ITP001 Axioms: ITP047^4.ax
%------------------------------------------------------------------------------
% File : ITP047^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : fcp.ax [Gau19]
% : HL4047^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 468 ( 170 unt; 234 typ; 0 def)
% Number of atoms : 446 ( 291 equ; 8 cnn)
% Maximal formula atoms : 10 ( 0 avg)
% Number of connectives : 8149 ( 8 ~; 13 |; 35 &;8007 @)
% ( 32 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg;8007 nst)
% Number of types : 7 ( 6 usr)
% Number of type conns : 337 ( 337 >; 0 *; 0 +; 0 <<)
% Number of symbols : 230 ( 228 usr; 89 con; 0-4 aty)
% Number of variables : 799 ( 0 ^ 778 !; 21 ?; 799 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Eone_2Eone,type,
mono_2Etyop_2Eone_2Eone: $tType ).
thf(tyop_2Ebool_2Eitself,type,
tyop_2Ebool_2Eitself: d > d ).
thf(tyop_2Efcp_2Ebit0,type,
tyop_2Efcp_2Ebit0: d > d ).
thf(tyop_2Efcp_2Ebit1,type,
tyop_2Efcp_2Ebit1: d > d ).
thf(tyop_2Efcp_2Ecart,type,
tyop_2Efcp_2Ecart: d > d > d ).
thf(tyop_2Efcp_2Efinite__image,type,
tyop_2Efcp_2Efinite__image: d > d ).
thf(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: d > d ).
thf(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Esum_2Esum,type,
tyop_2Esum_2Esum: d > d > d ).
thf(s,type,
s: d > u > du ).
thf(app_2E2,type,
app_2E2: du > du > u ).
thf(combin_i_2E0,type,
combin_i_2E0: u ).
thf(combin_k_2E0,type,
combin_k_2E0: u ).
thf(combin_s_2E0,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: u ).
thf(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: u ).
thf(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: du > du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: u ).
thf(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: du > du > u ).
thf(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: u ).
thf(c_2Efcp_2E_3A_2B_2E0,type,
c_2Efcp_2E_3A_2B_2E0: u ).
thf(c_2Efcp_2E_3A_2B_2E3,type,
c_2Efcp_2E_3A_2B_2E3: du > du > du > u ).
thf(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: u ).
thf(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0: u ).
thf(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1: du > u ).
thf(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0: u ).
thf(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1: du > u ).
thf(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0: u ).
thf(c_2Efcp_2EBIT0A_2E0,type,
c_2Efcp_2EBIT0A_2E0: u ).
thf(c_2Efcp_2EBIT0A_2E1,type,
c_2Efcp_2EBIT0A_2E1: du > u ).
thf(c_2Efcp_2EBIT0B_2E0,type,
c_2Efcp_2EBIT0B_2E0: u ).
thf(c_2Efcp_2EBIT0B_2E1,type,
c_2Efcp_2EBIT0B_2E1: du > u ).
thf(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: u ).
thf(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: du > u ).
thf(c_2Efcp_2EBIT1A_2E0,type,
c_2Efcp_2EBIT1A_2E0: u ).
thf(c_2Efcp_2EBIT1A_2E1,type,
c_2Efcp_2EBIT1A_2E1: du > u ).
thf(c_2Efcp_2EBIT1B_2E0,type,
c_2Efcp_2EBIT1B_2E0: u ).
thf(c_2Efcp_2EBIT1B_2E1,type,
c_2Efcp_2EBIT1B_2E1: du > u ).
thf(c_2Efcp_2EBIT1C_2E0,type,
c_2Efcp_2EBIT1C_2E0: u ).
thf(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: u ).
thf(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: du > u ).
thf(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0: u ).
thf(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0: u ).
thf(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0: u ).
thf(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2: du > du > u ).
thf(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0: u ).
thf(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3: du > du > du > u ).
thf(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0: u ).
thf(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1: du > u ).
thf(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0: u ).
thf(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2: du > du > u ).
thf(c_2Elist_2EEVERY_2E0,type,
c_2Elist_2EEVERY_2E0: u ).
