%------------------------------------------------------------------------------
% File     : ITP065^4 : 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    : finite_map.ax [Gau19]
%          : HL4065^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  861 ( 390 unt; 284 typ;   0 def)
%            Number of atoms       : 1153 ( 667 equ;  32 cnn)
%            Maximal formula atoms :   11 (   1 avg)
%            Number of connectives : 33852 (  32   ~;  11   |; 121   &;33388   @)
%                                         (  83 <=>; 217  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   38 (   9 avg;33388 nst)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  503 ( 503   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  281 ( 279 usr; 117 con; 0-4 aty)
%            Number of variables   : 2652 (   0   ^2624   !;  28   ?;2652   :)
% 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_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

thf(mono_2Etyop_2Eone_2Eone,type,
    mono_2Etyop_2Eone_2Eone: $tType ).

thf(tyop_2Efinite__map_2Efmap,type,
    tyop_2Efinite__map_2Efmap: d > 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_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > 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_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_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_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_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_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: u ).

thf(c_2Elist_2EALL__DISTINCT_2E1,type,
    c_2Elist_2EALL__DISTINCT_2E1: du > u ).

thf(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

thf(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: du > du > u ).

thf(c_2Ebool_2EARB_2E0,type,
    c_2Ebool_2EARB_2E0: u ).

thf(c_2Ecombin_2EASSOC_2E0,type,
    c_2Ecombin_2EASSOC_2E0: u ).

thf(c_2Ecombin_2EASSOC_2E1,type,
    c_2Ecombin_2EASSOC_2E1: du > u ).

thf(c_2Epred__set_2EBIJ_2E0,type,
    c_2Epred__set_2EBIJ_2E0: u ).

thf(c_2Epred__set_2EBIJ_2E3,type,
    c_2Epred__set_2EBIJ_2E3: du > du > 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_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_2E0: u ).

thf(c_2Ecombin_2EC_2E1,type,
    c_2Ecombin_2EC_2E1: du > 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_2Ecombin_2ECOMM_2E0,type,
    c_2Ecombin_2ECOMM_2E0: u ).

thf(c_2Ecombin_2ECOMM_2E1,type,
    c_2Ecombin_2ECOMM_2E1: du > u ).

thf(c_2Epred__set_2ECOMPL_2E0,type,
    c_2Epred__set_2ECOMPL_2E0: u ).

thf(c_2Epred__set_2ECOMPL_2E1,type,
    c_2Epred__set_2ECOMPL_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_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: u ).

thf(c_2Epred__set_2EDELETE_2E2,type,
    c_2Epred__set_2EDELETE_2E2: du > du > u ).

thf(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: u ).

thf(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: du > du > u ).

thf(c_2Epred__set_2EDISJOINT_2E0,type,
    c_2Epred__set_2EDISJOINT_2E0: u ).

thf(c_2Epred__set_2EDISJOINT_2E2,type,
    c_2Epred__set_2EDISJOINT_2E2: du > du > u ).

thf(c_2Efinite__map_2EDRESTRICT_2E0,type,
    c_2Efinite__map_2EDRESTRICT_2E0: u ).

thf(c_2Efinite__map_2EDRESTRICT_2E2,type,
    c_2Efinite__map_2EDRESTRICT_2E2: du > 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_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: 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_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Efinite__map_2EFAPPLY_2E0,type,
    c_2Efinite__map_2EFAPPLY_2E0: u ).

thf(c_2Efinite__map_2EFAPPLY_2E1,type,
    c_2Efinite__map_2EFAPPLY_2E1: du > u ).

thf(c_2Efinite__map_2EFAPPLY_2E2,type,
    c_2Efinite__map_2EFAPPLY_2E2: du > du > u ).

thf(c_2Efinite__map_2EFCARD_2E0,type,
    c_2Efinite__map_2EFCARD_2E0: u ).

thf(c_2Efinite__map_2EFCARD_2E1,type,
    c_2Efinite__map_2EFCARD_2E1: du > u ).

thf(c_2Efinite__map_2EFDOM_2E0,type,
    c_2Efinite__map_2EFDOM_2E0: u ).

thf(c_2Efinite__map_2EFDOM_2E1,type,
    c_2Efinite__map_2EFDOM_2E1: du > u ).

thf(c_2Efinite__map_2EFDOM_2E2,type,
    c_2Efinite__map_2EFDOM_2E2: du > du > u ).

thf(c_2Efinite__map_2EFEMPTY_2E0,type,
    c_2Efinite__map_2EFEMPTY_2E0: u ).

thf(c_2Efinite__map_2EFEVERY_2E0,type,
    c_2Efinite__map_2EFEVERY_2E0: u ).

thf(c_2Efinite__map_2EFEVERY_2E2,type,
    c_2Efinite__map_2EFEVERY_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_2Efinite__map_2EFLOOKUP_2E0,type,
    c_2Efinite__map_2EFLOOKUP_2E0: u ).

thf(c_2Efinite__map_2EFLOOKUP_2E1,type,
    c_2Efinite__map_2EFLOOKUP_2E1: du > u ).

thf(c_2Efinite__map_2EFLOOKUP_2E2,type,
    c_2Efinite__map_2EFLOOKUP_2E2: du > du > u ).

thf(c_2Efinite__map_2EFMAP__MAP2_2E0,type,
    c_2Efinite__map_2EFMAP__MAP2_2E0: u ).

thf(c_2Efinite__map_2EFMAP__MAP2_2E2,type,
    c_2Efinite__map_2EFMAP__MAP2_2E2: du > du > u ).

thf(c_2Efinite__map_2EFMERGE_2E0,type,
    c_2Efinite__map_2EFMERGE_2E0: u ).

thf(c_2Efinite__map_2EFMERGE_2E1,type,
    c_2Efinite__map_2EFMERGE_2E1: du > u ).

thf(c_2Efinite__map_2EFMERGE_2E3,type,
    c_2Efinite__map_2EFMERGE_2E3: du > du > du > u ).

thf(c_2Elist_2EFOLDL_2E0,type,
    c_2Elist_2EFOLDL_2E0: u ).

thf(c_2Elist_2EFOLDL_2E1,type,
    c_2Elist_2EFOLDL_2E1: du > u ).

thf(c_2Elist_2EFOLDL_2E3,type,
    c_2Elist_2EFOLDL_2E3: du > du > du > u ).

thf(c_2Elist_2EFOLDL2_2E0,type,
    c_2Elist_2EFOLDL2_2E0: u ).

thf(c_2Elist_2EFOLDL2_2E4,type,
    c_2Elist_2EFOLDL2_2E4: du > du > du > du > u ).

thf(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: u ).

thf(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: du > du > du > u ).

thf(c_2Efinite__map_2EFRANGE_2E0,type,
    c_2Efinite__map_2EFRANGE_2E0: u ).

