0,c_2Epath_2Elast_2E1(A_27a,A_27b,V2p_2E0)) ) ) ).

tff(thm_2Epath_2Efinite__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Efinite_2E1(A_27c,A_27d,c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27c,A_27d,V0f_2E0,V1g_2E0,V2p_2E0)) = c_2Epath_2Efinite_2E1(A_27a,A_27b,V2p_2E0) ) ).

tff(thm_2Epath_2Elength__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Elength_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
      & ! [V1x_2E0: A_27c,V2r_2E0: A_27d,V3p_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Elength_2E1(A_27c,A_27d,c_2Epath_2Epcons_2E3(A_27c,A_27d,V1x_2E0,V2r_2E0,V3p_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Efinite_2E1(A_27c,A_27d,V3p_2E0),c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Eoption_2ETHE_2E1(tyop_2Enum_2Enum,c_2Epath_2Elength_2E1(A_27c,A_27d,V3p_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum)) ) ) ).

tff(thm_2Epath_2Ealt__length__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Elength_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
      & ! [V1x_2E0: A_27c,V2r_2E0: A_27d,V3p_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Elength_2E1(A_27c,A_27d,c_2Epath_2Epcons_2E3(A_27c,A_27d,V1x_2E0,V2r_2E0,V3p_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,c_2Epath_2Elength_2E1(A_27c,A_27d,V3p_2E0)) ) ) ).

tff(thm_2Epath_2Elength__never__zero,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elength_2E1(A_27a,A_27b,V0p_2E0) != c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ) ).

tff(thm_2Epath_2Efinite__length,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0))
      <=> ? [V1n_2E0: tyop_2Enum_2Enum] : ( c_2Epath_2Elength_2E1(A_27a,A_27b,V0p_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,V1n_2E0) ) )
      & ( ~ p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0))
      <=> ( c_2Epath_2Elength_2E1(A_27a,A_27b,V0p_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum) ) ) ) ).

tff(thm_2Epath_2Elength__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27c,A_27d),V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] : ( c_2Epath_2Elength_2E1(A_27b,A_27d,c_2Epath_2Epmap_2E3(A_27a,A_27c,A_27b,A_27d,V0f_2E0,V1g_2E0,V2p_2E0)) = c_2Epath_2Elength_2E1(A_27a,A_27c,V2p_2E0) ) ).

tff(thm_2Epath_2Eel__def__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2p_2E0) = c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2Etail_2E1(A_27a,A_27b,V2p_2E0)) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4p_2E0) = c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Epath_2Etail_2E1(A_27a,A_27b,V4p_2E0)) ) ) ).

tff(thm_2Epath_2Enth__label__def__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = c_2Epath_2Efirst__label_2E1(A_27b,A_27a,V0p_2E0) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2p_2E0) = c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2Etail_2E1(A_27b,A_27a,V2p_2E0)) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4p_2E0: tyop_2Epath_2Epath(A_27b,A_27a)] : ( c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4p_2E0) = c_2Epath_2Enth__label_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Epath_2Etail_2E1(A_27b,A_27a,V4p_2E0)) ) ) ).

tff(thm_2Epath_2Epath__Axiom,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))))),F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c))))] :
      ( ! [V3y_2E0: A_27b,V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),V6l_2E0: A_27c,V7v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)))),F2_2E0,V3y_2E0),V1g_2E0),V6l_2E0),V7v_2E0) = c_2Epath_2Epcons_2E3(A_27b,A_27c,V3y_2E0,V6l_2E0,app_2E2(A_27a,tyop_2Epath_2Epath(A_27b,A_27c),V1g_2E0,V7v_2E0)) )
     => ( ! [V3y_2E0: A_27b,V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),V5v3_2E0: tyop_2Epair_2Eprod(A_27c,A_27a)] : ( app_2E2(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c))),F1_2E0,V3y_2E0),V1g_2E0),V5v3_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27c,A_27a,V5v3_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)))),F2_2E0,V3y_2E0),V1g_2E0)) )
       => ( ! [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),V3y_2E0: A_27b,V4v2_2E0: tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))] : ( app_2E2(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c))),F0_2E0,V1g_2E0),V3y_2E0),V4v2_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c),V4v2_2E0,c_2Epath_2Estopped__at_2E1(A_27b,A_27c,V3y_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epath_2Epath(A_27b,A_27c))),F1_2E0,V3y_2E0),V1g_2E0)) )
         => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))))] :
            ? [V1g_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c))] :
            ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epath_2Epath(A_27b,A_27c),V1g_2E0,V2x_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V0f_2E0,V2x_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epath_2Epath(A_27b,A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Epath_2Epath(A_27b,A_27c))),F0_2E0,V1g_2E0)) ) ) ) ) ).

tff(thm_2Epath_2Epconcat__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0x_2E0: A_27a,V1lab_2E0: A_27b,V2p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Epconcat_2E3(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0),V1lab_2E0,V2p2_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1lab_2E0,V2p2_2E0) )
      & ! [V3x_2E0: A_27c,V4r_2E0: A_27d,V5p_2E0: tyop_2Epath_2Epath(A_27c,A_27d),V6lab_2E0: A_27d,V7p2_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Epconcat_2E3(A_27c,A_27d,c_2Epath_2Epcons_2E3(A_27c,A_27d,V3x_2E0,V4r_2E0,V5p_2E0),V6lab_2E0,V7p2_2E0) = c_2Epath_2Epcons_2E3(A_27c,A_27d,V3x_2E0,V4r_2E0,c_2Epath_2Epconcat_2E3(A_27c,A_27d,V5p_2E0,V6lab_2E0,V7p2_2E0)) ) ) ).

tff(thm_2Epath_2Epconcat__eq__stopped,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1lab_2E0: A_27b,V2p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V3x_2E0: A_27a] :
      ( ( c_2Epath_2Epconcat_2E3(A_27a,A_27b,V0p1_2E0,V1lab_2E0,V2p2_2E0) != c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V3x_2E0) )
      & ( c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V3x_2E0) != c_2Epath_2Epconcat_2E3(A_27a,A_27b,V0p1_2E0,V1lab_2E0,V2p2_2E0) ) ) ).