thf(c_2Elist_2EEVERY_2E2,type,
c_2Elist_2EEVERY_2E2: du > du > u ).
thf(c_2Elist_2EEXISTS_2E0,type,
c_2Elist_2EEXISTS_2E0: u ).
thf(c_2Elist_2EEXISTS_2E2,type,
c_2Elist_2EEXISTS_2E2: du > du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Ecombin_2EFAIL_2E0,type,
c_2Ecombin_2EFAIL_2E0: u ).
thf(c_2Ecombin_2EFAIL_2E2,type,
c_2Ecombin_2EFAIL_2E2: du > du > u ).
thf(c_2Efcp_2EFCP_2E0,type,
c_2Efcp_2EFCP_2E0: u ).
thf(c_2Efcp_2EFCP_2E1,type,
c_2Efcp_2EFCP_2E1: du > u ).
thf(c_2Efcp_2EFCP__CONCAT_2E0,type,
c_2Efcp_2EFCP__CONCAT_2E0: u ).
thf(c_2Efcp_2EFCP__CONCAT_2E2,type,
c_2Efcp_2EFCP__CONCAT_2E2: du > du > u ).
thf(c_2Efcp_2EFCP__CONS_2E0,type,
c_2Efcp_2EFCP__CONS_2E0: u ).
thf(c_2Efcp_2EFCP__CONS_2E2,type,
c_2Efcp_2EFCP__CONS_2E2: du > du > u ).
thf(c_2Efcp_2EFCP__EVERY_2E0,type,
c_2Efcp_2EFCP__EVERY_2E0: u ).
thf(c_2Efcp_2EFCP__EVERY_2E2,type,
c_2Efcp_2EFCP__EVERY_2E2: du > du > u ).
thf(c_2Efcp_2EFCP__EXISTS_2E0,type,
c_2Efcp_2EFCP__EXISTS_2E0: u ).
thf(c_2Efcp_2EFCP__EXISTS_2E2,type,
c_2Efcp_2EFCP__EXISTS_2E2: du > du > u ).
thf(c_2Efcp_2EFCP__FOLD_2E0,type,
c_2Efcp_2EFCP__FOLD_2E0: u ).
thf(c_2Efcp_2EFCP__FOLD_2E3,type,
c_2Efcp_2EFCP__FOLD_2E3: du > du > du > u ).
thf(c_2Efcp_2EFCP__HD_2E0,type,
c_2Efcp_2EFCP__HD_2E0: u ).
thf(c_2Efcp_2EFCP__HD_2E1,type,
c_2Efcp_2EFCP__HD_2E1: du > u ).
thf(c_2Efcp_2EFCP__MAP_2E0,type,
c_2Efcp_2EFCP__MAP_2E0: u ).
thf(c_2Efcp_2EFCP__MAP_2E2,type,
c_2Efcp_2EFCP__MAP_2E2: du > du > u ).
thf(c_2Efcp_2EFCP__TL_2E0,type,
c_2Efcp_2EFCP__TL_2E0: u ).
thf(c_2Efcp_2EFCP__TL_2E1,type,
c_2Efcp_2EFCP__TL_2E1: du > u ).
thf(c_2Efcp_2EFCP__ZIP_2E0,type,
c_2Efcp_2EFCP__ZIP_2E0: u ).
thf(c_2Efcp_2EFCP__ZIP_2E2,type,
c_2Efcp_2EFCP__ZIP_2E2: du > du > u ).
thf(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1: du > u ).
thf(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0: u ).
thf(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3: du > du > du > u ).
thf(c_2Elist_2EGENLIST_2E0,type,
c_2Elist_2EGENLIST_2E0: u ).
thf(c_2Elist_2EGENLIST_2E2,type,
c_2Elist_2EGENLIST_2E2: du > du > u ).
thf(c_2Efcp_2EHAS__SIZE_2E0,type,
c_2Efcp_2EHAS__SIZE_2E0: u ).
thf(c_2Efcp_2EHAS__SIZE_2E2,type,
c_2Efcp_2EHAS__SIZE_2E2: du > du > u ).