thf(c_2Efinite__map_2EFRANGE_2E1,type,
    c_2Efinite__map_2EFRANGE_2E1: du > u ).

thf(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

thf(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: du > u ).

thf(c_2Efinite__map_2EFUNION_2E0,type,
    c_2Efinite__map_2EFUNION_2E0: u ).

thf(c_2Efinite__map_2EFUNION_2E2,type,
    c_2Efinite__map_2EFUNION_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUN__FMAP_2E0,type,
    c_2Efinite__map_2EFUN__FMAP_2E0: u ).

thf(c_2Efinite__map_2EFUN__FMAP_2E2,type,
    c_2Efinite__map_2EFUN__FMAP_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUPDATE_2E0,type,
    c_2Efinite__map_2EFUPDATE_2E0: u ).

thf(c_2Efinite__map_2EFUPDATE_2E2,type,
    c_2Efinite__map_2EFUPDATE_2E2: du > du > u ).

thf(c_2Efinite__map_2EFUPDATE__LIST_2E0,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E0: u ).

thf(c_2Efinite__map_2EFUPDATE__LIST_2E2,type,
    c_2Efinite__map_2EFUPDATE__LIST_2E2: du > du > u ).

thf(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

thf(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

thf(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: u ).

thf(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: du > du > u ).

thf(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

thf(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: du > du > u ).

thf(c_2Epred__set_2EINJ_2E0,type,
    c_2Epred__set_2EINJ_2E0: u ).

thf(c_2Epred__set_2EINJ_2E3,type,
    c_2Epred__set_2EINJ_2E3: du > du > du > u ).

thf(c_2Esum_2EINL_2E0,type,
    c_2Esum_2EINL_2E0: u ).

thf(c_2Esum_2EINL_2E1,type,
    c_2Esum_2EINL_2E1: du > u ).

thf(c_2Esum_2EINR_2E0,type,
    c_2Esum_2EINR_2E0: u ).

thf(c_2Esum_2EINR_2E1,type,
    c_2Esum_2EINR_2E1: du > u ).

thf(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: u ).

thf(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: du > du > u ).

thf(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: u ).

thf(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: du > du > u ).

thf(c_2Esum_2EISL_2E0,type,
    c_2Esum_2EISL_2E0: u ).

thf(c_2Esum_2EISL_2E1,type,
    c_2Esum_2EISL_2E1: du > u ).

thf(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

thf(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_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_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

thf(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: du > du > u ).

thf(c_2Epred__set_2ELINV_2E0,type,
    c_2Epred__set_2ELINV_2E0: u ).

thf(c_2Epred__set_2ELINV_2E2,type,
    c_2Epred__set_2ELINV_2E2: du > du > u ).

thf(c_2Elist_2ELIST__REL_2E0,type,
    c_2Elist_2ELIST__REL_2E0: u ).

thf(c_2Elist_2ELIST__REL_2E3,type,
    c_2Elist_2ELIST__REL_2E3: du > du > du > u ).

thf(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

thf(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_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_2EMAP2_2E0,type,
    c_2Elist_2EMAP2_2E0: u ).

thf(c_2Elist_2EMAP2_2E3,type,
    c_2Elist_2EMAP2_2E3: du > du > du > u ).

thf(c_2Efinite__map_2EMAP__KEYS_2E0,type,
    c_2Efinite__map_2EMAP__KEYS_2E0: u ).

thf(c_2Efinite__map_2EMAP__KEYS_2E2,type,
    c_2Efinite__map_2EMAP__KEYS_2E2: du > du > u ).

thf(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

thf(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: 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_2Eoption_2EOPTION__BIND_2E0,type,
    c_2Eoption_2EOPTION__BIND_2E0: u ).

thf(c_2Eoption_2EOPTION__BIND_2E2,type,
    c_2Eoption_2EOPTION__BIND_2E2: du > du > u ).

thf(c_2Eoption_2EOPTREL_2E0,type,
    c_2Eoption_2EOPTREL_2E0: u ).

thf(c_2Eoption_2EOPTREL_2E3,type,
    c_2Eoption_2EOPTREL_2E3: du > du > du > u ).

thf(c_2Esum_2EOUTL_2E0,type,
    c_2Esum_2EOUTL_2E0: u ).

thf(c_2Esum_2EOUTL_2E1,type,
    c_2Esum_2EOUTL_2E1: du > u ).

thf(c_2Esorting_2EPERM_2E0,type,
    c_2Esorting_2EPERM_2E0: u ).

thf(c_2Esorting_2EPERM_2E2,type,
    c_2Esorting_2EPERM_2E2: du > du > u ).

thf(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: u ).

thf(c_2Elist_2EREVERSE_2E1,type,
    c_2Elist_2EREVERSE_2E1: du > u ).

thf(c_2Efinite__map_2ERRESTRICT_2E0,type,
    c_2Efinite__map_2ERRESTRICT_2E0: u ).

thf(c_2Efinite__map_2ERRESTRICT_2E2,type,
    c_2Efinite__map_2ERRESTRICT_2E2: du > du > u ).

thf(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

thf(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: du > u ).

thf(c_2Elist_2ESNOC_2E0,type,
    c_2Elist_2ESNOC_2E0: u ).

thf(c_2Elist_2ESNOC_2E2,type,
    c_2Elist_2ESNOC_2E2: du > du > u ).

thf(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

thf(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: du > u ).

thf(c_2Efinite__map_2ESUBMAP_2E0,type,
    c_2Efinite__map_2ESUBMAP_2E0: u ).

thf(c_2Efinite__map_2ESUBMAP_2E2,type,
    c_2Efinite__map_2ESUBMAP_2E2: du > du > u ).

thf(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

thf(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: du > 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_2Epred__set_2ESUM__IMAGE_2E0,type,
    c_2Epred__set_2ESUM__IMAGE_2E0: u ).

thf(c_2Epred__set_2ESUM__IMAGE_2E2,type,
    c_2Epred__set_2ESUM__IMAGE_2E2: du > du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: 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_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

thf(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: du > u ).

thf(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: u ).

thf(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: du > du > u ).

thf(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: u ).

thf(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

thf(c_2Elist_2EZIP_2E0,type,
    c_2Elist_2EZIP_2E0: u ).

thf(c_2Elist_2EZIP_2E1,type,
    c_2Elist_2EZIP_2E1: du > 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_2Efinite__map_2Ef__o_2E0,type,
    c_2Efinite__map_2Ef__o_2E0: u ).

thf(c_2Efinite__map_2Ef__o_2E2,type,
    c_2Efinite__map_2Ef__o_2E2: du > du > u ).

thf(c_2Efinite__map_2Ef__o__f_2E0,type,
    c_2Efinite__map_2Ef__o__f_2E0: u ).

thf(c_2Efinite__map_2Ef__o__f_2E2,type,
    c_2Efinite__map_2Ef__o__f_2E2: du > du > u ).