tff(thm_2Epath_2Epconcat__eq__pcons,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: A_27b,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V3p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V4lab_2E0: A_27b,V5p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( ( c_2Epath_2Epconcat_2E3(A_27a,A_27b,V3p1_2E0,V4lab_2E0,V5p2_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2p_2E0) )
      <=> ( ( ( V4lab_2E0 = V1r_2E0 )
            & ( V3p1_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0) )
            & ( V2p_2E0 = V5p2_2E0 ) )
          | ? [V6p1_27_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
              ( ( V3p1_2E0 = c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V6p1_27_2E0) )
              & ( V2p_2E0 = c_2Epath_2Epconcat_2E3(A_27a,A_27b,V6p1_27_2E0,V4lab_2E0,V5p2_2E0) ) ) ) )
      & ( ( c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2p_2E0) = c_2Epath_2Epconcat_2E3(A_27a,A_27b,V3p1_2E0,V4lab_2E0,V5p2_2E0) )
      <=> ( ( ( V4lab_2E0 = V1r_2E0 )
            & ( V3p1_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0) )
            & ( V2p_2E0 = V5p2_2E0 ) )
          | ? [V7p1_27_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
              ( ( V3p1_2E0 = c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V7p1_27_2E0) )
              & ( V2p_2E0 = c_2Epath_2Epconcat_2E3(A_27a,A_27b,V7p1_27_2E0,V4lab_2E0,V5p2_2E0) ) ) ) ) ) ).

tff(thm_2Epath_2Efinite__pconcat,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1lab_2E0: A_27b,V2p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Epconcat_2E3(A_27a,A_27b,V0p1_2E0,V1lab_2E0,V2p2_2E0)))
    <=> ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p1_2E0))
        & p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V2p2_2E0)) ) ) ).

tff(thm_2Epath_2Einfinite__PL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ~ p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0))
     => ! [V1i_2E0: tyop_2Enum_2Enum] : p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0))) ) ).

tff(thm_2Epath_2EPL__pcons,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1r_2E0: A_27b,V2q_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V0x_2E0,V1r_2E0,V2q_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V2q_2E0))) ) ).

tff(thm_2Epath_2EPL__stopped__at,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) ) ).

tff(thm_2Epath_2EPL__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) )
      & ! [V1x_2E0: A_27a,V2r_2E0: A_27b,V3q_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Epcons_2E3(A_27a,A_27b,V1x_2E0,V2r_2E0,V3q_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V3q_2E0))) ) ) ).

tff(thm_2Epath_2EPL__0,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0))) ).

tff(thm_2Epath_2EPL__downward__closed,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
     => ! [V2j_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Eprim__rec_2E_3C_2E2(V2j_2E0,V0i_2E0))
         => p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0))) ) ) ).

tff(thm_2Epath_2EPL__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27c,A_27d),V1g_2E0: tyop_2Emin_2Efun(A_27d,A_27b),V2f_2E0: tyop_2Emin_2Efun(A_27c,A_27a)] : ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Epmap_2E3(A_27c,A_27d,A_27a,A_27b,V2f_2E0,V1g_2E0,V0p_2E0)) = c_2Epath_2EPL_2E1(A_27c,A_27d,V0p_2E0) ) ).

tff(thm_2Epath_2Eel__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27d),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V2i_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V3p_2E0)))
     => ( c_2Epath_2Eel_2E2(A_27c,A_27d,V2i_2E0,c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27c,A_27d,V1f_2E0,V0g_2E0,V3p_2E0)) = app_2E2(A_27a,A_27c,V1f_2E0,c_2Epath_2Eel_2E2(A_27a,A_27b,V2i_2E0,V3p_2E0)) ) ) ).

tff(thm_2Epath_2Enth__label__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0g_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27d),V2i_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(V2i_2E0),c_2Epath_2EPL_2E1(A_27a,A_27b,V3p_2E0)))
     => ( c_2Epath_2Enth__label_2E2(A_27c,A_27d,V2i_2E0,c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27d,A_27c,V1f_2E0,V0g_2E0,V3p_2E0)) = app_2E2(A_27b,A_27c,V0g_2E0,c_2Epath_2Enth__label_2E2(A_27b,A_27a,V2i_2E0,V3p_2E0)) ) ) ).

tff(thm_2Epath_2EfirstP__at__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a,V2n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0),V2n_2E0))
        <=> ( ( V2n_2E0 = c_2Enum_2E0_2E0 )
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0)) ) )
      & ! [V3P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4n_2E0: tyop_2Enum_2Enum,V5x_2E0: A_27a,V6r_2E0: A_27b,V7p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V3P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V5x_2E0,V6r_2E0,V7p_2E0),V4n_2E0))
        <=> ( ( ( V4n_2E0 = c_2Enum_2E0_2E0 )
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V5x_2E0)) )
            | ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V4n_2E0))
              & ~ p(app_2E2(A_27a,tyop_2Emin_2Ebool,V3P_2E0,V5x_2E0))
              & p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V3P_2E0,V7p_2E0,c_2Earithmetic_2E_2D_2E2(V4n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ) ) ).

tff(thm_2Epath_2EfirstP__at__zero,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V0P_2E0,V1p_2E0,c_2Enum_2E0_2E0) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Efirst_2E1(A_27a,A_27b,V1p_2E0)) ) ).

tff(thm_2Epath_2Eexists__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V1x_2E0: A_27a] : ( c_2Epath_2Eexists_2E2(A_27a,A_27b,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0)) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0) )
      & ! [V2x_2E0: A_27a,V3r_2E0: A_27c,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] :
          ( p(c_2Epath_2Eexists_2E2(A_27a,A_27c,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27c,V2x_2E0,V3r_2E0,V4p_2E0)))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
            | p(c_2Epath_2Eexists_2E2(A_27a,A_27c,V0P_2E0,V4p_2E0)) ) ) ) ).