thf(c_2Elist_2EHD_2E0,type,
c_2Elist_2EHD_2E0: u ).
thf(c_2Elist_2EHD_2E1,type,
c_2Elist_2EHD_2E1: du > u ).
thf(c_2Efcp_2EL2V_2E0,type,
c_2Efcp_2EL2V_2E0: u ).
thf(c_2Efcp_2EL2V_2E1,type,
c_2Efcp_2EL2V_2E1: du > u ).
thf(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0: u ).
thf(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1: du > u ).
thf(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0: u ).
thf(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2: du > du > u ).
thf(c_2Elist_2ENULL_2E0,type,
c_2Elist_2ENULL_2E0: u ).
thf(c_2Elist_2ENULL_2E1,type,
c_2Elist_2ENULL_2E1: du > u ).
thf(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: du > u ).
thf(c_2Eprim__rec_2EPRE_2E0,type,
c_2Eprim__rec_2EPRE_2E0: u ).
thf(c_2Eprim__rec_2EPRE_2E1,type,
c_2Eprim__rec_2EPRE_2E1: du > u ).
thf(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: u ).
thf(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Elist_2ETL_2E0,type,
c_2Elist_2ETL_2E0: u ).
thf(c_2Elist_2ETL_2E1,type,
c_2Elist_2ETL_2E1: du > u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).
thf(c_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0: u ).
thf(c_2Efcp_2EV2L_2E0,type,
c_2Efcp_2EV2L_2E0: u ).
thf(c_2Efcp_2EV2L_2E1,type,
c_2Efcp_2EV2L_2E1: du > u ).
thf(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Efcp_2Ebit0__CASE_2E0,type,
c_2Efcp_2Ebit0__CASE_2E0: u ).
thf(c_2Efcp_2Ebit0__CASE_2E3,type,
c_2Efcp_2Ebit0__CASE_2E3: du > du > du > u ).
thf(c_2Efcp_2Ebit0__size_2E0,type,
c_2Efcp_2Ebit0__size_2E0: u ).
thf(c_2Efcp_2Ebit0__size_2E2,type,
c_2Efcp_2Ebit0__size_2E2: du > du > u ).
thf(c_2Efcp_2Ebit1__CASE_2E0,type,
c_2Efcp_2Ebit1__CASE_2E0: u ).
thf(c_2Efcp_2Ebit1__CASE_2E4,type,
c_2Efcp_2Ebit1__CASE_2E4: du > du > du > du > u ).
thf(c_2Efcp_2Ebit1__size_2E0,type,
c_2Efcp_2Ebit1__size_2E0: u ).
thf(c_2Efcp_2Ebit1__size_2E2,type,
c_2Efcp_2Ebit1__size_2E2: du > du > u ).
thf(c_2Efcp_2Edest__cart_2E0,type,
c_2Efcp_2Edest__cart_2E0: u ).
thf(c_2Efcp_2Edest__cart_2E1,type,
c_2Efcp_2Edest__cart_2E1: du > u ).
thf(c_2Efcp_2Edest__cart_2E2,type,
c_2Efcp_2Edest__cart_2E2: du > du > u ).
thf(c_2Efcp_2Edest__finite__image_2E0,type,
c_2Efcp_2Edest__finite__image_2E0: u ).
thf(c_2Efcp_2Edest__finite__image_2E1,type,
c_2Efcp_2Edest__finite__image_2E1: du > u ).
thf(c_2Efcp_2Edimindex_2E0,type,
c_2Efcp_2Edimindex_2E0: u ).
thf(c_2Efcp_2Edimindex_2E1,type,
c_2Efcp_2Edimindex_2E1: du > u ).
thf(c_2Efcp_2Efcp__CASE_2E0,type,
c_2Efcp_2Efcp__CASE_2E0: u ).
thf(c_2Efcp_2Efcp__CASE_2E2,type,
c_2Efcp_2Efcp__CASE_2E2: du > du > u ).
thf(c_2Efcp_2Efcp__index_2E0,type,
c_2Efcp_2Efcp__index_2E0: u ).
thf(c_2Efcp_2Efcp__index_2E1,type,
c_2Efcp_2Efcp__index_2E1: du > u ).