thf(c_2Efinite__map_2Efdomsub_2E0,type,
    c_2Efinite__map_2Efdomsub_2E0: u ).

thf(c_2Efinite__map_2Efdomsub_2E2,type,
    c_2Efinite__map_2Efdomsub_2E2: du > du > u ).

thf(c_2Efinite__map_2Efmap__ABS_2E0,type,
    c_2Efinite__map_2Efmap__ABS_2E0: u ).

thf(c_2Efinite__map_2Efmap__ABS_2E1,type,
    c_2Efinite__map_2Efmap__ABS_2E1: du > u ).

thf(c_2Efinite__map_2Efmap__EQ__UPTO_2E0,type,
    c_2Efinite__map_2Efmap__EQ__UPTO_2E0: u ).

thf(c_2Efinite__map_2Efmap__EQ__UPTO_2E3,type,
    c_2Efinite__map_2Efmap__EQ__UPTO_2E3: du > du > du > u ).

thf(c_2Efinite__map_2Efmap__REP_2E0,type,
    c_2Efinite__map_2Efmap__REP_2E0: u ).

thf(c_2Efinite__map_2Efmap__REP_2E1,type,
    c_2Efinite__map_2Efmap__REP_2E1: du > u ).

thf(c_2Efinite__map_2Efmap__REP_2E2,type,
    c_2Efinite__map_2Efmap__REP_2E2: du > du > u ).

thf(c_2Efinite__map_2Efmap__inverse_2E0,type,
    c_2Efinite__map_2Efmap__inverse_2E0: u ).

thf(c_2Efinite__map_2Efmap__inverse_2E2,type,
    c_2Efinite__map_2Efmap__inverse_2E2: du > du > u ).

thf(c_2Efinite__map_2Efmap__rel_2E0,type,
    c_2Efinite__map_2Efmap__rel_2E0: u ).

thf(c_2Efinite__map_2Efmap__rel_2E3,type,
    c_2Efinite__map_2Efmap__rel_2E3: du > du > du > u ).

thf(c_2Efinite__map_2Efmap__size_2E0,type,
    c_2Efinite__map_2Efmap__size_2E0: u ).

thf(c_2Efinite__map_2Efmap__size_2E3,type,
    c_2Efinite__map_2Efmap__size_2E3: du > du > du > u ).

thf(c_2Efinite__map_2Eis__fmap_2E0,type,
    c_2Efinite__map_2Eis__fmap_2E0: u ).

thf(c_2Efinite__map_2Eis__fmap_2E1,type,
    c_2Efinite__map_2Eis__fmap_2E1: du > u ).

thf(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

thf(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: du > du > u ).

thf(c_2Efinite__map_2Eo__f_2E0,type,
    c_2Efinite__map_2Eo__f_2E0: u ).

thf(c_2Efinite__map_2Eo__f_2E2,type,
    c_2Efinite__map_2Eo__f_2E2: du > du > u ).

thf(c_2Eone_2Eone_2E0,type,
    c_2Eone_2Eone_2E0: u ).

thf(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

thf(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).

thf(c_2Eoption_2Esome_2E0,type,
    c_2Eoption_2Esome_2E0: u ).

thf(c_2Eoption_2Esome_2E1,type,
    c_2Eoption_2Esome_2E1: du > 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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( ( 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 > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > 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_2B,type,
    mono_2Ec_2Earithmetic_2E_2B: 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_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( 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_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_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2Epred__set_2ELINV_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2ELINV_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
    mono_2Ec_2Earithmetic_2ENUMERAL: 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_2Enum_2Enum,type,
    mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > $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_2Eone_2Eone,type,
    mono_2Ec_2Eone_2Eone: mono_2Etyop_2Eone_2Eone ).

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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > 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_2Enum_2Enum,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(i_mono_2Etyop_2Eone_2Eone,type,
    i_mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Eone_2Eone > 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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > 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_2Enum_2Enum,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

thf(j_mono_2Etyop_2Eone_2Eone,type,
    j_mono_2Etyop_2Eone_2Eone: du > mono_2Etyop_2Eone_2Eone ).

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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( 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_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( 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_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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).

thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_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_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(ij_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0_2E0: u] :
      ( ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ V0_2E0 ) ) ) )
      = ( s @ tyop_2Eone_2Eone @ 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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( 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_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_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_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(ji_2Emono_2Etyop_2Eone_2Eone,axiom,
    ! [V0: mono_2Etyop_2Eone_2Eone] :
      ( ( j_mono_2Etyop_2Eone_2Eone @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ 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_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_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(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ A_27d @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ A_27d @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27c: d,X0_2E0: u,X1: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X1 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27d @ X0_2E0 ) @ ( s @ A_27e @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27d @ X0_2E0 ) ) ) @ ( s @ A_27e @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2Etyop_2Elist_2Elist_28A_27e_29,axiom,
    ! [A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27e ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27e ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27e ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27e ) @ X1_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_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_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_2EALL__DISTINCT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Elist_2EALL__DISTINCT_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EAPPEND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EASSOC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecombin_2EASSOC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_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_2Ecombin_2EASSOC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecombin_2EASSOC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X2_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EBIJ_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( c_2Ecombin_2EC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ c_2Ecombin_2EC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ 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(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2ECOMM_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecombin_2ECOMM_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_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_2Ecombin_2ECOMM_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ tyop_2Emin_2Ebool ) @ c_2Ecombin_2ECOMM_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ECOMPL_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(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ A_27b @ X1_2E0 ) @ ( s @ A_27b @ X2_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) @ ( s @ A_27b @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29,axiom,
    ! [A_27b: d,A_27c: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ECONS_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( 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 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDELETE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ 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 @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDIFF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EDIFF_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EDISJOINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EDISJOINT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EDRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2EDRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EDRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2EDRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_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_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ A_27b ) ) @ c_2Elist_2EEL_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_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_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2EEVERY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFAPPLY_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFAPPLY_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) @ c_2Efinite__map_2EFAPPLY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFCARD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Enum_2Enum ) @ c_2Efinite__map_2EFCARD_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFDOM_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_2Efinite__map_2EFDOM_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ 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 @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFDOM_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFDOM_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFEVERY_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_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFEVERY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFEVERY_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFEVERY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ 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_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFLOOKUP_2E1_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFLOOKUP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27b ) ) ) @ c_2Efinite__map_2EFLOOKUP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFMAP__MAP2_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_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFMAP__MAP2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2EFMERGE_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) ) @ c_2Efinite__map_2EFMERGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFMERGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Efinite__map_2EFMERGE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Efinite__map_2EFMERGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2EFMERGE_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Efinite__map_2EFMERGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2EFMERGE_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) ) @ c_2Efinite__map_2EFMERGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EFOLDL_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Elist_2EFOLDL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFOLDL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFOLDL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) ) @ c_2Elist_2EFOLDL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27c_2CA_27d_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Elist_2EFOLDL2_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) ) @ c_2Elist_2EFOLDL2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X3_2E0 ) ) ) ) ).

