%------------------------------------------------------------------------------
% File     : ITP047_4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : fcp.ax [Gau19]
%          : HL4047_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  512 ( 179 unt; 265 typ;   0 def)
%            Number of atoms       :  391 ( 299 equ)
%            Maximal formula atoms :   10 (   0 avg)
%            Number of connectives :  154 (  10   ~;  15   |;  36   &)
%                                         (  37 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :   14 (   2 avg)
%            Number of types       :   18 (  17 usr)
%            Number of type conns  :  211 ( 140   >;  71   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  247 ( 247 usr; 108 con; 0-4 aty)
%            Number of variables   :  811 ( 790   !;  21   ?; 811   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(u,type,
    u: $tType ).

tff(d,type,
    d: $tType ).

tff(du,type,
    du: $tType ).

tff(mono_2Etyop_2Emin_2Ebool,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: $tType ).

tff(mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

tff(tyop_2Ebool_2Eitself,type,
    tyop_2Ebool_2Eitself: d > d ).

tff(tyop_2Efcp_2Ebit0,type,
    tyop_2Efcp_2Ebit0: d > d ).

tff(tyop_2Efcp_2Ebit1,type,
    tyop_2Efcp_2Ebit1: d > d ).

tff(tyop_2Efcp_2Ecart,type,
    tyop_2Efcp_2Ecart: ( d * d ) > d ).

tff(tyop_2Efcp_2Efinite__image,type,
    tyop_2Efcp_2Efinite__image: d > d ).

tff(tyop_2Eind__type_2Erecspace,type,
    tyop_2Eind__type_2Erecspace: d > d ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: d > d ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( d * d ) > d ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

tff(tyop_2Eone_2Eone,type,
    tyop_2Eone_2Eone: d ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( d * d ) > d ).

tff(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: ( d * d ) > d ).

tff(s,type,
    s: ( d * u ) > du ).

tff(app_2E2,type,
    app_2E2: ( du * du ) > u ).

tff(p,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: du > u ).

tff(c_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: u ).

tff(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( du * du ) > u ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( du * du ) > u ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_2Efcp_2E_3A_2B_2E0,type,
    c_2Efcp_2E_3A_2B_2E0: u ).

tff(c_2Efcp_2E_3A_2B_2E3,type,
    c_2Efcp_2E_3A_2B_2E3: ( du * du * du ) > u ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: ( du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: du > u ).

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: u ).

tff(c_2Ebool_2E_3F_21_2E1,type,
    c_2Ebool_2E_3F_21_2E1: du > u ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: du > u ).

tff(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: u ).

tff(c_2Efcp_2EBIT0A_2E0,type,
    c_2Efcp_2EBIT0A_2E0: u ).

tff(c_2Efcp_2EBIT0A_2E1,type,
    c_2Efcp_2EBIT0A_2E1: du > u ).

tff(c_2Efcp_2EBIT0B_2E0,type,
    c_2Efcp_2EBIT0B_2E0: u ).

tff(c_2Efcp_2EBIT0B_2E1,type,
    c_2Efcp_2EBIT0B_2E1: du > u ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: du > u ).

tff(c_2Efcp_2EBIT1A_2E0,type,
    c_2Efcp_2EBIT1A_2E0: u ).

tff(c_2Efcp_2EBIT1A_2E1,type,
    c_2Efcp_2EBIT1A_2E1: du > u ).

tff(c_2Efcp_2EBIT1B_2E0,type,
    c_2Efcp_2EBIT1B_2E0: u ).

tff(c_2Efcp_2EBIT1B_2E1,type,
    c_2Efcp_2EBIT1B_2E1: du > u ).

tff(c_2Efcp_2EBIT1C_2E0,type,
    c_2Efcp_2EBIT1C_2E0: u ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: du > u ).

tff(c_2Eind__type_2EBOTTOM_2E0,type,
    c_2Eind__type_2EBOTTOM_2E0: u ).

tff(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: u ).

tff(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: du > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: ( du * du ) > u ).

tff(c_2Eind__type_2ECONSTR_2E0,type,
    c_2Eind__type_2ECONSTR_2E0: u ).

tff(c_2Eind__type_2ECONSTR_2E3,type,
    c_2Eind__type_2ECONSTR_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2EDATATYPE_2E0,type,
    c_2Ebool_2EDATATYPE_2E0: u ).

tff(c_2Ebool_2EDATATYPE_2E1,type,
    c_2Ebool_2EDATATYPE_2E1: du > u ).

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEVERY_2E0,type,
    c_2Elist_2EEVERY_2E0: u ).

tff(c_2Elist_2EEVERY_2E2,type,
    c_2Elist_2EEVERY_2E2: ( du * du ) > u ).

tff(c_2Elist_2EEXISTS_2E0,type,
    c_2Elist_2EEXISTS_2E0: u ).

tff(c_2Elist_2EEXISTS_2E2,type,
    c_2Elist_2EEXISTS_2E2: ( du * du ) > u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Ecombin_2EFAIL_2E0,type,
    c_2Ecombin_2EFAIL_2E0: u ).

tff(c_2Ecombin_2EFAIL_2E2,type,
    c_2Ecombin_2EFAIL_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EFCP_2E0,type,
    c_2Efcp_2EFCP_2E0: u ).

tff(c_2Efcp_2EFCP_2E1,type,
    c_2Efcp_2EFCP_2E1: du > u ).

tff(c_2Efcp_2EFCP__CONCAT_2E0,type,
    c_2Efcp_2EFCP__CONCAT_2E0: u ).

tff(c_2Efcp_2EFCP__CONCAT_2E2,type,
    c_2Efcp_2EFCP__CONCAT_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EFCP__CONS_2E0,type,
    c_2Efcp_2EFCP__CONS_2E0: u ).

tff(c_2Efcp_2EFCP__CONS_2E2,type,
    c_2Efcp_2EFCP__CONS_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EFCP__EVERY_2E0,type,
    c_2Efcp_2EFCP__EVERY_2E0: u ).

tff(c_2Efcp_2EFCP__EVERY_2E2,type,
    c_2Efcp_2EFCP__EVERY_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EFCP__EXISTS_2E0,type,
    c_2Efcp_2EFCP__EXISTS_2E0: u ).

tff(c_2Efcp_2EFCP__EXISTS_2E2,type,
    c_2Efcp_2EFCP__EXISTS_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EFCP__FOLD_2E0,type,
    c_2Efcp_2EFCP__FOLD_2E0: u ).

tff(c_2Efcp_2EFCP__FOLD_2E3,type,
    c_2Efcp_2EFCP__FOLD_2E3: ( du * du * du ) > u ).