thf(c_2Efcp_2Efcp__index_2E2,type,
c_2Efcp_2Efcp__index_2E2: du > du > u ).
thf(c_2Efcp_2Efinite__index_2E0,type,
c_2Efcp_2Efinite__index_2E0: u ).
thf(c_2Efcp_2Efinite__index_2E1,type,
c_2Efcp_2Efinite__index_2E1: du > u ).
thf(c_2Efcp_2Emk__cart_2E0,type,
c_2Efcp_2Emk__cart_2E0: u ).
thf(c_2Efcp_2Emk__cart_2E1,type,
c_2Efcp_2Emk__cart_2E1: du > u ).
thf(c_2Efcp_2Emk__finite__image_2E0,type,
c_2Efcp_2Emk__finite__image_2E0: u ).
thf(c_2Efcp_2Emk__finite__image_2E1,type,
c_2Efcp_2Emk__finite__image_2E1: du > u ).
thf(c_2Ebool_2Ethe__value_2E0,type,
c_2Ebool_2Ethe__value_2E0: u ).
thf(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Eapp_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_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Eone_2Eone > $o ) > $o ) > ( mono_2Etyop_2Eone_2Eone > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2A,type,
mono_2Ec_2Earithmetic_2E_2A: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2D,type,
mono_2Ec_2Earithmetic_2E_2D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2E_3C_3D,type,
mono_2Ec_2Earithmetic_2E_3C_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EBIT2,type,
mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Eone_2Eone: ( mono_2Etyop_2Eone_2Eone > $o ) > $o ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eprim__rec_2EPRE,type,
mono_2Ec_2Eprim__rec_2EPRE: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > $o ).
thf(mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Efcp_2Edimindex_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Efcp_2Edimindex_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2Ethe__value_2Emono_2Etyop_2Eone_2Eone,type,
mono_2Ec_2Ebool_2Ethe__value_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(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: ( $o > $o ) > u ).
thf(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: ( $o > $o > $o ) > u ).
thf(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: ( $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(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_2Enum_2Enum > $o ) > $o ) > u ).
thf(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_2Eone_2Eone > $o ) > $o ) > u ).
thf(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_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ) > u ).
thf(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_2Enum_2Enum > $o ) > u ).
thf(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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(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_2Eone_2Eone > $o ) > u ).
thf(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 ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(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 > $o > $o ).
thf(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 > $o > $o > $o ).
thf(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 > $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(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_2Enum_2Enum > $o ) > $o ).
thf(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_2Eone_2Eone > $o ) > $o ).
thf(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_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum ).
thf(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_2Enum_2Enum > $o ).
thf(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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(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_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(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_2Eone_2Eone > $o ).
thf(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 ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(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 ) ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( 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 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_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 ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( 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 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_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 ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( 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 ) ) ) ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(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 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(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: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Eone_2Eone > $o ) > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > $o] :
( ( 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29,axiom,
! [V0: 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 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(arityeq3_2Ec_2Efcp_2E_3A_2B_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0: 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 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Efcp_2E_3A_2B_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0: 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 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(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 ) )
<=> ( 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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: 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 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
( ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( 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 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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: $o] :
( ( 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Efcp_2EHAS__SIZE_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1: 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 ) ) ) ) )
= ( 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 ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,X0_2E0: u,X1: 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1: 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Efcp_2Efcp__index_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: d,A_27c: d,X0_2E0: u,X1: 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Efcp_2Efinite__index_2E1_2Emono_2Etyop_2Efcp_2Efinite__image_28A_27b_29,axiom,
! [A_27b: d,X0: 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 ) ) ) )
= ( 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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(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: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( 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 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Eone_2Eone > $o ) > $o,V1: mono_2Etyop_2Eone_2Eone > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ ( tyop_2Ebool_2Eitself @ tyop_2Eone_2Eone ) @ ( i_mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: 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 @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: 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 @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( 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 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(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_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 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( 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 ) ) ) ) ) ).
thf(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_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 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: $o,V1: mono_2Etyop_2Enum_2Enum,V2: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2 ) ) ) ) ) ).
thf(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_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).