tff(thm_2Epath_2Eevery__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V1x_2E0: A_27a] : ( c_2Epath_2Eevery_2E2(A_27a,A_27b,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0)) = app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V1x_2E0) )
      & ! [V2x_2E0: A_27a,V3r_2E0: A_27c,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27c)] :
          ( p(c_2Epath_2Eevery_2E2(A_27a,A_27c,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27c,V2x_2E0,V3r_2E0,V4p_2E0)))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
            & p(c_2Epath_2Eevery_2E2(A_27a,A_27c,V0P_2E0,V4p_2E0)) ) ) ) ).

tff(thm_2Epath_2Enot__every,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ~ p(c_2Epath_2Eevery_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
    <=> p(c_2Epath_2Eexists_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1p_2E0)) ) ).

tff(thm_2Epath_2Enot__exists,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ~ p(c_2Epath_2Eexists_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
    <=> p(c_2Epath_2Eevery_2E2(A_27a,A_27b,c_2Ecombin_2Eo_2E2(A_27a,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0P_2E0),V1p_2E0)) ) ).

tff(thm_2Epath_2Eexists__el,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eexists_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
    <=> ? [V2i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
          & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Eel_2E2(A_27a,A_27b,V2i_2E0,V1p_2E0))) ) ) ).

tff(thm_2Epath_2Eevery__el,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eevery_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
    <=> ! [V2i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Eel_2E2(A_27a,A_27b,V2i_2E0,V1p_2E0))) ) ) ).

tff(thm_2Epath_2Eevery__coinduction,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ! [V2x_2E0: A_27a] :
            ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0)))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
        & ! [V3x_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
            ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_2E0,V4r_2E0,V5p_2E0)))
           => ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0))
              & p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V5p_2E0)) ) ) )
     => ! [V6p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V6p_2E0))
         => p(c_2Epath_2Eevery_2E2(A_27a,A_27b,V1Q_2E0,V6p_2E0)) ) ) ).

tff(thm_2Epath_2Eexists__induction,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ( ! [V2x_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0Q_2E0,V2x_2E0))
           => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0))) )
        & ! [V3x_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0Q_2E0,V3x_2E0))
           => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_2E0,V4r_2E0,V5p_2E0))) )
        & ! [V6x_2E0: A_27a,V7r_2E0: A_27b,V8p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
            ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,V8p_2E0))
           => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V6x_2E0,V7r_2E0,V8p_2E0))) ) )
     => ! [V9p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(c_2Epath_2Eexists_2E2(A_27a,A_27b,V0Q_2E0,V9p_2E0))
         => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,V9p_2E0)) ) ) ).

tff(thm_2Epath_2Emem__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0x_2E0: A_27a,V1s_2E0: A_27a] :
          ( p(c_2Epath_2Emem_2E2(A_27a,A_27b,V1s_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)))
        <=> ( V1s_2E0 = V0x_2E0 ) )
      & ! [V2x_2E0: A_27c,V3r_2E0: A_27d,V4p_2E0: tyop_2Epath_2Epath(A_27c,A_27d),V5s_2E0: A_27c] :
          ( p(c_2Epath_2Emem_2E2(A_27c,A_27d,V5s_2E0,c_2Epath_2Epcons_2E3(A_27c,A_27d,V2x_2E0,V3r_2E0,V4p_2E0)))
        <=> ( ( V5s_2E0 = V2x_2E0 )
            | p(c_2Epath_2Emem_2E2(A_27c,A_27d,V5s_2E0,V4p_2E0)) ) ) ) ).

tff(thm_2Epath_2Edrop__def__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = V0p_2E0 )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2p_2E0) = c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2Etail_2E1(A_27a,A_27b,V2p_2E0)) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4p_2E0) = c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Epath_2Etail_2E1(A_27a,A_27b,V4p_2E0)) ) ) ).

tff(thm_2Epath_2Enumeral__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),V1p_2E0) = c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V0n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2Etail_2E1(A_27a,A_27b,V1p_2E0)) )
      & ! [V2n_2E0: tyop_2Enum_2Enum,V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V2n_2E0)),V3p_2E0) = c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V2n_2E0)),c_2Epath_2Etail_2E1(A_27a,A_27b,V3p_2E0)) ) ) ).

tff(thm_2Epath_2Efinite__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1n_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)))
     => ( c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V1n_2E0,V0p_2E0)) = c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0) ) ) ).

tff(thm_2Epath_2Elength__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum,V2m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),F0_2E0,V1n_2E0),V2m_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2D_2E2(V2m_2E0,V1n_2E0)) )
     => ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1n_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)))
         => ( c_2Epath_2Elength_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V1n_2E0,V0p_2E0)) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Epath_2Elength_2E1(A_27a,A_27b,V0p_2E0),c_2Eoption_2ENONE_2E0(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),F0_2E0,V1n_2E0)) ) ) ) ).

tff(thm_2Epath_2EPL__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] :
      ( ! [V1i_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V1i_2E0),V2n_2E0) = c_2Earithmetic_2E_2D_2E2(V2n_2E0,V1i_2E0) )
     => ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)))
         => ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V1i_2E0,V0p_2E0)) = c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0,V1i_2E0),c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)) ) ) ) ).

tff(thm_2Epath_2EIN__PL__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0)))
     => ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V0i_2E0,V2p_2E0))) = c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V0i_2E0,V1j_2E0),c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0)) ) ) ).

tff(thm_2Epath_2Efirst__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
     => ( c_2Epath_2Efirst_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0)) = c_2Epath_2Eel_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0) ) ) ).

tff(thm_2Epath_2Efirst__label__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
     => ( c_2Epath_2Efirst__label_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0)) = c_2Epath_2Enth__label_2E2(A_27b,A_27a,V0i_2E0,V1p_2E0) ) ) ).

tff(thm_2Epath_2Etail__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V0i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
     => ( c_2Epath_2Etail_2E1(A_27a,A_27b,c_2Epath_2Edrop_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0)) = c_2Epath_2Edrop_2E2(A_27a,A_27b,c_2Earithmetic_2E_2B_2E2(V0i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1p_2E0) ) ) ).

tff(thm_2Epath_2Eel__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V0i_2E0,V1j_2E0),c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0)))
     => ( c_2Epath_2Eel_2E2(A_27a,A_27b,V0i_2E0,c_2Epath_2Edrop_2E2(A_27a,A_27b,V1j_2E0,V2p_2E0)) = c_2Epath_2Eel_2E2(A_27a,A_27b,c_2Earithmetic_2E_2B_2E2(V0i_2E0,V1j_2E0),V2p_2E0) ) ) ).