tff(c_2Efcp_2EFCP__HD_2E0,type,
    c_2Efcp_2EFCP__HD_2E0: u ).

tff(c_2Efcp_2EFCP__HD_2E1,type,
    c_2Efcp_2EFCP__HD_2E1: du > u ).

tff(c_2Efcp_2EFCP__MAP_2E0,type,
    c_2Efcp_2EFCP__MAP_2E0: u ).

tff(c_2Efcp_2EFCP__MAP_2E2,type,
    c_2Efcp_2EFCP__MAP_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EFCP__TL_2E0,type,
    c_2Efcp_2EFCP__TL_2E0: u ).

tff(c_2Efcp_2EFCP__TL_2E1,type,
    c_2Efcp_2EFCP__TL_2E1: du > u ).

tff(c_2Efcp_2EFCP__ZIP_2E0,type,
    c_2Efcp_2EFCP__ZIP_2E0: u ).

tff(c_2Efcp_2EFCP__ZIP_2E2,type,
    c_2Efcp_2EFCP__ZIP_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: u ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: du > u ).

tff(c_2Elist_2EFOLDL_2E0,type,
    c_2Elist_2EFOLDL_2E0: u ).

tff(c_2Elist_2EFOLDL_2E3,type,
    c_2Elist_2EFOLDL_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EGENLIST_2E0,type,
    c_2Elist_2EGENLIST_2E0: u ).

tff(c_2Elist_2EGENLIST_2E2,type,
    c_2Elist_2EGENLIST_2E2: ( du * du ) > u ).

tff(c_2Efcp_2EHAS__SIZE_2E0,type,
    c_2Efcp_2EHAS__SIZE_2E0: u ).

tff(c_2Efcp_2EHAS__SIZE_2E2,type,
    c_2Efcp_2EHAS__SIZE_2E2: ( du * du ) > u ).

tff(c_2Elist_2EHD_2E0,type,
    c_2Elist_2EHD_2E0: u ).

tff(c_2Elist_2EHD_2E1,type,
    c_2Elist_2EHD_2E1: du > u ).

tff(c_2Efcp_2EL2V_2E0,type,
    c_2Efcp_2EL2V_2E0: u ).

tff(c_2Efcp_2EL2V_2E1,type,
    c_2Efcp_2EL2V_2E1: du > u ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

tff(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: du > u ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: ( du * du ) > u ).

tff(c_2Elist_2ENULL_2E0,type,
    c_2Elist_2ENULL_2E0: u ).

tff(c_2Elist_2ENULL_2E1,type,
    c_2Elist_2ENULL_2E1: du > u ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: du > u ).

tff(c_2Eprim__rec_2EPRE_2E0,type,
    c_2Eprim__rec_2EPRE_2E0: u ).

tff(c_2Eprim__rec_2EPRE_2E1,type,
    c_2Eprim__rec_2EPRE_2E1: du > u ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: du > u ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Elist_2ETL_2E0,type,
    c_2Elist_2ETL_2E0: u ).

tff(c_2Elist_2ETL_2E1,type,
    c_2Elist_2ETL_2E1: du > u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
    c_2Ebool_2ETYPE__DEFINITION_2E2: ( du * du ) > u ).

tff(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: u ).

tff(c_2Efcp_2EV2L_2E0,type,
    c_2Efcp_2EV2L_2E0: u ).

tff(c_2Efcp_2EV2L_2E1,type,
    c_2Efcp_2EV2L_2E1: du > u ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( du * du ) > u ).

tff(c_2Efcp_2Ebit0__CASE_2E0,type,
    c_2Efcp_2Ebit0__CASE_2E0: u ).

tff(c_2Efcp_2Ebit0__CASE_2E3,type,
    c_2Efcp_2Ebit0__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Efcp_2Ebit0__size_2E0,type,
    c_2Efcp_2Ebit0__size_2E0: u ).

tff(c_2Efcp_2Ebit0__size_2E2,type,
    c_2Efcp_2Ebit0__size_2E2: ( du * du ) > u ).

tff(c_2Efcp_2Ebit1__CASE_2E0,type,
    c_2Efcp_2Ebit1__CASE_2E0: u ).

tff(c_2Efcp_2Ebit1__CASE_2E4,type,
    c_2Efcp_2Ebit1__CASE_2E4: ( du * du * du * du ) > u ).

tff(c_2Efcp_2Ebit1__size_2E0,type,
    c_2Efcp_2Ebit1__size_2E0: u ).

tff(c_2Efcp_2Ebit1__size_2E2,type,
    c_2Efcp_2Ebit1__size_2E2: ( du * du ) > u ).

tff(c_2Efcp_2Edest__cart_2E0,type,
    c_2Efcp_2Edest__cart_2E0: u ).

tff(c_2Efcp_2Edest__cart_2E1,type,
    c_2Efcp_2Edest__cart_2E1: du > u ).

tff(c_2Efcp_2Edest__cart_2E2,type,
    c_2Efcp_2Edest__cart_2E2: ( du * du ) > u ).

tff(c_2Efcp_2Edest__finite__image_2E0,type,
    c_2Efcp_2Edest__finite__image_2E0: u ).

tff(c_2Efcp_2Edest__finite__image_2E1,type,
    c_2Efcp_2Edest__finite__image_2E1: du > u ).

tff(c_2Efcp_2Edimindex_2E0,type,
    c_2Efcp_2Edimindex_2E0: u ).

tff(c_2Efcp_2Edimindex_2E1,type,
    c_2Efcp_2Edimindex_2E1: du > u ).

tff(c_2Efcp_2Efcp__CASE_2E0,type,
    c_2Efcp_2Efcp__CASE_2E0: u ).

tff(c_2Efcp_2Efcp__CASE_2E2,type,
    c_2Efcp_2Efcp__CASE_2E2: ( du * du ) > u ).

tff(c_2Efcp_2Efcp__index_2E0,type,
    c_2Efcp_2Efcp__index_2E0: u ).

tff(c_2Efcp_2Efcp__index_2E1,type,
    c_2Efcp_2Efcp__index_2E1: du > u ).

tff(c_2Efcp_2Efcp__index_2E2,type,
    c_2Efcp_2Efcp__index_2E2: ( du * du ) > u ).

tff(c_2Efcp_2Efinite__index_2E0,type,
    c_2Efcp_2Efinite__index_2E0: u ).

tff(c_2Efcp_2Efinite__index_2E1,type,
    c_2Efcp_2Efinite__index_2E1: du > u ).