thf(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_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 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Eone_2Eone > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( 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 ) ) ) ) ) ).
thf(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_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).
thf(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_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ tyop_2Eone_2Eone ) @ tyop_2Enum_2Enum ) @ c_2Efcp_2Edimindex_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Efcp_2Edimindex_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [V0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Efcp_2Edimindex_2Emono_2Etyop_2Eone_2Eone @ V0 ) ) )
= ( 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 ) ) ) ) ) ).
thf(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_2Emono_2Etyop_2Eone_2Eone ) )
= ( s @ ( tyop_2Ebool_2Eitself @ tyop_2Eone_2Eone ) @ c_2Ebool_2Ethe__value_2E0 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: $o > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Eone_2Eone > $o ) > $o,V1: mono_2Etyop_2Eone_2Eone > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Efcp_2EHAS__SIZE__def,axiom,
! [A_27a: d,V0s_2E0: u,V1n: 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 ) @ V0s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1n ) ) ) ) )
<=> ( ( 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 ) ) ) ).
thf(thm_2Efcp_2Efinite__image__TY__DEF,axiom,
! [A_27a: d,F0_2E0: u] :
( ! [V1x_2E0: u] :
( ( 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 ) )
| ( 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] : ( 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 ) ) ) ) ) ).
thf(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 ) )
| ( 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 ) ) ) ) ).
thf(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_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 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Efcp_2Efinite__index__def,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V0f_2E0: u,V1x_2E0: u,V2n: mono_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 ) ) ) @ V2n )
<=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ ( 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 ) ) ) )
= ( s @ A_27a @ V1x_2E0 ) ) ) )
=> ( ! [V0f_2E0: u] :
( ( 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] : ( mono_2Ec_2Ebool_2E_3F_21_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 ) ) ) ) ) ) ).
thf(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 )
=> ? [V0rep_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 ) @ 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 ) ) ) ) ) ).
thf(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] :
( mono_2Ec_2Ebool_2ET
<=> ( ( 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 ) ) ) ) ).
thf(thm_2Efcp_2Efcp__index,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1i: 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 ) ) ) )
= ( 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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(thm_2Efcp_2EFCP,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0x_2E0: u,V1f_2E0: u] :
( ( 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: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ ( 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 ) ) ) )
= ( 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 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2Ebit0__TY__DEF,axiom,
! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V7n: 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 ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V5n: 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 ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V1a0_2E0: u] :
( ( 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 ) ) @ ( 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 @ mono_2Ec_2Enum_2E0 ) ) ) @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F2_2E0 ) ) ) ) )
=> ( 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 ) ) ) ) )
=> ( 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] : ( 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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2Ebit1__TY__DEF,axiom,
! [A_27a: d,F3_2E0: u,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
( ! [V8n: 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 ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V7n: 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 ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V5n: 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 ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ A_27a ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V1a0_2E0: u] :
( ( 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 ) ) @ ( 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 @ mono_2Ec_2Enum_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 @ ( mono_2Ec_2Enum_2ESUC @ mono_2Ec_2Enum_2E0 ) ) ) ) @ ( s @ A_27a @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ A_27a ) ) @ F3_2E0 ) ) ) ) )
=> ( 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 ) ) ) ) )
=> ( 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] : ( 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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 ) ) ).
thf(thm_2Efcp_2EFCP__UPDATE__def,axiom,
! [A_27a: d,A_27b: d,F1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,F0_2E0: u] :
( ! [V0a: mono_2Etyop_2Enum_2Enum,V3c: mono_2Etyop_2Enum_2Enum] :
( ( F1 @ V0a @ V3c )
<=> ( V0a = V3c ) )
=> ( ! [V0a: mono_2Etyop_2Enum_2Enum,V1b_2E0: u,V2x_2E0: u,V3c: 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 ) ) ) ) @ ( 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 ) ) ) )
= ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F1 @ V0a @ V3c ) ) ) @ ( 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 ) ) ) ) ) ) )
=> ! [V0a: 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 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27a @ V1b_2E0 ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ V2x_2E0 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__TL__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
( ! [V0v_2E0: u,V1i: 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 ) ) ) )
= ( 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 @ V1i ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__CONS__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
( ! [V1v_2E0: u,V2i: 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 ) ) ) )
= ( 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 @ V2i ) ) ) ) ) )
=> ! [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 ) ) @ ( 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 ) ) ) ) ) ) ) ) ) ).