thf(arityeq4_2Ec_2Elist_2EFOLDL2_2E4_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27d_2CA_27e_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( c_2Elist_2EFOLDL2_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X3_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) @ c_2Elist_2EFOLDL2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X3_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2EFOLDR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2EFRANGE_2E1_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2EFRANGE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUNION_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUN__FMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EFUN__FMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2EFUN__FMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUN__FMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2EFUN__FMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EFUPDATE__LIST_2E2_2Emono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27c_20mono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2EGSPEC_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EIMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27c @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Efinite__map_2Efmap_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_2EIN_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_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_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_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_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2EIN_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X2_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINJ_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27b: d,X0: mono_2Etyop_2Eone_2Eone] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ X0 ) ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Eone_2Eone @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ X0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27b @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINSERT_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ 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 @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EINTER_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EISL_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ 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(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_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_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ tyop_2Enum_2Enum ) @ c_2Elist_2ELENGTH_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27c_29_2Ctyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ELET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ELINV_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( c_2Epred__set_2ELINV_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) ) @ c_2Epred__set_2ELINV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ELIST__REL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Elist_2ELIST__REL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Elist_2ELIST__TO__SET_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_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 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_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 @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27a ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ ( tyop_2Elist_2Elist @ A_27c ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27b ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ ( tyop_2Elist_2Elist @ A_27c ) ) ) @ c_2Elist_2EMAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27c ) ) ) ) @ c_2Elist_2EMAP2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27b ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) ) @ c_2Elist_2EMAP2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27d_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27d ) ) ) ) @ c_2Elist_2EMAP2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Elist_2EMAP2_2E3_2Emono_2EA_27e_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27e: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ A_27e ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( tyop_2Elist_2Elist @ A_27e ) ) ) ) @ c_2Elist_2EMAP2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_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_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2EMAP__KEYS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X0 ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) ) ) @ c_2Efinite__map_2EMAP__KEYS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ X0 ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( tyop_2Eoption_2Eoption @ A_27c ) ) ) @ c_2Eoption_2EOPTION__BIND_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EOUTL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ A_27b @ ( c_2Esum_2EOUTL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X0_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ A_27b ) @ c_2Esum_2EOUTL_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Epair_2Eprod_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_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Esorting_2EPERM_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Elist_2EREVERSE_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2ERRESTRICT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2ERRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2ERRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2ERRESTRICT_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Elist_2ESNOC_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ESNOC_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) ) @ c_2Elist_2ESNOC_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2ESUBMAP_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_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2ESUBMAP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2ESUBMAP_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2ESUBMAP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ESUM__IMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) ) @ c_2Epred__set_2ESUM__IMAGE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29_29_20mono_2Etyop_2Efinite__map_2Efmap_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 @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_2Ctyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27e,axiom,
    ! [A_27b: d,A_27c: d,A_27e: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Efinite__map_2Efmap_28A_27d_2CA_27e_29,axiom,
    ! [A_27b: d,A_27c: d,A_27d: d,A_27e: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ c_2Epair_2EUNCURRY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ 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 @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EUNION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) ) @ c_2Elist_2EZIP_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Elist_2EZIP_2E1_2Emono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27d: d,A_27e: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) ) @ c_2Elist_2EZIP_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2Ef__o_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ c_2Efinite__map_2Ef__o_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o_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_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2Ef__o_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) ) ) @ c_2Efinite__map_2Ef__o_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ c_2Efinite__map_2Ef__o_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o__f_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2Ef__o__f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o__f_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2Ef__o__f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Ef__o__f_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_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2Ef__o__f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efdomsub_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ A_27c @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2Efdomsub_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27c @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2Efmap__ABS_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efmap__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ c_2Efinite__map_2Efmap__ABS_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2Efmap__EQ__UPTO_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Efinite__map_2Efmap__EQ__UPTO_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2Efmap__REP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( c_2Efinite__map_2Efmap__REP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ c_2Efinite__map_2Efmap__REP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efmap__REP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Efinite__map_2Efmap__REP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ c_2Efinite__map_2Efmap__REP_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Efmap__inverse_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_2Efinite__map_2Efmap__inverse_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ c_2Efinite__map_2Efmap__inverse_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2Efmap__rel_2E3_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Efinite__map_2Efmap__rel_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2Efmap__rel_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] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Efinite__map_2Efmap__rel_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Efinite__map_2Efmap__size_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2Efmap__size_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ X1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Enum_2Enum ) ) ) @ c_2Efinite__map_2Efmap__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Efinite__map_2Eis__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ c_2Efinite__map_2Eis__fmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_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_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) ) ) @ c_2Efinite__map_2Eo__f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27c_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Esome_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ c_2Eoption_2Esome_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ 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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( 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 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( 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_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( 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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_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_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( 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_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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 > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_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_2Epred__set_2EBIJ_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epred__set_2EBIJ_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o,V2: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 @ V2 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( 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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V2 ) ) ) ) ) ).