tff(c_2Efcp_2Emk__cart_2E0,type,
    c_2Efcp_2Emk__cart_2E0: u ).

tff(c_2Efcp_2Emk__cart_2E1,type,
    c_2Efcp_2Emk__cart_2E1: du > u ).

tff(c_2Efcp_2Emk__finite__image_2E0,type,
    c_2Efcp_2Emk__finite__image_2E0: u ).

tff(c_2Efcp_2Emk__finite__image_2E1,type,
    c_2Efcp_2Emk__finite__image_2E1: du > u ).

tff(c_2Ebool_2Ethe__value_2E0,type,
    c_2Ebool_2Ethe__value_2E0: u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: du > u ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2A_2E0,type,
    mono_2Ec_2Earithmetic_2E_2A_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2A_2E2,type,
    mono_2Ec_2Earithmetic_2E_2A_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E0,type,
    mono_2Ec_2Earithmetic_2E_2B_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E2,type,
    mono_2Ec_2Earithmetic_2E_2B_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E0,type,
    mono_2Ec_2Earithmetic_2E_2D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2D_2E2,type,
    mono_2Ec_2Earithmetic_2E_2D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_2F_5C_2E2,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Enum_2E0_2E0,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E0,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E2,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E2,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E2,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2E_3F_21_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2E_3F_21_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2EBIT2_2E1,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E1,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2EPRE_2E0,type,
    mono_2Ec_2Eprim__rec_2EPRE_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eprim__rec_2EPRE_2E1,type,
    mono_2Ec_2Eprim__rec_2EPRE_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Enum_2ESUC_2E0,type,
    mono_2Ec_2Enum_2ESUC_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Enum_2ESUC_2E1,type,
    mono_2Ec_2Enum_2ESUC_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Earithmetic_2EZERO_2E0,type,
    mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E2,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Efcp_2Edimindex_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Efcp_2Edimindex_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2Ethe__value_2E0_2Emono_2Etyop_2Eone_2Eone,type,
    mono_2Ec_2Ebool_2Ethe__value_2E0_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2E_7E_2E1,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

tff(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,type,
    i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > u ).

tff(i_mono_2Etyop_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

tff(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,type,
    j_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: du > mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 ).

tff(j_mono_2Etyop_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

tff(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) )
     => ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) ) ) ).

tff(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(reserved_2Eho_2Etruth,axiom,
    p(mono_2Ec_2Ebool_2ET_2E0) ).

tff(reserved_2Eho_2Enotfalse,axiom,
    ~ p(mono_2Ec_2Ebool_2EF_2E0) ).

tff(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = mono_2Ec_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = mono_2Ec_2Ebool_2EF_2E0 ) ) ).

tff(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a: d,V0x_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) = s(A_27a,V0x_2E0) ) ).

tff(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ) ).

tff(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] : ( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(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))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ) ).

tff(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( p(mono_2Ec_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))))
    <=> ( s(A_27a,V0_2E0) = s(A_27a,V1_2E0) ) ) ).

tff(reserved_2Equant_2E_21,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
    <=> ! [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).

tff(reserved_2Equant_2E_3F,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))))
    <=> ? [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0))))) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,V0_2E0)))) = s(tyop_2Emin_2Ebool,V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(j_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),V0_2E0)))) = s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,V0_2E0)))) = s(tyop_2Enum_2Enum,V0_2E0) ) ).

tff(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] : ( j_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0))) = V0_2E0 ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

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

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq3_2Ec_2Efcp_2E_3A_2B_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X2_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27b)))),c_2Efcp_2E_3A_2B_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Efcp_2E_3A_2B_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X2_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27c)))),c_2Efcp_2E_3A_2B_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))))) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_3F_21_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Efcp_2Ecart_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Efcp_2Ecart(A_27a,A_27b)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Emin_2E_40_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EBIT0A_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Ebit0(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),c_2Efcp_2EBIT0A_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EBIT0B_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Ebit0(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),c_2Efcp_2EBIT0B_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT1_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Efcp_2EBIT1A_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Ebit1(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),c_2Efcp_2EBIT1A_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EBIT1B_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Ebit1(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),c_2Efcp_2EBIT1B_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EBIT2_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Epred__set_2ECARD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2ECONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) = s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))),c_2Eind__type_2ECONSTR_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] : ( mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EEXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EEXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2EFAIL_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efcp_2Ecart_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),c_2Ecombin_2EFAIL_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)),c_2Efcp_2EFCP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,A_27c)),c_2Efcp_2EFCP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c))),c_2Efcp_2EFCP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Efcp_2Ecart(A_27b,A_27c)),c_2Efcp_2EFCP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)),c_2Efcp_2EFCP_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__CONCAT_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),c_2Efcp_2EFCP__CONCAT_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X1_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)))),c_2Efcp_2EFCP__CONCAT_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__CONS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP__CONS_2E2(s(A_27a,X0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c))),c_2Efcp_2EFCP__CONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__CONS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efcp_2EFCP__CONS_2E2(s(A_27a,X0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),c_2Efcp_2EFCP__CONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__EVERY_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Efcp_2EFCP__EVERY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__EVERY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Efcp_2Ecart(A_27b,A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Efcp_2EFCP__EVERY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27b,A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__EXISTS_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Efcp_2EFCP__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__EXISTS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Efcp_2Ecart(A_27b,A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Efcp_2EFCP__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27b,A_27a),X1_2E0)))) ) ).