thf(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: 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 ) ) ) )
= ( 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 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__EXISTS__def,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_27b @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27b @ A_27a ) @ V1v_2E0 ) ) ) )
<=> ? [V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ ( 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_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 ) ) ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__EVERY__def,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_27b @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27b @ A_27a ) @ V1v_2E0 ) ) ) )
<=> ! [V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( 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 )
| ( 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 ) ) ) ) ) ) ) ) ) ).
thf(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: 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 ) ) ) )
= ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ ( 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 ) ) ) ) @ ( 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 @ V2i @ ( 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 ) ) ) ) ) ) ) ).
thf(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: 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 ) ) ) )
= ( 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 ) ) ) ) @ ( 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 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(thm_2Efcp_2EL2V__def,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0L_2E0: u,V1i: 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 ) ) ) )
= ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1i ) ) @ ( 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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(thm_2Efcp_2ENOT__FINITE__IMP__dimindex__1,axiom,
! [A_27a: d] :
( ( (~) @ ( 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 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Efcp_2EDIMINDEX__GE__1,axiom,
! [A_27a: d] : ( mono_2Ec_2Earithmetic_2E_3C_3D @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efcp_2Edimindex_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ A_27a ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(thm_2Efcp_2Efcp__ind,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ! [V1f_2E0: u] : ( 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] : ( 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 ) ) ) ) ) ).
thf(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: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ ( 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 ) ) ) )
= ( 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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__BETA,axiom,
! [A_27a: d,A_27b: d,V0g_2E0: u,V1i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V1i @ ( 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 ) ) ) )
= ( 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 ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__UNIQUE,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2i: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V2i @ ( 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 ) ) ) )
= ( 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 ) ) ) ) ) )
<=> ( ( 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 ) ) ) ).
thf(thm_2Efcp_2EFCP__ETA,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0g_2E0: u,V1i: 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 ) ) ) )
= ( 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 ) ) ) ) )
=> ! [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 ) ) ) ).
thf(thm_2Efcp_2Ecard__dimindex,axiom,
! [A_27a: d] :
( ( 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 ) ) ) ) ) ) ).
thf(thm_2Efcp_2Eindex__sum,axiom,
! [A_27a: d,A_27b: d,F0: $o] :
( ( F0
<=> ( ( 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_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_2Emono_2Etyop_2Enum_2Enum @ F0 @ ( mono_2Ec_2Earithmetic_2E_2B @ ( 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 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Efcp_2Efinite__sum,axiom,
! [A_27a: d,A_27b: d] :
( ( 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 ) ) ) )
<=> ( ( 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_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 ) ) ) ) ) ) ).
thf(thm_2Efcp_2Edatatype__bit0,axiom,
! [A_27a: d,V0bit0_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(thm_2Efcp_2Ebit0__induction,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1a_2E0: u] : ( 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] : ( 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] : ( 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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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_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 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(thm_2Efcp_2Edatatype__bit1,axiom,
! [A_27a: d,V0bit1_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_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 ) ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ) ).
thf(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 ) ) ) ).
thf(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 ) ) ) ).
thf(thm_2Efcp_2Ebit1__induction,axiom,
! [A_27a: d,V0P_2E0: u] :
( ( ! [V1a_2E0: u] : ( 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] : ( 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 ) ) ) ) ) )
& ( 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] : ( 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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(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_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 @ ( mono_2Ec_2Earithmetic_2E_2A @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(thm_2Efcp_2Eindex__one,axiom,
( ( mono_2Ec_2Efcp_2Edimindex_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Ebool_2Ethe__value_2Emono_2Etyop_2Eone_2Eone )
= ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Efcp_2Efinite__one,axiom,
mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Eone_2Eone ).