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_2Epred__set_2ELINV_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Epred__set_2ELINV_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Epred__set_2ELINV_2E0 ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2ELINV_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Epred__set_2ELINV_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Epred__set_2ELINV_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_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( 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_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_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 > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( 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_2Efinite__map_2Efmap__inverse__def,axiom,
    ! [A_27a: d,A_27b: d,V0m1_2E0: u,V1m2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__inverse_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1m2_2E0 ) ) ) )
    <=> ! [V2k_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m1_2E0 ) ) ) ) ) )
         => ? [V3v_2E0: u] :
              ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m1_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v_2E0 ) ) ) )
              & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1m2_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) )
                = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V2k_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMAP__MAP2__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1m_2E0: u,V2x_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1m_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1m_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) )
     => ! [V0f_2E0: u,V1m_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1m_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1m_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1m_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE__LIST_2E0 )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Elist_2EFOLDL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUPDATE_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
    <=> ! [V2x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) )
            & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
              = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFCARD__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_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_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFDOM_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Efinite__map_2Efmap__REP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFAPPLY__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
      = ( s @ A_27b @ ( c_2Esum_2EOUTL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Efinite__map_2Efmap__REP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFEMPTY__DEF,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) )
          = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efmap__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__DEF,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3a_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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V3a_2E0 )
            = ( s @ A_27a @ V1x_2E0 ) ) )
     => ( ! [V1x_2E0: u,V2y_2E0: u,V0f_2E0: u,V3a_2E0: u] :
            ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) )
            = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Efinite__map_2Efmap__REP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) ) ) )
       => ! [V0f_2E0: u,V1x_2E0: u,V2y_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efmap__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27b @ V2y_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__ISO__DEF,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efmap__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( c_2Efinite__map_2Efmap__REP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0a_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0a_2E0 ) )
      & ! [V1r_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1r_2E0 ) ) ) )
        <=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( c_2Efinite__map_2Efmap__REP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efmap__ABS_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1r_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1r_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__TY__DEF,axiom,
    ! [A_27a: d,A_27b: d] :
    ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ c_2Efinite__map_2Eis__fmap_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ V0rep_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Eis__fmap__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V7x_2E0: u,V5a_2E0: u] :
          ( ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27a @ V5a_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V7x_2E0 )
            = ( s @ A_27a @ V5a_2E0 ) ) )
     => ! [V0x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V0x_2E0 ) ) ) )
        <=> ! [V1is__fmap_27_2E0: u] :
              ( ! [V2a0_2E0: u] :
                  ( ( ! [V3x_2E0: u] :
                        ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2a0_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) )
                        = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) ) ) ) )
                    | ? [V4f_2E0: u,V5a_2E0: u,V6b_2E0: u] :
                        ( ! [V7x_2E0: u] :
                            ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2a0_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) )
                            = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) @ ( s @ A_27a @ V5a_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V6b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V4f_2E0 ) @ ( s @ A_27a @ V7x_2E0 ) ) ) ) ) )
                        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V1is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V4f_2E0 ) ) ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V1is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2a0_2E0 ) ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V1is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V0x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1r_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) )
      & ! [V2x_2E0: u] :
          ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) )
      & ! [V2x_2E0: u] :
          ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__domsub,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Ef__o__DEF,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1g_2E0: u,V0f_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( 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_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
     => ! [V0f_2E0: u,V1g_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUN__FMAP__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1P_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 ) @ V1P_2E0 ) ) ) )
     => ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) )
        & ! [V2x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ERRESTRICT__DEF,axiom,
    ! [A_27a: d,A_27b: d,F2_2E0: u,F0_2E0: u,F1_2E0: u] :
      ( ! [V2x_2E0: u,V0f_2E0: u,V1r_2E0: u] :
          ( ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) )
        <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) )
     => ( ! [V0f_2E0: u,V1r_2E0: u,V2x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F2_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) )
       => ( ! [V3x_2E0: u,V0f_2E0: u,V1r_2E0: u] :
              ( ( 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 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) )
            <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) )
         => ! [V0f_2E0: u,V1r_2E0: u] :
              ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) )
              & ! [V3x_2E0: u] :
                  ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
                  = ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__DEF,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) )
        <=> ? [V2x_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
              & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
                = ( s @ A_27b @ V1y_2E0 ) ) ) )
     => ( ! [V0f_2E0: u,V1y_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V1y_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) ) ) ) )
       => ! [V0f_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__DEF,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
      & ! [V2x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ) )
         => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
            = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Ef__o__f__DEF,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1g_2E0: u,V0f_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
     => ! [V0f_2E0: u,V1g_2E0: u] :
          ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
          & ! [V3x_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ) )
             => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
                = ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) )
    <=> ! [V2x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__DEF,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__DEF,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V3x_2E0: u,V1f_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) )
        <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) ) ) ) ) )
     => ! [V0m_2E0: u,V1f_2E0: u,V2g_2E0: u] :
          ( ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) ) ) ) ) )
          & ! [V3x_2E0: u] :
              ( ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) ) ) @ ( s @ A_27b @ V3x_2E0 ) ) )
              = ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V3x_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 ) ) @ V0m_2E0 ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) ) ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) @ ( s @ A_27b @ V3x_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EMAP__KEYS__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1fm_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
       => ! [V2x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) ) ) )
           => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
              = ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R_2E0: u,V1f1_2E0: u,V2f2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V2f2_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V2f2_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) ) ) )
        & ! [V3x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27c @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ A_27c @ V3x_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V2f2_2E0 ) @ ( s @ A_27c @ V3x_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__UPTO__def,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2vs_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2vs_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2vs_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2vs_2E0 ) ) ) ) ) )
        & ! [V3x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2vs_2E0 ) ) ) ) ) ) ) )
           => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) )
              = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__size__def,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0kz_2E0: u,V1vz_2E0: u,V2fm_2E0: u,V3k_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0kz_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ V1vz_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) @ ( s @ A_27a @ V3k_2E0 ) ) ) )
          = ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0kz_2E0 ) @ ( s @ A_27a @ V3k_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ V1vz_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ A_27a @ V3k_2E0 ) ) ) ) ) ) ) )
     => ! [V0kz_2E0: u,V1vz_2E0: u,V2fm_2E0: u] :
          ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2Efmap__size_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0kz_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ V1vz_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) )
          = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Epred__set_2ESUM__IMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0kz_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Enum_2Enum ) @ V1vz_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efevery__funion,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1m1_2E0: u,V2m2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1m1_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2m2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1m1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2m2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Edrestrict__iter__list,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2k_2E0: u,V3m_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3m_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3m_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) )
     => ! [V0m_2E0: u,V1l_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V1l_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Edisjoint__drestrict,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1m_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1m_2E0 ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1m_2E0 ) ) ) ).

thf(thm_2Efinite__map_2Efmap__to__list,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u] :
    ? [V1l_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) )
      & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efupdate__list__foldl,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V2env_2E0: u,V3k_2E0: u,V4v_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2env_2E0 ) ) ) @ ( s @ A_27a @ V3k_2E0 ) ) ) @ ( s @ A_27b @ V4v_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2env_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) )
     => ( ! [V2env_2E0: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2env_2E0 ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2env_2E0 ) ) ) ) ) )
       => ! [V0m_2E0: u,V1l_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efupdate__list__foldr,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2k_2E0: u,V3v_2E0: u,V4env_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ A_27b @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V4env_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V4env_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) )
     => ! [V0m_2E0: u,V1l_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) ) @ F0_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__EQ__FUPDATE__LIST,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1kv_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eflookup__thm,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2v_2E0: u] :
      ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
      <=> ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) ) )
      & ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V2v_2E0 ) ) ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
          & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
            = ( s @ A_27b @ V2v_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efdom__fupdate__list2,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1fm_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efupdate__list__map,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V4a_2E0: u,V5b_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) ) ) @ ( s @ A_27a @ V4a_2E0 ) ) ) @ ( s @ A_27b @ V5b_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27b @ V5b_2E0 ) ) ) ) ) )
     => ! [V0l_2E0: u,V1f_2E0: u,V2x_2E0: u,V3y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) ) ) ) )
         => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
            = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__sym,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u] :
      ( ! [V1x_2E0: u,V2y_2E0: u] :
          ( ( 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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V2y_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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
     => ! [V3x_2E0: u,V4y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V3x_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V4y_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V4y_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V3x_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__trans,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u] :
      ( ! [V1x_2E0: u,V2y_2E0: u,V3z_2E0: u] :
          ( ( ( 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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V2y_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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) @ ( s @ A_27a @ V3z_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 ) ) @ V0R_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ A_27a @ V3z_2E0 ) ) ) ) )
     => ! [V4x_2E0: u,V5y_2E0: u,V6z_2E0: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V4x_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V5y_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V5y_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V6z_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V4x_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V6z_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Ef__o__f__FUPDATE__compose,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f1_2E0: u,V1f2_2E0: u,V2k_2E0: u,V3x_2E0: u,V4v_2E0: u] :
      ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f2_2E0 ) ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2s_2E0: u,V3t_2E0: u] :
      ( ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FDOM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ).