tff(arityeq3_2Ec_2Efcp_2EFCP__FOLD_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Efcp_2EFCP__FOLD_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),A_27b))),c_2Efcp_2EFCP__FOLD_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP__HD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(A_27a,c_2Efcp_2EFCP__HD_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),A_27a),c_2Efcp_2EFCP__HD_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EFCP__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X1_2E0))) = s(tyop_2Efcp_2Ecart(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27b,A_27c))),c_2Efcp_2EFCP__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP__TL_2E1_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP__TL_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Efcp_2Ecart(A_27a,A_27c)),c_2Efcp_2EFCP__TL_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EFCP__TL_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP__TL_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27c),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Efcp_2Ecart(A_27a,A_27b)),c_2Efcp_2EFCP__TL_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2EFCP__ZIP_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),c_2Efcp_2EFCP__ZIP_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0),s(tyop_2Efcp_2Ecart(A_27c,A_27b),X1_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b))),c_2Efcp_2EFCP__ZIP_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))),s(tyop_2Efcp_2Ecart(A_27c,A_27b),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Efcp_2Ebit1_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2EHAS__SIZE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EHAS__SIZE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Efcp_2EHAS__SIZE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EHD_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)),c_2Efcp_2EL2V_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,A_27c)),c_2Efcp_2EL2V_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),c_2Efcp_2EL2V_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EL2V_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Efcp_2Ecart(A_27b,A_27c)),c_2Efcp_2EL2V_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ENULL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2ENULL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eprim__rec_2EPRE_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eprim__rec_2EPRE_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Enum_2ESUC_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ETL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ETL_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2EA_27a_20mono_2Etyop_2Efcp_2Efinite__image_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efcp_2Efinite__image_28A_27b_29_2CA_27a_29_20mono_2Etyop_2Efcp_2Ecart_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Efcp_2Ebit0_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Efcp_2Ebit1_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2EV2L_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Elist_2Elist(A_27a)),c_2Efcp_2EV2L_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2EV2L_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27c),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Elist_2Elist(A_27a)),c_2Efcp_2EV2L_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq3_2Ec_2Efcp_2Ebit0__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))),c_2Efcp_2Ebit0__CASE_2E0),s(tyop_2Efcp_2Ebit0(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2Ebit0__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit0__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Efcp_2Ebit0(A_27a),X1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Enum_2Enum)),c_2Efcp_2Ebit0__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Efcp_2Ebit0(A_27a),X1_2E0)))) ) ).

tff(arityeq4_2Ec_2Efcp_2Ebit1__CASE_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27b,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Efcp_2Ebit1__CASE_2E0),s(tyop_2Efcp_2Ebit1(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27b,X3_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2Ebit1__size_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit1__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Efcp_2Ebit1(A_27a),X1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Enum_2Enum)),c_2Efcp_2Ebit1__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Efcp_2Ebit1(A_27a),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edest__cart_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),c_2Efcp_2Edest__cart_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),c_2Efcp_2Edest__cart_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2Edest__cart_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(A_27a,c_2Efcp_2Edest__cart_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0),s(tyop_2Efcp_2Efinite__image(A_27b),X1_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),c_2Efcp_2Edest__cart_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))),s(tyop_2Efcp_2Efinite__image(A_27b),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edest__finite__image_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Efcp_2Edest__finite__image_2E1(s(tyop_2Efcp_2Efinite__image(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),c_2Efcp_2Edest__finite__image_2E0),s(tyop_2Efcp_2Efinite__image(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27a),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27b),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(A_27c),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(A_27c),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Efcp_2Ebit0_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(A_27a)),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(A_27a)),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(A_27a)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Efcp_2Ebit1_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit1(A_27a)),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit1(A_27a)),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit1(A_27a)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [X0_2E0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] : ( mono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Efcp_2Edimindex_2E0_2Emono_2Etyop_2Eone_2Eone,X0_2E0) ) ).

tff(arityeq1_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Esum_2Esum(A_27a,A_27b)),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0),s(tyop_2Ebool_2Eitself(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2Efcp__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(A_27c,c_2Efcp_2Efcp__CASE_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),A_27c)),c_2Efcp_2Efcp__CASE_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2Efcp__index_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Efcp_2Efcp__index_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27c),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27b,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27b,A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Efcp_2Ecart(A_27b,A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27c,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27c,A_27b),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27c)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Efcp_2Ecart(A_27c,A_27b),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Efinite__index_2E1_2Emono_2Etyop_2Efcp_2Efinite__image_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Efcp_2Efinite__image(A_27b),c_2Efcp_2Efinite__index_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) = s(tyop_2Efcp_2Efinite__image(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Efcp_2Efinite__image(A_27b)),c_2Efcp_2Efinite__index_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Efcp_2Emk__cart_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),X0_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Efcp_2Ecart(A_27a,A_27b)),c_2Efcp_2Emk__cart_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Efcp_2Emk__finite__image_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Efcp_2Efinite__image(A_27a),c_2Efcp_2Emk__finite__image_2E1(s(A_27a,X0_2E0))) = s(tyop_2Efcp_2Efinite__image(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Efinite__image(A_27a)),c_2Efcp_2Emk__finite__image_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2E_3F_21_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_3F_21_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Enum_2Enum,V2_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2EDATATYPE_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E1(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0) ).

tff(monoeq_2Emono_2Ec_2Efcp_2Edimindex_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Efcp_2Edimindex_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Emin_2Efun(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),tyop_2Enum_2Enum),c_2Efcp_2Edimindex_2E0) ).

tff(monoeq_2Emono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone(V0_2E0))) = s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2Ethe__value_2E0_2Emono_2Etyop_2Eone_2Eone,axiom,
    s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29(mono_2Ec_2Ebool_2Ethe__value_2E0_2Emono_2Etyop_2Eone_2Eone)) = s(tyop_2Ebool_2Eitself(tyop_2Eone_2Eone),c_2Ebool_2Ethe__value_2E0) ).

tff(thm_2Efcp_2EHAS__SIZE__def,axiom,
    ! [A_27a: d,V0s_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EHAS__SIZE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))))
        & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) = V1n_2E0 ) ) ) ).

tff(thm_2Efcp_2Efinite__image__TY__DEF,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(A_27a,V1x_2E0)))))
        <=> ( ( s(A_27a,V1x_2E0) = s(A_27a,c_2Ebool_2EARB_2E0) )
            | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) ) )
     => ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27a),A_27a),V0rep_2E0))))) ) ).

tff(thm_2Efcp_2Efinite__image__tybij,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] : ( s(tyop_2Efcp_2Efinite__image(A_27a),c_2Efcp_2Emk__finite__image_2E1(s(A_27a,c_2Efcp_2Edest__finite__image_2E1(s(tyop_2Efcp_2Efinite__image(A_27a),V0a_2E0))))) = s(tyop_2Efcp_2Efinite__image(A_27a),V0a_2E0) )
      & ! [V1r_2E0: u] :
          ( ( ( s(A_27a,V1r_2E0) = s(A_27a,c_2Ebool_2EARB_2E0) )
            | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) )
        <=> ( s(A_27a,c_2Efcp_2Edest__finite__image_2E1(s(tyop_2Efcp_2Efinite__image(A_27a),c_2Efcp_2Emk__finite__image_2E1(s(A_27a,V1r_2E0))))) = s(A_27a,V1r_2E0) ) ) ) ).

tff(thm_2Efcp_2Edimindex__def,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ).

tff(thm_2Efcp_2Efinite__index__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1x_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(A_27a,V1x_2E0)))),V2n_2E0))
        <=> ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
            & ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(A_27a,V1x_2E0) ) ) )
     => ( ! [V0f_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0)))))
          <=> ! [V1x_2E0: u] : p(mono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(A_27a,V1x_2E0)))))) )
       => ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Efcp_2Efinite__index_2E0) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),F0_2E0))) ) ) ) ).