tff(thm_2Epath_2Enth__label__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(c_2Earithmetic_2E_2B_2E2(V0i_2E0,V1j_2E0)),c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0)))
     => ( c_2Epath_2Enth__label_2E2(A_27b,A_27a,V0i_2E0,c_2Epath_2Edrop_2E2(A_27a,A_27b,V1j_2E0,V2p_2E0)) = c_2Epath_2Enth__label_2E2(A_27b,A_27a,c_2Earithmetic_2E_2B_2E2(V0i_2E0,V1j_2E0),V2p_2E0) ) ) ).

tff(thm_2Epath_2Etake__def__compute,axiom,
    ! [A_27a: $tType,A_27b: $tType] :
      ( ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Enum_2E0_2E0,V0p_2E0) = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p_2E0)) )
      & ! [V1n_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),V2p_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,c_2Epath_2Efirst_2E1(A_27a,A_27b,V2p_2E0),c_2Epath_2Efirst__label_2E1(A_27a,A_27b,V2p_2E0),c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1n_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2Etail_2E1(A_27a,A_27b,V2p_2E0))) )
      & ! [V3n_2E0: tyop_2Enum_2Enum,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3n_2E0)),V4p_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,c_2Epath_2Efirst_2E1(A_27a,A_27b,V4p_2E0),c_2Epath_2Efirst__label_2E1(A_27a,A_27b,V4p_2E0),c_2Epath_2Etake_2E2(A_27a,A_27b,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)),c_2Epath_2Etail_2E1(A_27a,A_27b,V4p_2E0))) ) ) ).

tff(thm_2Epath_2Efirst__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] : ( c_2Epath_2Efirst_2E1(A_27a,A_27b,c_2Epath_2Etake_2E2(A_27a,A_27b,V1i_2E0,V0p_2E0)) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p_2E0) ) ).

tff(thm_2Epath_2Efinite__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)))
     => p(c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Etake_2E2(A_27a,A_27b,V1i_2E0,V0p_2E0))) ) ).

tff(thm_2Epath_2Elength__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)))
     => ( c_2Epath_2Elength_2E1(A_27a,A_27b,c_2Epath_2Etake_2E2(A_27a,A_27b,V1i_2E0,V0p_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).

tff(thm_2Epath_2EPL__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V1i_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1i_2E0),V2n_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V2n_2E0,c_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,V1i_2E0)) )
     => ! [V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0)))
         => ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Etake_2E2(A_27a,A_27b,V1i_2E0,V0p_2E0)) = c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V1i_2E0)) ) ) ) ).

tff(thm_2Epath_2Elast__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
     => ( c_2Epath_2Elast_2E1(A_27a,A_27b,c_2Epath_2Etake_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0)) = c_2Epath_2Eel_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0) ) ) ).

tff(thm_2Epath_2Enth__label__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Eprim__rec_2E_3C_2E2(V2i_2E0,V0n_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0))) )
     => ( c_2Epath_2Enth__label_2E2(A_27b,A_27a,V2i_2E0,c_2Epath_2Etake_2E2(A_27a,A_27b,V0n_2E0,V1p_2E0)) = c_2Epath_2Enth__label_2E2(A_27b,A_27a,V2i_2E0,V1p_2E0) ) ) ).

tff(thm_2Epath_2Esingleton__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
     => ( c_2Epath_2Eseg_2E3(A_27a,A_27b,V0i_2E0,V0i_2E0,V1p_2E0) = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,c_2Epath_2Eel_2E2(A_27a,A_27b,V0i_2E0,V1p_2E0)) ) ) ).

tff(thm_2Epath_2Erecursive__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Eprim__rec_2E_3C_2E2(V0i_2E0,V1j_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0))) )
     => ( c_2Epath_2Eseg_2E3(A_27a,A_27b,V0i_2E0,V1j_2E0,V2p_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,c_2Epath_2Eel_2E2(A_27a,A_27b,V0i_2E0,V2p_2E0),c_2Epath_2Enth__label_2E2(A_27b,A_27a,V0i_2E0,V2p_2E0),c_2Epath_2Eseg_2E3(A_27a,A_27b,c_2Earithmetic_2E_2B_2E2(V0i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),V1j_2E0,V2p_2E0)) ) ) ).

tff(thm_2Epath_2EPL__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
      ( ! [V1j_2E0: tyop_2Enum_2Enum,V0i_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1j_2E0),V0i_2E0),V3n_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V3n_2E0,c_2Earithmetic_2E_3C_3D_2E2(V3n_2E0,c_2Earithmetic_2E_2D_2E2(V1j_2E0,V0i_2E0))) )
     => ! [V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0i_2E0,V1j_2E0))
            & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0))) )
         => ( c_2Epath_2EPL_2E1(A_27a,A_27b,c_2Epath_2Eseg_2E3(A_27a,A_27b,V0i_2E0,V1j_2E0,V2p_2E0)) = c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1j_2E0),V0i_2E0)) ) ) ) ).

tff(thm_2Epath_2Efinite__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1i_2E0: tyop_2Enum_2Enum,V2j_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V1i_2E0,V2j_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V0p_2E0))) )
     => p(c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Eseg_2E3(A_27a,A_27b,V1i_2E0,V2j_2E0,V0p_2E0))) ) ).

tff(thm_2Epath_2Efirst__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0i_2E0,V1j_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0))) )
     => ( c_2Epath_2Efirst_2E1(A_27a,A_27b,c_2Epath_2Eseg_2E3(A_27a,A_27b,V0i_2E0,V1j_2E0,V2p_2E0)) = c_2Epath_2Eel_2E2(A_27a,A_27b,V0i_2E0,V2p_2E0) ) ) ).

tff(thm_2Epath_2Elast__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0i_2E0: tyop_2Enum_2Enum,V1j_2E0: tyop_2Enum_2Enum,V2p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V0i_2E0,V1j_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V2p_2E0))) )
     => ( c_2Epath_2Elast_2E1(A_27a,A_27b,c_2Epath_2Eseg_2E3(A_27a,A_27b,V0i_2E0,V1j_2E0,V2p_2E0)) = c_2Epath_2Eel_2E2(A_27a,A_27b,V1j_2E0,V2p_2E0) ) ) ).