thf(thm_2Efinite__map_2EFRANGE__DRESTRICT__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1fm_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__DOMSUB__suff,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1fm_2E0: u,V2P_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
     => ! [V4v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ A_27b @ V0k_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V4v_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__DOMSUB__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1fm_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ A_27b @ V0k_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__FUNION__suff,axiom,
    ! [A_27a: d,A_27b: d,V0f2_2E0: u,V1f1_2E0: u,V2P_2E0: u] :
      ( ( ! [V3v_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f1_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
        & ! [V4v_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f2_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V4v_2E0 ) ) ) ) ) )
     => ! [V5v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f2_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V5v_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FUNION__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0f2_2E0: u,V1f1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f2_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__FUPDATE__LIST__suff,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1fm_2E0: u,V2P_2E0: u] :
      ( ( ! [V3v_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
        & ! [V4v_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V4v_2E0 ) ) ) ) ) )
     => ! [V5v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V5v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V0ls_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V5v_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FUPDATE__LIST__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1fm_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V1v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
    <=> ? [V2k_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V1v_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V1v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
    <=> ? [V2k_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
          & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) )
            = ( s @ A_27b @ V1v_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__REVERSE,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) )
     => ! [V1fm_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EREVERSE_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__APPLY__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1ls_2E0: u,V2k_2E0: u,V3v_2E0: u,V4fm_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1ls_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V2k_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1ls_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V4fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V1ls_2E0 ) ) ) @ ( s @ A_27b @ V2k_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__SAME__LIST__APPLY,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1fm1_2E0: u,V2fm2_2E0: u,V3x_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__SAME__APPLY,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1kv_2E0: u,V2fm2_2E0: u,V3fm1_2E0: u] :
      ( ( ( ( s @ A_27a @ V0x_2E0 )
          = ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) ) ) )
        | ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3fm1_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
          = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm2_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3fm1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) ) ) @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__HO__THM,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1f_2E0: u,V2kvl_2E0: u,V3k_2E0: u] :
      ( ( ? [V4n: mono_2Etyop_2Enum_2Enum] :
            ( ( mono_2Ec_2Eprim__rec_2E_3C @ V4n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) ) )
            & ( ( s @ A_27b @ V3k_2E0 )
              = ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) ) ) ) ) )
            & ! [V5m: mono_2Etyop_2Enum_2Enum] :
                ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V4n @ V5m )
                  & ( mono_2Ec_2Eprim__rec_2E_3C @ V5m @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) ) ) )
               => ( (~)
                  @ ( ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) ) )
                    = ( s @ A_27b @ V3k_2E0 ) ) ) ) )
        | ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ A_27b ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) ) @ V2kvl_2E0 ) ) ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__NOT__MEM__matchable,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1f_2E0: u,V2k_2E0: u,V3v_2E0: u] :
      ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) )
        & ( ( s @ A_27b @ V3v_2E0 )
          = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
        = ( s @ A_27b @ V3v_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FUNION__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0s2_2E0: u,V1s1_2E0: u,V2g_2E0: u,V3f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) ) )
     => ? [V4h_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2g_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V4h_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFOLDL2__FUPDATE__LIST__paired,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,F2_2E0: u,F3_2E0: u,F0_2E0: u,F1_2E0: u] :
      ( ! [V1f2_2E0: u,V10b_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) ) ) @ ( s @ A_27a @ V10b_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) @ ( s @ A_27a @ V10b_2E0 ) ) ) ) ) )
     => ( ! [V5fm_2E0: u,V0f1_2E0: u,V6b_2E0: u,V1f2_2E0: u,V7c_2E0: u,V8d_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ V5fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) ) ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) ) ) @ ( s @ A_27b @ V7c_2E0 ) ) ) @ ( s @ A_27c @ V8d_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ V5fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ A_27b @ V7c_2E0 ) ) ) @ ( s @ A_27c @ V8d_2E0 ) ) ) @ ( s @ A_27e @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ A_27b @ V7c_2E0 ) ) ) @ ( s @ A_27c @ V8d_2E0 ) ) ) ) ) ) ) )
       => ( ! [V0f1_2E0: u,V1f2_2E0: u,V5fm_2E0: u,V6b_2E0: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ V5fm_2E0 ) ) ) @ ( s @ A_27a @ V6b_2E0 ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ V5fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) ) ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) ) ) ) ) )
         => ( ! [V0f1_2E0: u,V9b_2E0: u] :
                ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) ) ) @ ( s @ A_27a @ V9b_2E0 ) ) )
                = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) @ ( s @ A_27a @ V9b_2E0 ) ) ) ) ) )
           => ! [V0f1_2E0: u,V1f2_2E0: u,V2bs_2E0: u,V3cs_2E0: u,V4a_2E0: u] :
                ( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) ) ) )
                  = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V3cs_2E0 ) ) ) ) )
               => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( c_2Elist_2EFOLDL2_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ V4a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V3cs_2E0 ) ) )
                  = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27d @ A_27e ) @ V4a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27d @ A_27e ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27d ) @ ( tyop_2Elist_2Elist @ A_27e ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27d ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V3cs_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27e ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ A_27e ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27c @ A_27e ) ) ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ V3cs_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFOLDL2__FUPDATE__LIST,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u,V5fm_2E0: u,V6b_2E0: u,V7c_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) ) @ ( 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 @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V5fm_2E0 ) ) ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ A_27b @ V7c_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V5fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) @ ( c_2Epair_2E_2C_2E2 @ ( 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 ) ) @ V0f1_2E0 ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ A_27b @ V7c_2E0 ) ) ) @ ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ V1f2_2E0 ) @ ( s @ A_27a @ V6b_2E0 ) ) ) @ ( s @ A_27b @ V7c_2E0 ) ) ) ) ) ) ) )
     => ! [V0f1_2E0: u,V1f2_2E0: u,V2bs_2E0: u,V3cs_2E0: u,V4a_2E0: u] :
          ( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) ) ) )
            = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V3cs_2E0 ) ) ) ) )
         => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Elist_2EFOLDL2_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) ) @ ( 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 @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V4a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V3cs_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V4a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27d ) ) @ ( c_2Elist_2EZIP_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A_27c ) @ ( tyop_2Elist_2Elist @ A_27d ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V3cs_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27d ) @ ( c_2Elist_2EMAP2_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2bs_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ V3cs_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__EQ__DRESTRICT__SAME,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1f2_2E0: u,V2f1_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) )
    <=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
        & ! [V3x_2E0: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) ) ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) )
           => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) )
              = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FUNION__SAME,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1s_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP__gen,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2s_2E0: u,V3t_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3t_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_2E0: u,V2k_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__DOMSUB__gen,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2k_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__mono__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIMAGE__FRANGE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1fm_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1fm_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1fm_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICTED__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2s_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0s2_2E0: u,V1s1_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__SUBMAP__gen,axiom,
    ! [A_27a: d,A_27b: d,V0g_2E0: u,V1f_2E0: u,V2P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__o__f__suff,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0fm_2E0: u,V1f_2E0: u,V2P_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0fm_2E0 ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) ) ) )
     => ! [V4v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27c @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0fm_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27c @ V4v_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__FUPDATE__suff,axiom,
    ! [A_27a: d,A_27b: d,V0kv_2E0: u,V1fm_2E0: u,V2P_2E0: u] :
      ( ( ! [V3v_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V0kv_2E0 ) ) ) ) ) ) )
     => ! [V4v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V0kv_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V4v_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FUPDATE__SUBSET,axiom,
    ! [A_27a: d,A_27b: d,V0kv_2E0: u,V1fm_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V0kv_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ V0kv_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FRANGE__DRESTRICT__suff,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1fm_2E0: u,V2P_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) ) ) )
     => ! [V4v_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V4v_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__ASSOC,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2h_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__COMM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1g_2E0: u,V2f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V0k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__EQ__IMPL,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2f3_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) )
        & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2f3_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) ) )
     => ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) )
      <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFEMPTY__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0h_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUNION__ID,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
      & ! [V2f1_2E0: u,V3f2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V2f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V3f2_2E0 ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V3f2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2f3_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) )
        | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUNION__EQ,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u,V2f3_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f3_2E0 ) ) ) ) ) )
      & ! [V3f1_2E0: u,V4f2_2E0: u,V5f3_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V3f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V5f3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V4f2_2E0 ) ) ) ) ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V4f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V5f3_2E0 ) ) ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ V4f2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__EQ__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0h1_2E0: u,V1h2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1h2_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