tff(thm_2Efcp_2Ecart__TY__DEF,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V1f_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
     => ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a)),V0rep_2E0))))) ) ).

tff(thm_2Efcp_2Ecart__tybij,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),c_2Efcp_2Edest__cart_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0))))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0) )
      & ! [V1r_2E0: u] :
          ( p(mono_2Ec_2Ebool_2ET_2E0)
        <=> ( s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),c_2Efcp_2Edest__cart_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V1r_2E0) ) ) ) ).

tff(thm_2Efcp_2Efcp__index,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) = s(A_27a,c_2Efcp_2Edest__cart_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0x_2E0),s(tyop_2Efcp_2Efinite__image(A_27b),c_2Efcp_2Efinite__index_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))))) ) ).

tff(thm_2Efcp_2Efcp__case__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0h_2E0: u,V1f_2E0: u] : ( s(A_27c,c_2Efcp_2Efcp__CASE_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V0h_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),V1f_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V0h_2E0))) ) ).

tff(thm_2Efcp_2EFCP,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1f_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0x_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1f_2E0)))))
        <=> ! [V2i_2E0: mono_2Etyop_2Enum_2Enum] :
              ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
             => ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) ) ) )
     => ! [V0x_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0x_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0x_2E0))))) ) ) ).

tff(thm_2Efcp_2Ebit0__TY__DEF,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V7n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
     => ( ! [V5n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
       => ( ! [V1a0_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_2E0)))))
            <=> ! [V2_27bit0_27_2E0: u] :
                  ( ! [V3a0_2E0: u] :
                      ( ( ? [V4a_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0))) )
                        | ? [V6a_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))),s(A_27a,V6a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0))) ) )
                     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27bit0_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0))))) )
                 => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27bit0_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_2E0))))) ) )
         => ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),V0rep_2E0))))) ) ) ) ).

tff(thm_2Efcp_2Ebit0__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u,V1f_2E0: u,V2f1_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V0a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V0a_2E0))) )
      & ! [V3a_2E0: u,V4f_2E0: u,V5f1_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V3a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0),s(A_27a,V3a_2E0))) ) ) ).

tff(thm_2Efcp_2Ebit0__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u,V1a_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit0__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V1a_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1a_2E0))))) )
      & ! [V2f_2E0: u,V3a_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit0__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V3a_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(A_27a,V3a_2E0))))) ) ) ).

tff(thm_2Efcp_2Ebit1__TY__DEF,axiom,
    ! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V8n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F3_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
     => ( ! [V7n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
       => ( ! [V5n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eind__type_2Erecspace(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)))) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2EBOTTOM_2E0) )
         => ( ! [V1a0_2E0: u] :
                ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_2E0)))))
              <=> ! [V2_27bit1_27_2E0: u] :
                    ( ! [V3a0_2E0: u] :
                        ( ( ? [V4a_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V4a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0))) )
                          | ? [V6a_2E0: u] : ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0))),s(A_27a,V6a_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0))) )
                          | ( s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0) = s(tyop_2Eind__type_2Erecspace(A_27a),c_2Eind__type_2ECONSTR_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2ESUC_2E1(mono_2Ec_2Enum_2E0_2E0)))),s(A_27a,c_2Ebool_2EARB_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F3_2E0))) ) )
                       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27bit1_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V3a0_2E0))))) )
                   => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),V2_27bit1_27_2E0),s(tyop_2Eind__type_2Erecspace(A_27a),V1a0_2E0))))) ) )
           => ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),V0rep_2E0))))) ) ) ) ) ).

tff(thm_2Efcp_2Ebit1__case__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u,V1f_2E0: u,V2f1_2E0: u,V3v_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V0a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27b,V3v_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V0a_2E0))) )
      & ! [V4a_2E0: u,V5f_2E0: u,V6f1_2E0: u,V7v_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V4a_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(A_27b,V7v_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(A_27a,V4a_2E0))) )
      & ! [V8f_2E0: u,V9f1_2E0: u,V10v_2E0: u] : ( s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V8f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V9f1_2E0),s(A_27b,V10v_2E0))) = s(A_27b,V10v_2E0) ) ) ).

tff(thm_2Efcp_2Ebit1__size__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u,V1a_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit1__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V1a_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0f_2E0),s(A_27a,V1a_2E0))))) )
      & ! [V2f_2E0: u,V3a_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit1__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V3a_2E0)))))) = mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2f_2E0),s(A_27a,V3a_2E0))))) )
      & ! [V4f_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Ebit1__size_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4f_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0)))) = mono_2Ec_2Enum_2E0_2E0 ) ) ).

tff(thm_2Efcp_2EFCP__UPDATE__def,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,F0_2E0: u] :
      ( ! [V0a_2E0: mono_2Etyop_2Enum_2Enum,V3c_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F1_2E0,V0a_2E0),V3c_2E0))
        <=> ( V0a_2E0 = V3c_2E0 ) )
     => ( ! [V0a_2E0: mono_2Etyop_2Enum_2Enum,V1b_2E0: u,V2x_2E0: u,V3c_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0a_2E0)))),s(A_27a,V1b_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V2x_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3c_2E0)))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F1_2E0,V0a_2E0),V3c_2E0))),s(A_27a,V1b_2E0),s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V2x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3c_2E0)))))) )
       => ! [V0a_2E0: mono_2Etyop_2Enum_2Enum,V1b_2E0: u,V2x_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0a_2E0)),s(A_27a,V1b_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V2x_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0a_2E0)))),s(A_27a,V1b_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V2x_2E0))))) ) ) ) ).

tff(thm_2Efcp_2EFCP__HD__def,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u] : ( s(A_27a,c_2Efcp_2EFCP__HD_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ) ).

tff(thm_2Efcp_2EFCP__TL__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0v_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V0v_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V0v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1i_2E0))))) )
     => ! [V0v_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP__TL_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V0v_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V0v_2E0))))) ) ) ).

tff(thm_2Efcp_2EFCP__CONS__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1v_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E1(V2i_2E0))))) )
     => ! [V0h_2E0: u,V1v_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP__CONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(A_27a,V0h_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0))))))) ) ) ).

tff(thm_2Efcp_2EFCP__MAP__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1v_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1v_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))))) )
     => ! [V0f_2E0: u,V1v_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EFCP__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1v_2E0))) = s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1v_2E0))))) ) ) ).