tff(thm_2Epath_2EfirstP__at__unique,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V0P_2E0,V1p_2E0,V2n_2E0))
     => ! [V3m_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Epath_2EfirstP__at_2E3(A_27a,A_27b,V0P_2E0,V1p_2E0,V3m_2E0))
        <=> ( V3m_2E0 = V2n_2E0 ) ) ) ).

tff(thm_2Epath_2Eis__stopped__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType] :
      ( ! [V0x_2E0: A_27a] : ( c_2Epath_2Eis__stopped_2E1(A_27a,A_27b,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V0x_2E0)) = c_2Ebool_2ET_2E0 )
      & ! [V1x_2E0: A_27c,V2r_2E0: A_27d,V3p_2E0: tyop_2Epath_2Epath(A_27c,A_27d)] : ( c_2Epath_2Eis__stopped_2E1(A_27c,A_27d,c_2Epath_2Epcons_2E3(A_27c,A_27d,V1x_2E0,V2r_2E0,V3p_2E0)) = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Epath_2Efilter__every,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eexists_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))
     => p(c_2Epath_2Eevery_2E2(A_27a,A_27b,V0P_2E0,c_2Epath_2Efilter_2E2(A_27a,A_27b,V0P_2E0,V1p_2E0))) ) ).

tff(thm_2Epath_2Epgenerate__infinite,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ~ p(c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0))) ).

tff(thm_2Epath_2Epgenerate__not__stopped,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V2x_2E0: A_27a] : ( c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0) != c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V0f_2E0,V1g_2E0) ) ).

tff(thm_2Epath_2Eel__pgenerate,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Epath_2Eel_2E2(A_27a,A_27b,V0n_2E0,c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V1f_2E0,V2g_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V0n_2E0) ) ).

tff(thm_2Epath_2Enth__label__pgenerate,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( c_2Epath_2Enth__label_2E2(A_27b,A_27a,V0n_2E0,c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V1f_2E0,V2g_2E0)) = app_2E2(tyop_2Enum_2Enum,A_27b,V2g_2E0,V0n_2E0) ) ).

tff(thm_2Epath_2Epgenerate__11,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V3g2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] :
      ( ( c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V0f1_2E0,V1g1_2E0) = c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V2f2_2E0,V3g2_2E0) )
    <=> ( ( V0f1_2E0 = V2f2_2E0 )
        & ( V1g1_2E0 = V3g2_2E0 ) ) ) ).

tff(thm_2Epath_2Epgenerate__onto,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ~ p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0))
     => ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2g_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)] : ( V0p_2E0 = c_2Epath_2Epgenerate_2E2(A_27a,A_27b,V1f_2E0,V2g_2E0) ) ) ).

tff(thm_2Epath_2Eokpath__monotone,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] : p(c_2EfixedPoint_2Emonotone_2E1(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Epath_2Epath(A_27a,A_27b),c_2Epath_2Eokpath__f_2E1(A_27a,A_27b,V0R_2E0))) ).

tff(thm_2Epath_2Eokpath__co__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a,V3r_2E0: A_27b,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,V4p_2E0)))
         => ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,V2x_2E0),V3r_2E0),c_2Epath_2Efirst_2E1(A_27a,A_27b,V4p_2E0)))
            & p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,V4p_2E0)) ) )
     => ! [V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V1P_2E0,V5p_2E0))
         => p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V5p_2E0)) ) ) ).

tff(thm_2Epath_2Eokpath__cases,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1x_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1x_2E0))
    <=> ( ? [V2x_27_2E0: A_27a] : ( V1x_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_27_2E0) )
        | ? [V3x_27_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
            ( ( V1x_2E0 = c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_27_2E0,V4r_2E0,V5p_2E0) )
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,V3x_27_2E0),V4r_2E0),c_2Epath_2Efirst_2E1(A_27a,A_27b,V5p_2E0)))
            & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V5p_2E0)) ) ) ) ).

tff(thm_2Epath_2Eokpath__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1x_2E0: A_27a] : p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0)))
      & ! [V2x_2E0: A_27a,V3r_2E0: A_27b,V4p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V2x_2E0,V3r_2E0,V4p_2E0)))
        <=> ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,V2x_2E0),V3r_2E0),c_2Epath_2Efirst_2E1(A_27a,A_27b,V4p_2E0)))
            & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V4p_2E0)) ) ) ) ).

tff(thm_2Epath_2Efinite__okpath__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool),V1R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ( ! [V2x_2E0: A_27a] : p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V2x_2E0)))
        & ! [V3x_2E0: A_27a,V4r_2E0: A_27b,V5p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
            ( ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V1R_2E0,V5p_2E0))
              & p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V5p_2E0))
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0,V3x_2E0),V4r_2E0),c_2Epath_2Efirst_2E1(A_27a,A_27b,V5p_2E0)))
              & p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V5p_2E0)) )
           => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,V3x_2E0,V4r_2E0,V5p_2E0))) ) )
     => ! [V6sigma_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V1R_2E0,V6sigma_2E0))
            & p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V6sigma_2E0)) )
         => p(app_2E2(tyop_2Epath_2Epath(A_27a,A_27b),tyop_2Emin_2Ebool,V0P_2E0,V6sigma_2E0)) ) ) ).

tff(thm_2Epath_2Eokpath__pmap,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a),V2g_2E0: tyop_2Emin_2Efun(A_27b,A_27b),V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V3p_2E0))
        & ! [V4x_2E0: A_27a,V5r_2E0: A_27b,V6y_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,V4x_2E0),V5r_2E0),V6y_2E0))
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0,app_2E2(A_27a,A_27a,V1f_2E0,V4x_2E0)),app_2E2(A_27b,A_27b,V2g_2E0,V5r_2E0)),app_2E2(A_27a,A_27a,V1f_2E0,V6y_2E0))) ) )
     => p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Epmap_2E3(A_27a,A_27b,A_27a,A_27b,V1f_2E0,V2g_2E0,V3p_2E0))) ) ).