    <=> ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h1_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
        & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1h2_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__DRESTRICT__COMPL,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1s_2E0: u,V2k_2E0: u,V3f_2E0: u,V4P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) ) ) ) )
    <=> ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__ELIM,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1v_2E0: u,V2f_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) ) ) )
        & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) )
          = ( s @ A_27b @ V1v_2E0 ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0k_2E0 ) @ ( s @ A_27b @ V1v_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__STRENGTHEN__THM,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2f_2E0: u,V3P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) )
      & ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMAP__MAP2__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1v_2E0: u,V2m_2E0: u,V3f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2m_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27c @ V1v_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2m_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ A_27c @ V1v_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMAP__MAP2__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFMAP__MAP2__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0m_2E0: u,V1f_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) )
      & ! [V2x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) ) ) )
         => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMAP__MAP2_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
            = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__PURGE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMEQ__SINGLE__SIMPLE__DISJ__ELIM,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u,V2v_2E0: u,V3ck_2E0: u,V4cv_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3ck_2E0 ) @ ( s @ A_27b @ V4cv_2E0 ) ) ) ) ) )
    <=> ( ( ( s @ A_27a @ V1k_2E0 )
          = ( s @ A_27a @ V3ck_2E0 ) )
        & ( ( s @ A_27b @ V2v_2E0 )
          = ( s @ A_27b @ V4cv_2E0 ) )
        & ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
          | ? [V5v_27_2E0: u] :
              ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V5v_27_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMEQ__SINGLE__SIMPLE__ELIM,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1k_2E0: u,V2v_2E0: u,V3ck_2E0: u,V4cv_2E0: u,V5nv_2E0: u] :
      ( ? [V6fm_2E0: u] :
          ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V6fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3ck_2E0 ) @ ( s @ A_27b @ V4cv_2E0 ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V6fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V5nv_2E0 ) ) ) ) ) ) ) ) )
    <=> ( ( ( s @ A_27a @ V1k_2E0 )
          = ( s @ A_27a @ V3ck_2E0 ) )
        & ( ( s @ A_27b @ V2v_2E0 )
          = ( s @ A_27b @ V4cv_2E0 ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3ck_2E0 ) @ ( s @ A_27b @ V5nv_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMEQ__ENUMERATE__CASES,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1kvl_2E0: u,V2p_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2p_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V2p_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__SAME__KEYS__UNWIND,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2kvl1_2E0: u,V3kvl2_2E0: u] :
      ( ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2kvl1_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3kvl2_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2kvl1_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3kvl2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2kvl1_2E0 ) ) ) ) ) ) )
     => ( ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2kvl1_2E0 )
          = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V3kvl2_2E0 ) )
        & ! [V4kvl_2E0: u] :
            ( ( ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4kvl_2E0 ) ) )
              = ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2kvl1_2E0 ) ) ) )
           => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4kvl_2E0 ) ) )
              = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V4kvl_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__SAME__UPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1f1_2E0: u,V2f2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FUPDATE__LIST,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1fm_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPD11__SAME__UPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2k_2E0: u,V3v_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPD__SAME__KEY__UNWIND,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2k_2E0: u,V3v1_2E0: u,V4v2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v1_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V4v2_2E0 ) ) ) ) ) )
     => ( ( ( s @ A_27b @ V3v1_2E0 )
          = ( s @ A_27b @ V4v2_2E0 ) )
        & ! [V5v_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V5v_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V5v_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPD11__SAME__BASE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1k1_2E0: u,V2v1_2E0: u,V3k2_2E0: u,V4v2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ A_27b @ V2v1_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k2_2E0 ) @ ( s @ A_27b @ V4v2_2E0 ) ) ) ) ) )
    <=> ( ( ( ( s @ A_27a @ V1k1_2E0 )
            = ( s @ A_27a @ V3k2_2E0 ) )
          & ( ( s @ A_27b @ V2v1_2E0 )
            = ( s @ A_27b @ V4v2_2E0 ) ) )
        | ( ( (~)
            @ ( ( s @ A_27a @ V1k1_2E0 )
              = ( s @ A_27a @ V3k2_2E0 ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3k2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
          & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ A_27b @ V2v1_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) )
          & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k2_2E0 ) @ ( s @ A_27b @ V4v2_2E0 ) ) ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESAME__KEY__UPDATES__DIFFER,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2k_2E0: u,V3v1_2E0: u,V4v2_2E0: u] :
      ( ( (~)
        @ ( ( s @ A_27b @ V3v1_2E0 )
          = ( s @ A_27b @ V4v2_2E0 ) ) )
     => ( (~)
        @ ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V4v2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPD11__SAME__NEW__KEY,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2k_2E0: u,V3v1_2E0: u,V4v2_2E0: u] :
      ( ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) ) ) ) )
        & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) ) ) )
     => ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V4v2_2E0 ) ) ) ) ) )
      <=> ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) )
          & ( ( s @ A_27b @ V3v1_2E0 )
            = ( s @ A_27b @ V4v2_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPD11__SAME__KEY__AND__BASE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1k_2E0: u,V2v1_2E0: u,V3v2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v1_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V3v2_2E0 ) ) ) ) ) )
    <=> ( ( s @ A_27b @ V2v1_2E0 )
        = ( s @ A_27b @ V3v2_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__SNOC,axiom,
    ! [A_27a: d,A_27b: d,V0xs_2E0: u,V1x_2E0: u,V2fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ESNOC_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1x_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0xs_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0xs_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1x_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFOLDL__FUPDATE__LIST,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0f1_2E0: u,V1f2_2E0: u,V4fm_2E0: u,V5k_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4fm_2E0 ) ) ) @ ( s @ A_27a @ V5k_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V4fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ A_27a @ V5k_2E0 ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f2_2E0 ) @ ( s @ A_27a @ V5k_2E0 ) ) ) ) ) ) ) )
     => ( ! [V0f1_2E0: u,V1f2_2E0: u,V6k_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f2_2E0 ) ) ) @ ( s @ A_27a @ V6k_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ A_27a @ V6k_2E0 ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f2_2E0 ) @ ( s @ A_27a @ V6k_2E0 ) ) ) ) ) )
       => ! [V0f1_2E0: u,V1f2_2E0: u,V2ls_2E0: u,V3a_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Elist_2EFOLDL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2ls_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3a_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V2ls_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1f_2E0: u,V2k_2E0: u,V3v_2E0: u,V4n: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V4n @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) )
        & ( ( s @ A_27a @ V2k_2E0 )
          = ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) )
        & ( ( s @ A_27b @ V3v_2E0 )
          = ( s @ A_27b @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4n ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) )
        & ! [V5m: mono_2Etyop_2Enum_2Enum] :
            ( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V4n @ V5m )
              & ( mono_2Ec_2Eprim__rec_2E_3C @ V5m @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Elist_2ELENGTH_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) )
           => ( (~)
              @ ( ( s @ A_27a @ ( c_2Elist_2EEL_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V5m ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) )
                = ( s @ A_27a @ V2k_2E0 ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
        = ( s @ A_27b @ V3v_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__FUPDATE__LIST,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1fm_2E0: u,V2P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) )
      <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__FUPDATE__LIST__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1kvl_2E0: u,V2k_2E0: u,V3fm_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__FUPDATE__LIST__COMMUTES,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1kvl_2E0: u,V2k_2E0: u,V3fm_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0kvl2_2E0: u,V1kvl1_2E0: u,V2fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2EAPPEND_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1kvl1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl2_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__NOT__MEM,axiom,
    ! [A_27a: d,A_27b: d,V0kvl_2E0: u,V1f_2E0: u,V2k_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0kvl_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__THM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ c_2Elist_2ENIL_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) )
      & ! [V1h_2E0: u,V2t_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( c_2Elist_2ECONS_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1h_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1h_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2t_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) )
        & ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ A_27b @ V3y_2E0 ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__TRANS,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2h_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__ANTISYM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__REFL,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EXT,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) )
    <=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
        & ! [V2x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
           => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
              = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__THM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
        & ! [V2x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
           => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
              = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFAPPLY_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(thm_2Efinite__map_2ENOT__FDOM__FAPPLY__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFM__PULL__APART,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) )
     => ? [V2fm0_2E0: u,V3v_2E0: u] :
          ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) )
          & ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm0_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__INDUCT,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) )
        & ! [V1f_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) )
           => ! [V2x_2E0: u,V3y_2E0: u] :
                ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ) ) ) )
     => ! [V4f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V4f_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFCARD__SUC,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1n: mono_2Etyop_2Enum_2Enum] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) )
        = ( mono_2Ec_2Enum_2ESUC @ V1n ) )
    <=> ? [V2f_27_2E0: u,V3x_2E0: u,V4y_2E0: u] :
          ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_27_2E0 ) ) ) ) ) ) )
          & ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_27_2E0 ) ) ) )
            = V1n )
          & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_27_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFCARD__0__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) )
        = mono_2Ec_2Enum_2E0 )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFCARD__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) ) ) )
      = ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_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 @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFCARD__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Efinite__map_2EFCARD_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) )
      = mono_2Ec_2Enum_2E0 ) ).