tff(thm_2Efcp_2EFCP__EXISTS__def,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1v_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ecart(A_27b,A_27a),V1v_2E0)))))
    <=> ? [V2i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27b,A_27a),V1v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))))))) ) ) ).

tff(thm_2Efcp_2EFCP__EVERY__def,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1v_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EVERY_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ecart(A_27b,A_27a),V1v_2E0)))))
    <=> ! [V2i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))),V2i_2E0))
          | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0),s(A_27b,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27b,A_27a),V1v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))))))) ) ) ).

tff(thm_2Efcp_2EFCP__CONCAT__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1b_2E0: u,V0a_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1b_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0))))))),s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1b_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0))))))))))) )
     => ! [V0a_2E0: u,V1b_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),c_2Efcp_2EFCP__CONCAT_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1b_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1b_2E0))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0))))) ) ) ).

tff(thm_2Efcp_2EFCP__ZIP__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0a_2E0: u,V1b_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Epair_2Eprod(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)))),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0))),s(tyop_2Efcp_2Ecart(A_27c,A_27b),V1b_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epair_2E_2C_2E2(s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(A_27c,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27c,A_27b),V1b_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))))) )
     => ! [V0a_2E0: u,V1b_2E0: u] : ( s(tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),c_2Efcp_2EFCP__ZIP_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0),s(tyop_2Efcp_2Ecart(A_27c,A_27b),V1b_2E0))) = s(tyop_2Efcp_2Ecart(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(A_27a,A_27c)))),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0a_2E0))),s(tyop_2Efcp_2Ecart(A_27c,A_27b),V1b_2E0))))) ) ) ).

tff(thm_2Efcp_2EV2L__def,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Efcp_2Efcp__index_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))),s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))) ) ).

tff(thm_2Efcp_2EL2V__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0L_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0L_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) )
     => ! [V0L_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),V0L_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0L_2E0))))) ) ) ).

tff(thm_2Efcp_2EFCP__FOLD__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1i_2E0: u,V2v_2E0: u] : ( s(A_27b,c_2Efcp_2EFCP__FOLD_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1i_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V2v_2E0))) = s(A_27b,c_2Elist_2EFOLDL_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(A_27b,V1i_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V2v_2E0))))) ) ).

tff(thm_2Efcp_2ENOT__FINITE__IMP__dimindex__1,axiom,
    ! [A_27a: d] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ) ) ).

tff(thm_2Efcp_2EDIMINDEX__GE__1,axiom,
    ! [A_27a: d] : p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))))) ).

tff(thm_2Efcp_2Efcp__Axiom,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
    ? [V1g_2E0: u] :
    ! [V2h_2E0: u] : ( s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),A_27c),V1g_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V2h_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),A_27c),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V2h_2E0))) ) ).

tff(thm_2Efcp_2Efcp__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ! [V1f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2Emk__cart_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Efinite__image(A_27b),A_27a),V1f_2E0)))))))
     => ! [V2a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V2a_2E0))))) ) ).

tff(thm_2Efcp_2ECART__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
      ( ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0x_2E0) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1y_2E0) )
    <=> ! [V2i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
         => ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1y_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) ) ) ) ).

tff(thm_2Efcp_2EFCP__BETA,axiom,
    ! [A_27a: d,A_27b: d,V0g_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0g_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) ) ) ).

tff(thm_2Efcp_2EFCP__UNIQUE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
         => ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))) ) )
    <=> ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1g_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0f_2E0) ) ) ).

tff(thm_2Efcp_2EFCP__ETA,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0g_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0g_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)))) )
     => ! [V0g_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0g_2E0))))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0g_2E0) ) ) ).

tff(thm_2Efcp_2Ecard__dimindex,axiom,
    ! [A_27a: d] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))) ) ) ).

tff(thm_2Efcp_2Eindex__sum,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(F0_2E0)
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) ) )
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Esum_2Esum(A_27a,A_27b)),c_2Ebool_2Ethe__value_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(F0_2E0,mono_2Ec_2Earithmetic_2E_2B_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ) ).

tff(thm_2Efcp_2Efinite__sum,axiom,
    ! [A_27a: d,A_27b: d] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))) ) ) ).

tff(thm_2Efcp_2Edatatype__bit0,axiom,
    ! [A_27a: d,V0bit0_2E0: u] : p(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),tyop_2Emin_2Ebool)),V0bit0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),c_2Efcp_2EBIT0A_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit0(A_27a)),c_2Efcp_2EBIT0B_2E0)))))) ).

tff(thm_2Efcp_2Ebit0__11,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1a_27_2E0: u] :
          ( ( s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V0a_2E0))) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V1a_27_2E0))) )
        <=> ( s(A_27a,V0a_2E0) = s(A_27a,V1a_27_2E0) ) )
      & ! [V2a_2E0: u,V3a_27_2E0: u] :
          ( ( s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V2a_2E0))) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V3a_27_2E0))) )
        <=> ( s(A_27a,V2a_2E0) = s(A_27a,V3a_27_2E0) ) ) ) ).

tff(thm_2Efcp_2Ebit0__distinct,axiom,
    ! [A_27a: d,V0a_27_2E0: u,V1a_2E0: u] : ( s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V1a_2E0))) != s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V0a_27_2E0))) ) ).

tff(thm_2Efcp_2Ebit0__nchotomy,axiom,
    ! [A_27a: d,V0bb_2E0: u] :
      ( ? [V1a_2E0: u] : ( s(tyop_2Efcp_2Ebit0(A_27a),V0bb_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V1a_2E0))) )
      | ? [V2a_2E0: u] : ( s(tyop_2Efcp_2Ebit0(A_27a),V0bb_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V2a_2E0))) ) ) ).

tff(thm_2Efcp_2Ebit0__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u] :
    ? [V2fn_2E0: u] :
      ( ! [V3a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),A_27b),V2fn_2E0),s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V3a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f0_2E0),s(A_27a,V3a_2E0))) )
      & ! [V4a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),A_27b),V2fn_2E0),s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V4a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f1_2E0),s(A_27a,V4a_2E0))) ) ) ).

tff(thm_2Efcp_2Ebit0__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V1a_2E0)))))))
        & ! [V2a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V2a_2E0))))))) )
     => ! [V3b_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit0(A_27a),V3b_2E0))))) ) ).