thf(thm_2Efcp_2EFCP__UPDATE__COMMUTES,axiom,
! [A_27a: d,A_27b: d,V0m_2E0: u,V1a: mono_2Etyop_2Enum_2Enum,V2b: mono_2Etyop_2Enum_2Enum,V3c_2E0: u,V4d_2E0: u] :
( ( (~) @ ( V1a = V2b ) )
=> ( ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ ( c_2Efcp_2E_3A_2B_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1a ) ) @ ( 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 ) ) @ ( 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 ) ) @ ( 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 ) ) @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ V0m_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__UPDATE__EQ,axiom,
! [A_27a: d,A_27b: d,V0m_2E0: u,V1a: 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 ) ) @ ( 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 ) ) @ ( 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 ) ) @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ V0m_2E0 ) ) ) ) ).
thf(thm_2Efcp_2EFCP__UPDATE__IMP__ID,axiom,
! [A_27a: d,A_27b: d,V0m_2E0: u,V1a: 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 ) ) ) )
= ( 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 ) ) @ ( 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 ) ) ) ).
thf(thm_2Efcp_2EAPPLY__FCP__UPDATE__ID,axiom,
! [A_27a: d,A_27b: d,V0m_2E0: u,V1a: 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 ) ) @ ( 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 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ V0m_2E0 ) ) )
= ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ V0m_2E0 ) ) ).
thf(thm_2Efcp_2EFCP__APPLY__UPDATE__THM,axiom,
! [A_27a: d,A_27b: d,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V2a: mono_2Etyop_2Enum_2Enum,V4b: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V2a @ V4b )
<=> ( V2a = V4b ) )
=> ! [V0index_20out_20of_20range: $o,V1m_2E0: u,V2a: mono_2Etyop_2Enum_2Enum,V3w_2E0: u,V4b: 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 ) ) @ ( 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 ) ) ) )
= ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V4b @ ( 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 @ ( F0 @ V2a @ V4b ) ) ) @ ( 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 ) ) ) ) ) ) @ ( 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 ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ A_27a @ A_27b ) @ ( c_2Efcp_2E_3A_2B_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V2a ) ) @ ( 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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ).
thf(thm_2Efcp_2EEL__V2L,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1v_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0i @ ( 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 ) ) @ ( 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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EFCP__TL,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0v_2E0: u] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( 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 @ ( 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 @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
=> ( ( 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 ) ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ).
thf(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 ) ) ) ) ) ) ) ) ).
thf(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 ) ) ) ).
thf(thm_2Efcp_2ENULL__V2L,axiom,
! [A_27a: d,A_27b: d,V0v_2E0: u] : ( (~) @ ( 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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EREAD__TL,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0i: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0i @ ( 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 ) ) ) )
= ( 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 @ V0i ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2EREAD__L2V,axiom,
! [A_27a: d,A_27b: d,V0i: mono_2Etyop_2Enum_2Enum,V1a_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0i @ ( 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 ) ) ) )
= ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0i ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1a_2E0 ) ) ) ) ) ).
thf(thm_2Efcp_2Eindex__comp,axiom,
! [A_27a: d,A_27b: d,V0FCP_20out_20of_20bounds: $o,V1f_2E0: u,V2n: 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 ) ) ) )
= ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Eprim__rec_2E_3C @ V2n @ ( 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 ) ) ) ) @ ( 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 ) ) ) ) @ ( 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 ) ) ) ) ) ) ) ).
thf(thm_2Efcp_2Efcp__subst__comp,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,F0_2E0: u] :
( ! [V1x: mono_2Etyop_2Enum_2Enum,V5c: mono_2Etyop_2Enum_2Enum] :
( ( F1 @ V1x @ V5c )
<=> ( V1x = V5c ) )
=> ( ! [V1x: mono_2Etyop_2Enum_2Enum,V0y_2E0: u,V4f_2E0: u,V5c: 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 ) ) ) ) @ ( 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 ) ) ) )
= ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( F1 @ V1x @ V5c ) ) ) @ ( 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 ) ) ) ) ) ) )
=> ! [V0y_2E0: u,V1x: 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 ) ) @ ( 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 ) ) ) ) @ ( s @ A_27a @ V0y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V4f_2E0 ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------