tff(thm_2Epath_2Efinite__plink,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,c_2Epath_2Eplink_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0)))
    <=> ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p1_2E0))
        & p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V1p2_2E0)) ) ) ).

tff(thm_2Epath_2Efirst__plink,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( c_2Epath_2Elast_2E1(A_27a,A_27b,V0p1_2E0) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V1p2_2E0) )
     => ( c_2Epath_2Efirst_2E1(A_27a,A_27b,c_2Epath_2Eplink_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0)) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V0p1_2E0) ) ) ).

tff(thm_2Epath_2Elast__plink,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p1_2E0))
        & p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V1p2_2E0))
        & ( c_2Epath_2Elast_2E1(A_27a,A_27b,V0p1_2E0) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V1p2_2E0) ) )
     => ( c_2Epath_2Elast_2E1(A_27a,A_27b,c_2Epath_2Eplink_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0)) = c_2Epath_2Elast_2E1(A_27a,A_27b,V1p2_2E0) ) ) ).

tff(thm_2Epath_2Eokpath__plink,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V1p1_2E0))
        & ( c_2Epath_2Elast_2E1(A_27a,A_27b,V1p1_2E0) = c_2Epath_2Efirst_2E1(A_27a,A_27b,V2p2_2E0) ) )
     => ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Eplink_2E2(A_27a,A_27b,V1p1_2E0,V2p2_2E0)))
      <=> ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p1_2E0))
          & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V2p2_2E0)) ) ) ) ).

tff(thm_2Epath_2Eokpath__take,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p_2E0)) )
     => p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Etake_2E2(A_27a,A_27b,V2i_2E0,V1p_2E0))) ) ).

tff(thm_2Epath_2Eokpath__drop,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2i_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p_2E0)) )
     => p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Edrop_2E2(A_27a,A_27b,V2i_2E0,V1p_2E0))) ) ).

tff(thm_2Epath_2Eokpath__seg,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2i_2E0: tyop_2Enum_2Enum,V3j_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Earithmetic_2E_3C_3D_2E2(V2i_2E0,V3j_2E0))
        & p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3j_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p_2E0)) )
     => p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,c_2Epath_2Eseg_2E3(A_27a,A_27b,V2i_2E0,V3j_2E0,V1p_2E0))) ) ).

tff(thm_2Epath_2ESN__finite__paths,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Epath_2ESN_2E1(A_27a,A_27b,V0R_2E0))
        & p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p_2E0)) )
     => p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V1p_2E0)) ) ).

tff(thm_2Epath_2Efinite__paths__SN,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( ! [V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p_2E0))
         => p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V1p_2E0)) )
     => p(c_2Epath_2ESN_2E1(A_27a,A_27b,V0R_2E0)) ) ).

tff(thm_2Epath_2ESN__finite__paths__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))] :
      ( p(c_2Epath_2ESN_2E1(A_27a,A_27b,V0R_2E0))
    <=> ! [V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
          ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0R_2E0,V1p_2E0))
         => p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V1p_2E0)) ) ) ).

tff(thm_2Epath_2Elabels__LMAP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elabels_2E1(A_27a,A_27b,V0p_2E0) = c_2Ellist_2ELMAP_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b,c_2Epair_2EFST_2E0(A_27b,A_27a),c_2Epair_2ESND_2E1(A_27a,tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Epath_2EfromPath_2E1(A_27a,A_27b,V0p_2E0))) ) ).

tff(thm_2Epath_2Elabels__plink,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V1p2_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Epath_2Elabels_2E1(A_27a,A_27b,c_2Epath_2Eplink_2E2(A_27a,A_27b,V0p1_2E0,V1p2_2E0)) = c_2Ellist_2ELAPPEND_2E2(A_27b,c_2Epath_2Elabels_2E1(A_27a,A_27b,V0p1_2E0),c_2Epath_2Elabels_2E1(A_27a,A_27b,V1p2_2E0)) ) ).

tff(thm_2Epath_2Efinite__labels,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] : ( c_2Ellist_2ELFINITE_2E1(A_27b,c_2Epath_2Elabels_2E1(A_27a,A_27b,V0p_2E0)) = c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0) ) ).

tff(thm_2Epath_2Eunfold__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)))))] :
      ( ! [V0proj_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),V4s_27_2E0: A_27a,V5l_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c)))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c))))),F1_2E0,V0proj_2E0),V2s_2E0),V1f_2E0),V4s_27_2E0),V5l_2E0) = c_2Epath_2Epcons_2E3(A_27b,A_27c,app_2E2(A_27a,A_27b,V0proj_2E0,V2s_2E0),V5l_2E0,c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V0proj_2E0,V1f_2E0,V4s_27_2E0)) )
     => ( ! [V0proj_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: A_27a,V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),V3v_2E0: tyop_2Epair_2Eprod(A_27a,A_27c)] : ( app_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)))),F0_2E0,V0proj_2E0),V2s_2E0),V1f_2E0),V3v_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Epath_2Epath(A_27b,A_27c),A_27a,A_27c,V3v_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c)))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Epath_2Epath(A_27b,A_27c))))),F1_2E0,V0proj_2E0),V2s_2E0),V1f_2E0)) )
       => ! [V0proj_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),V2s_2E0: A_27a] : ( c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V0proj_2E0,V1f_2E0,V2s_2E0) = c_2Eoption_2Eoption__CASE_2E3(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c),app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),V1f_2E0,V2s_2E0),c_2Epath_2Estopped__at_2E1(A_27b,A_27c,app_2E2(A_27a,A_27b,V0proj_2E0,V2s_2E0)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c))),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epath_2Epath(A_27b,A_27c)))),F0_2E0,V0proj_2E0),V2s_2E0),V1f_2E0)) ) ) ) ).