tff(thm_2Efcp_2Ebit0__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0f1_27_2E0: u,V1f_27_2E0: u,V2M_2E0: u,V3M_27_2E0: u,V4f_2E0: u,V5f1_2E0: u] :
      ( ( ( s(tyop_2Efcp_2Ebit0(A_27a),V2M_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0) )
        & ! [V6a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V6a_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V6a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(A_27a,V6a_2E0))) ) )
        & ! [V7a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V7a_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0),s(A_27a,V7a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_27_2E0),s(A_27a,V7a_2E0))) ) ) )
     => ( s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),V2M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f1_2E0))) = s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),V3M_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f1_27_2E0))) ) ) ).

tff(thm_2Efcp_2Ebit0__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_2E0: u,V2f1_2E0: u,V3f_2E0: u] :
      ( ( s(A_27b,c_2Efcp_2Ebit0__CASE_2E3(s(tyop_2Efcp_2Ebit0(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0))) = s(A_27b,V1v_2E0) )
    <=> ( ? [V4a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit0(A_27a),V0x_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0A_2E1(s(A_27a,V4a_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4a_2E0))) = s(A_27b,V1v_2E0) ) )
        | ? [V5a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit0(A_27a),V0x_2E0) = s(tyop_2Efcp_2Ebit0(A_27a),c_2Efcp_2EBIT0B_2E1(s(A_27a,V5a_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V5a_2E0))) = s(A_27b,V1v_2E0) ) ) ) ) ).

tff(thm_2Efcp_2Eindex__bit0,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit0(A_27a)),c_2Ebool_2Ethe__value_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ).

tff(thm_2Efcp_2Efinite__bit0,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit0(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) ) ).

tff(thm_2Efcp_2Edatatype__bit1,axiom,
    ! [A_27a: d,V0bit1_2E0: u] : p(mono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool))),V0bit1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),c_2Efcp_2EBIT1A_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Efcp_2Ebit1(A_27a)),c_2Efcp_2EBIT1B_2E0))),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0)))))) ).

tff(thm_2Efcp_2Ebit1__11,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1a_27_2E0: u] :
          ( ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V0a_2E0))) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V1a_27_2E0))) )
        <=> ( s(A_27a,V0a_2E0) = s(A_27a,V1a_27_2E0) ) )
      & ! [V2a_2E0: u,V3a_27_2E0: u] :
          ( ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V2a_2E0))) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V3a_27_2E0))) )
        <=> ( s(A_27a,V2a_2E0) = s(A_27a,V3a_27_2E0) ) ) ) ).

tff(thm_2Efcp_2Ebit1__distinct,axiom,
    ! [A_27a: d] :
      ( ! [V0a_27_2E0: u,V1a_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V1a_2E0))) != s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V0a_27_2E0))) )
      & ! [V2a_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V2a_2E0))) != s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0) )
      & ! [V3a_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V3a_2E0))) != s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0) ) ) ).

tff(thm_2Efcp_2Ebit1__nchotomy,axiom,
    ! [A_27a: d,V0bb_2E0: u] :
      ( ? [V1a_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),V0bb_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V1a_2E0))) )
      | ? [V2a_2E0: u] : ( s(tyop_2Efcp_2Ebit1(A_27a),V0bb_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V2a_2E0))) )
      | ( s(tyop_2Efcp_2Ebit1(A_27a),V0bb_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0) ) ) ).

tff(thm_2Efcp_2Ebit1__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f0_2E0: u,V1f1_2E0: u,V2f2_2E0: u] :
    ? [V3fn_2E0: u] :
      ( ! [V4a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),A_27b),V3fn_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V4a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f0_2E0),s(A_27a,V4a_2E0))) )
      & ! [V5a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),A_27b),V3fn_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V5a_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f1_2E0),s(A_27a,V5a_2E0))) )
      & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),A_27b),V3fn_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0))) = s(A_27b,V2f2_2E0) ) ) ).

tff(thm_2Efcp_2Ebit1__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V1a_2E0)))))))
        & ! [V2a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V2a_2E0)))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0))))) )
     => ! [V3b_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ebit1(A_27a),V3b_2E0))))) ) ).

tff(thm_2Efcp_2Ebit1__case__cong,axiom,
    ! [A_27a: d,A_27b: d,V0v_27_2E0: u,V1f1_27_2E0: u,V2f_27_2E0: u,V3M_2E0: u,V4M_27_2E0: u,V5f_2E0: u,V6f1_2E0: u,V7v_2E0: u] :
      ( ( ( s(tyop_2Efcp_2Ebit1(A_27a),V3M_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),V4M_27_2E0) )
        & ! [V8a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit1(A_27a),V4M_27_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V8a_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(A_27a,V8a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_27_2E0),s(A_27a,V8a_2E0))) ) )
        & ! [V9a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit1(A_27a),V4M_27_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V9a_2E0))) )
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(A_27a,V9a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f1_27_2E0),s(A_27a,V9a_2E0))) ) )
        & ( ( s(tyop_2Efcp_2Ebit1(A_27a),V4M_27_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0) )
         => ( s(A_27b,V7v_2E0) = s(A_27b,V0v_27_2E0) ) ) )
     => ( s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),V3M_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(A_27b,V7v_2E0))) = s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),V4M_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_27_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1f1_27_2E0),s(A_27b,V0v_27_2E0))) ) ) ).

tff(thm_2Efcp_2Ebit1__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_27_2E0: u,V2v_2E0: u,V3f1_2E0: u,V4f_2E0: u] :
      ( ( s(A_27b,c_2Efcp_2Ebit1__CASE_2E4(s(tyop_2Efcp_2Ebit1(A_27a),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f1_2E0),s(A_27b,V2v_2E0))) = s(A_27b,V1v_27_2E0) )
    <=> ( ? [V5a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit1(A_27a),V0x_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1A_2E1(s(A_27a,V5a_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V5a_2E0))) = s(A_27b,V1v_27_2E0) ) )
        | ? [V6a_2E0: u] :
            ( ( s(tyop_2Efcp_2Ebit1(A_27a),V0x_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1B_2E1(s(A_27a,V6a_2E0))) )
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f1_2E0),s(A_27a,V6a_2E0))) = s(A_27b,V1v_27_2E0) ) )
        | ( ( s(tyop_2Efcp_2Ebit1(A_27a),V0x_2E0) = s(tyop_2Efcp_2Ebit1(A_27a),c_2Efcp_2EBIT1C_2E0) )
          & ( s(A_27b,V2v_2E0) = s(A_27b,V1v_27_2E0) ) ) ) ) ).

tff(thm_2Efcp_2Eindex__bit1,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(tyop_2Efcp_2Ebit1(A_27a)),c_2Ebool_2Ethe__value_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))),mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2E_2A_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27a),c_2Ebool_2Ethe__value_2E0))))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ).

tff(thm_2Efcp_2Efinite__bit1,axiom,
    ! [A_27a: d] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ebit1(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) ) ).

tff(thm_2Efcp_2Eindex__one,axiom,
    mono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Ebool_2Ethe__value_2E0_2Emono_2Etyop_2Eone_2Eone) = mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)) ).

tff(thm_2Efcp_2Efinite__one,axiom,
    p(mono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone(mono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Eone_2Eone)) ).

tff(thm_2Efcp_2EFCP__UPDATE__COMMUTES,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1a_2E0: mono_2Etyop_2Enum_2Enum,V2b_2E0: mono_2Etyop_2Enum_2Enum,V3c_2E0: u,V4d_2E0: u] :
      ( ( V1a_2E0 != V2b_2E0 )
     => ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V3c_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2b_2E0)),s(A_27a,V4d_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0))))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2b_2E0)),s(A_27a,V4d_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V3c_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0))))) ) ) ).

tff(thm_2Efcp_2EFCP__UPDATE__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1a_2E0: mono_2Etyop_2Enum_2Enum,V2b_2E0: u,V3c_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V3c_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V2b_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0))))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V3c_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0))) ) ).

tff(thm_2Efcp_2EFCP__UPDATE__IMP__ID,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1a_2E0: mono_2Etyop_2Enum_2Enum,V2v_2E0: u] :
      ( ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)))) = s(A_27a,V2v_2E0) )
     => ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,V2v_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0) ) ) ).

tff(thm_2Efcp_2EAPPLY__FCP__UPDATE__ID,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1a_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)),s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a_2E0)))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0m_2E0) ) ).

tff(thm_2Efcp_2EFCP__APPLY__UPDATE__THM,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ! [V2a_2E0: mono_2Etyop_2Enum_2Enum,V4b_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V2a_2E0),V4b_2E0))
        <=> ( V2a_2E0 = V4b_2E0 ) )
     => ! [V0index_20out_20of_20range_2E0: mono_2Etyop_2Emin_2Ebool,V1m_2E0: u,V2a_2E0: mono_2Etyop_2Enum_2Enum,V3w_2E0: u,V4b_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2a_2E0)),s(A_27a,V3w_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1m_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4b_2E0)))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V4b_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F0_2E0,V2a_2E0),V4b_2E0))),s(A_27a,V3w_2E0),s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1m_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4b_2E0)))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0index_20out_20of_20range_2E0)))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2a_2E0)),s(A_27a,V3w_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1m_2E0))))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4b_2E0)))))) ) ) ).

tff(thm_2Efcp_2ELENGTH__V2L,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0)))) ) ).

tff(thm_2Efcp_2EEL__V2L,axiom,
    ! [A_27a: d,A_27b: d,V0i_2E0: mono_2Etyop_2Enum_2Enum,V1v_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0))))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)))) ) ) ).

tff(thm_2Efcp_2EFCP__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1v_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EFCP__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1v_2E0))) = s(tyop_2Efcp_2Ecart(A_27b,A_27c),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1v_2E0))))))) ) ).

tff(thm_2Efcp_2EFCP__TL,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0v_2E0: u] :
      ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
        & ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27c),c_2Ebool_2Ethe__value_2E0)))) = mono_2Ec_2Earithmetic_2E_2D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0)))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) )
     => ( s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EFCP__TL_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,A_27c),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))))))) ) ) ).

tff(thm_2Efcp_2EFCP__EXISTS,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0)))))) ) ).

tff(thm_2Efcp_2EFCP__EVERY,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Efcp_2EFCP__EVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0)))))) ) ).

tff(thm_2Efcp_2EFCP__HD,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u] : ( s(A_27a,c_2Efcp_2EFCP__HD_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))) = s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))))) ) ).

tff(thm_2Efcp_2EFCP__CONS,axiom,
    ! [A_27a: d,A_27b: d,V0a_2E0: u,V1v_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efcp_2EFCP__CONS_2E2(s(A_27a,V0a_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0))) = s(tyop_2Efcp_2Ecart(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V1v_2E0))))))) ) ).

tff(thm_2Efcp_2EV2L__L2V,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0)))) )
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))))) = s(tyop_2Elist_2Elist(A_27a),V0x_2E0) ) ) ).

tff(thm_2Efcp_2ENULL__V2L,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u] : ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Efcp_2EV2L_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27b),V0v_2E0))))))) ).

tff(thm_2Efcp_2EREAD__TL,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0i_2E0: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP__TL_2E1(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1a_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)))) = s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27c),V1a_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V0i_2E0))))) ) ) ).

tff(thm_2Efcp_2EREAD__L2V,axiom,
    ! [A_27a: d,A_27b: d,V0i_2E0: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))
     => ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EL2V_2E1(s(tyop_2Elist_2Elist(A_27a),V1a_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)),s(tyop_2Elist_2Elist(A_27a),V1a_2E0))) ) ) ).

tff(thm_2Efcp_2Eindex__comp,axiom,
    ! [A_27a: d,A_27b: d,V0FCP_20out_20of_20bounds_2E0: mono_2Etyop_2Emin_2Ebool,V1f_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,c_2Efcp_2Efcp__index_2E2(s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Efcp_2Edimindex_2E1(s(tyop_2Ebool_2Eitself(A_27b),c_2Ebool_2Ethe__value_2E0))))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Ecombin_2EFAIL_2E2(s(tyop_2Emin_2Efun(tyop_2Efcp_2Ecart(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),c_2Efcp_2Efcp__index_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0FCP_20out_20of_20bounds_2E0)))),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))) ) ).

tff(thm_2Efcp_2Efcp__subst__comp,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,F0_2E0: u] :
      ( ! [V1x_2E0: mono_2Etyop_2Enum_2Enum,V5c_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F1_2E0,V1x_2E0),V5c_2E0))
        <=> ( V1x_2E0 = V5c_2E0 ) )
     => ( ! [V1x_2E0: mono_2Etyop_2Enum_2Enum,V0y_2E0: u,V4f_2E0: u,V5c_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)))),s(A_27a,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5c_2E0)))) = s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(F1_2E0,V1x_2E0),V5c_2E0))),s(A_27a,V0y_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5c_2E0)))))) )
       => ! [V0y_2E0: u,V1x_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u,V3b_2E0: u,V4f_2E0: u] : ( s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2E_3A_2B_2E3(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)),s(A_27a,V0y_2E0),s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0))))) = s(tyop_2Efcp_2Ecart(A_27a,A_27b),c_2Efcp_2EFCP_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)))),s(A_27a,V0y_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4f_2E0))))) ) ) ) ).

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