tff(thm_2Epath_2Eunfold__thm2,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0proj_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),V2x_2E0: A_27a,V3v1_2E0: A_27a,V4v2_2E0: A_27c] :
      ( ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),V1f_2E0,V2x_2E0) = c_2Eoption_2ENONE_2E0(tyop_2Epair_2Eprod(A_27a,A_27c)) )
       => ( c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V0proj_2E0,V1f_2E0,V2x_2E0) = c_2Epath_2Estopped__at_2E1(A_27b,A_27c,app_2E2(A_27a,A_27b,V0proj_2E0,V2x_2E0)) ) )
      & ( ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),V1f_2E0,V2x_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(A_27a,A_27c,V3v1_2E0,V4v2_2E0)) )
       => ( c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V0proj_2E0,V1f_2E0,V2x_2E0) = c_2Epath_2Epcons_2E3(A_27b,A_27c,app_2E2(A_27a,A_27b,V0proj_2E0,V2x_2E0),V4v2_2E0,c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V0proj_2E0,V1f_2E0,V3v1_2E0)) ) ) ) ).

tff(thm_2Epath_2Elabels__unfold,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0proj_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),V2s_2E0: A_27a] : ( c_2Epath_2Elabels_2E1(A_27b,A_27c,c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V0proj_2E0,V1f_2E0,V2s_2E0)) = c_2Ellist_2ELUNFOLD_2E2(A_27c,A_27a,V1f_2E0,V2s_2E0) ) ).

tff(thm_2Epath_2Eokpath__unfold,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V2proj_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c))),V4s_2E0: A_27a] :
      ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4s_2E0))
        & ! [V5s_2E0: A_27a,V6s_27_2E0: A_27a,V7l_2E0: A_27c] :
            ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V5s_2E0))
              & ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),V3f_2E0,V5s_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(A_27a,A_27c,V6s_27_2E0,V7l_2E0)) ) )
           => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V6s_27_2E0)) )
        & ! [V8s_2E0: A_27a,V9s_27_2E0: A_27a,V10l_2E0: A_27c] :
            ( ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V8s_2E0))
              & ( app_2E2(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27c)),V3f_2E0,V8s_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(A_27a,A_27c,V9s_27_2E0,V10l_2E0)) ) )
           => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1m_2E0,app_2E2(A_27a,A_27b,V2proj_2E0,V8s_2E0)),V10l_2E0),app_2E2(A_27a,A_27b,V2proj_2E0,V9s_27_2E0))) ) )
     => p(c_2Epath_2Eokpath_2E2(A_27b,A_27c,V1m_2E0,c_2Epath_2Eunfold_2E3(A_27b,A_27c,A_27a,V2proj_2E0,V3f_2E0,V4s_2E0))) ) ).

tff(thm_2Epath_2Etrace__machine__thm,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V1tr_2E0: tyop_2Ellist_2Ellist(A_27a)] :
      ( ! [V2n_2E0: tyop_2Enum_2Enum,V3l_2E0: tyop_2Elist_2Elist(A_27a)] :
          ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V2n_2E0,V1tr_2E0) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V3l_2E0) )
         => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3l_2E0)) )
     => ? [V4p_2E0: tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a)] :
          ( ( V1tr_2E0 = c_2Epath_2Elabels_2E1(tyop_2Elist_2Elist(A_27a),A_27a,V4p_2E0) )
          & p(c_2Epath_2Eokpath_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Epath_2Etrace__machine_2E1(A_27a,V0P_2E0),V4p_2E0))
          & ( c_2Epath_2Efirst_2E1(tyop_2Elist_2Elist(A_27a),A_27a,V4p_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).

tff(thm_2Epath_2Etrace__machine__thm2,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a),V2P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),V3p_2E0: tyop_2Epath_2Epath(tyop_2Elist_2Elist(A_27a),A_27a),V4init_2E0: A_27b] :
      ( ( p(c_2Epath_2Eokpath_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Epath_2Etrace__machine_2E1(A_27a,V2P_2E0),V3p_2E0))
        & p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V2P_2E0,c_2Epath_2Efirst_2E1(tyop_2Elist_2Elist(A_27a),A_27a,V3p_2E0))) )
     => ( ( c_2Ellist_2ELTAKE_2E2(A_27a,V0n_2E0,c_2Epath_2Elabels_2E1(tyop_2Elist_2Elist(A_27a),A_27a,V3p_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27a),V1l_2E0) )
       => p(app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V2P_2E0,c_2Elist_2EAPPEND_2E2(A_27a,c_2Epath_2Efirst_2E1(tyop_2Elist_2Elist(A_27a),A_27a,V3p_2E0),V1l_2E0))) ) ) ).

tff(thm_2Epath_2ELTAKE__labels,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27b)] :
      ( ( c_2Ellist_2ELTAKE_2E2(A_27b,V0n_2E0,c_2Epath_2Elabels_2E1(A_27a,A_27b,V1p_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27b),V2l_2E0) )
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & ( c_2Ellist_2EtoList_2E1(A_27b,c_2Epath_2Elabels_2E1(A_27a,A_27b,c_2Epath_2Etake_2E2(A_27a,A_27b,V0n_2E0,V1p_2E0))) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27b),V2l_2E0) ) ) ) ).

tff(thm_2Epath_2Edrop__eq__pcons,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2h_2E0: A_27a,V3l_2E0: A_27b,V4t_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & ( c_2Epath_2Edrop_2E2(A_27a,A_27b,V0n_2E0,V1p_2E0) = c_2Epath_2Epcons_2E3(A_27a,A_27b,V2h_2E0,V3l_2E0,V4t_2E0) ) )
     => p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0))) ) ).

tff(thm_2Epath_2Eokpath__parallel__comp,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27c,A_27c),F0_2E0: tyop_2Emin_2Efun(A_27c,A_27c)] :
      ( ! [V4x_2E0: A_27c] : ( app_2E2(A_27c,A_27c,F1_2E0,V4x_2E0) = V4x_2E0 )
     => ( ! [V3x_2E0: A_27c] : ( app_2E2(A_27c,A_27c,F0_2E0,V3x_2E0) = V3x_2E0 )
       => ! [V0p_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),V1m1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2m2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))] :
            ( p(c_2Epath_2Eokpath_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,c_2Epath_2Eparallel__comp_2E2(A_27a,A_27c,A_27a,A_27b,A_27b,V1m1_2E0,V2m2_2E0),V0p_2E0))
          <=> ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27c,V1m1_2E0,c_2Epath_2Epmap_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27a,A_27c,c_2Epair_2EFST_2E0(A_27a,A_27b),F0_2E0,V0p_2E0)))
              & p(c_2Epath_2Eokpath_2E2(A_27b,A_27c,V2m2_2E0,c_2Epath_2Epmap_2E3(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27b,A_27c,c_2Epair_2ESND_2E0(A_27a,A_27b),F1_2E0,V0p_2E0))) ) ) ) ) ).

tff(thm_2Epath_2Ebuild__pcomp__trace,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0m1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V1p1_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2m2_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool))),V3p2_2E0: tyop_2Epath_2Epath(A_27c,A_27b)] :
      ( ( p(c_2Epath_2Eokpath_2E2(A_27a,A_27b,V0m1_2E0,V1p1_2E0))
        & p(c_2Epath_2Eokpath_2E2(A_27c,A_27b,V2m2_2E0,V3p2_2E0))
        & ( c_2Epath_2Elabels_2E1(A_27a,A_27b,V1p1_2E0) = c_2Epath_2Elabels_2E1(A_27c,A_27b,V3p2_2E0) ) )
     => ? [V4p_2E0: tyop_2Epath_2Epath(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)] :
          ( p(c_2Epath_2Eokpath_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,c_2Epath_2Eparallel__comp_2E2(A_27a,A_27b,A_27a,A_27c,A_27c,V0m1_2E0,V2m2_2E0),V4p_2E0))
          & ( c_2Epath_2Elabels_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,V4p_2E0) = c_2Epath_2Elabels_2E1(A_27a,A_27b,V1p1_2E0) )
          & ( c_2Epath_2Efirst_2E1(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b,V4p_2E0) = c_2Epair_2E_2C_2E2(A_27a,A_27c,c_2Epath_2Efirst_2E1(A_27a,A_27b,V1p1_2E0),c_2Epath_2Efirst_2E1(A_27c,A_27b,V3p2_2E0)) ) ) ) ).

tff(thm_2Epath_2Enth__label__LNTH,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2x_2E0: A_27b] :
      ( ( c_2Ellist_2ELNTH_2E2(A_27b,V0n_2E0,c_2Epath_2Elabels_2E1(A_27a,A_27b,V1p_2E0)) = c_2Eoption_2ESOME_2E1(A_27b,V2x_2E0) )
    <=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Epath_2EPL_2E1(A_27a,A_27b,V1p_2E0)))
        & ( c_2Epath_2Enth__label_2E2(A_27b,A_27a,V0n_2E0,V1p_2E0) = V2x_2E0 ) ) ) ).

tff(thm_2Epath_2Enth__label__LTAKE,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0n_2E0: tyop_2Enum_2Enum,V1p_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V2l_2E0: tyop_2Elist_2Elist(A_27b),V3i_2E0: tyop_2Enum_2Enum,V4v_2E0: A_27c] :
      ( ( ( c_2Ellist_2ELTAKE_2E2(A_27b,V0n_2E0,c_2Epath_2Elabels_2E1(A_27a,A_27b,V1p_2E0)) = c_2Eoption_2ESOME_2E1(tyop_2Elist_2Elist(A_27b),V2l_2E0) )
        & p(c_2Eprim__rec_2E_3C_2E2(V3i_2E0,c_2Elist_2ELENGTH_2E1(A_27b,V2l_2E0))) )
     => ( c_2Epath_2Enth__label_2E2(A_27b,A_27a,V3i_2E0,V1p_2E0) = c_2Elist_2EEL_2E2(A_27b,V3i_2E0,V2l_2E0) ) ) ).

tff(thm_2Epath_2Efinite__path__end__cases,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0p_2E0: tyop_2Epath_2Epath(A_27a,A_27b)] :
      ( p(c_2Epath_2Efinite_2E1(A_27a,A_27b,V0p_2E0))
     => ( ? [V1x_2E0: A_27a] : ( V0p_2E0 = c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V1x_2E0) )
        | ? [V2p_27_2E0: tyop_2Epath_2Epath(A_27a,A_27b),V3l_2E0: A_27b,V4s_2E0: A_27a] : ( V0p_2E0 = c_2Epath_2Eplink_2E2(A_27a,A_27b,V2p_27_2E0,c_2Epath_2Epcons_2E3(A_27a,A_27b,c_2Epath_2Elast_2E1(A_27a,A_27b,V2p_27_2E0),V3l_2E0,c_2Epath_2Estopped__at_2E1(A_27a,A_27b,V4s_2E0))) ) ) ) ).

tff(thm_2Epath_2Esimulation__trace__inclusion,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1M1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),V2M2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V3p_2E0: tyop_2Epath_2Epath(A_27a,A_27c),V4t__init_2E0: A_27b] :
      ( ( ! [V5s1_2E0: A_27a,V6l_2E0: A_27c,V7s2_2E0: A_27a,V8t1_2E0: A_27b] :
            ( ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V5s1_2E0),V8t1_2E0))
              & p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1M1_2E0,V5s1_2E0),V6l_2E0),V7s2_2E0)) )
           => ? [V9t2_2E0: A_27b] :
                ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V7s2_2E0),V9t2_2E0))
                & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2M2_2E0,V8t1_2E0),V6l_2E0),V9t2_2E0)) ) )
        & p(c_2Epath_2Eokpath_2E2(A_27a,A_27c,V1M1_2E0,V3p_2E0))
        & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,c_2Epath_2Efirst_2E1(A_27a,A_27c,V3p_2E0)),V4t__init_2E0)) )
     => ? [V10q_2E0: tyop_2Epath_2Epath(A_27b,A_27c)] :
          ( p(c_2Epath_2Eokpath_2E2(A_27b,A_27c,V2M2_2E0,V10q_2E0))
          & ( c_2Epath_2Elabels_2E1(A_27a,A_27c,V3p_2E0) = c_2Epath_2Elabels_2E1(A_27b,A_27c,V10q_2E0) )
          & ( c_2Epath_2Efirst_2E1(A_27b,A_27c,V10q_2E0) = V4t__init_2E0 ) ) ) ).

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