thf(thm_2Efinite__map_2EFDOM__FINITE,axiom,
    ! [A_27a: d,A_27b: d,V0fm_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 ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__F__FEMPTY1,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ! [V1a_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__EQ__EMPTY__SYM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__EQ__EMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ).

thf(thm_2Efinite__map_2Efmap__SIMPLE__INDUCT,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) )
        & ! [V1f_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) )
           => ! [V2x_2E0: u,V3y_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ) ) )
     => ! [V4f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V4f_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__EQ__FDOM__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) )
     => ! [V2y_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2ENOT__EQ__FEMPTY__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( (~)
      @ ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFAPPLY__FUPDATE__THM,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V3x_2E0: u,V1a_2E0: u] :
          ( ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V1a_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V3x_2E0 )
            = ( s @ A_27a @ V1a_2E0 ) ) )
     => ! [V0f_2E0: u,V1a_2E0: u,V2b_2E0: u,V3x_2E0: u] :
          ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
          = ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27b @ V2b_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2b_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2b_2E0: u,V3c_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V3c_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V3c_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__COMMUTES,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2b_2E0: u,V3c_2E0: u,V4d_2E0: u] :
      ( ( (~)
        @ ( ( s @ A_27a @ V1a_2E0 )
          = ( s @ A_27a @ V3c_2E0 ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ A_27b @ V4d_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3c_2E0 ) @ ( s @ A_27b @ V4d_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27b @ V2b_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ENOT__EQ__FAPPLY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1a_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( (~)
        @ ( ( s @ A_27a @ V1a_2E0 )
          = ( s @ A_27a @ V2x_2E0 ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ A_27a @ V1a_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFAPPLY__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2y_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) )
      = ( s @ A_27b @ V2y_2E0 ) ) ).

thf(thm_2Efinite__map_2Eis__fmap__cases,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V5x_2E0: u,V3a_2E0: u] :
          ( ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V5x_2E0 )
            = ( s @ A_27a @ V3a_2E0 ) ) )
     => ! [V0a0_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V0a0_2E0 ) ) ) )
        <=> ( ! [V1x_2E0: u] :
                ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V0a0_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
                = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) ) ) ) )
            | ? [V2f_2E0: u,V3a_2E0: u,V4b_2E0: u] :
                ( ! [V5x_2E0: u] :
                    ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V0a0_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) )
                    = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eis__fmap__strongind,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V1a_2E0: u] :
          ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) )
          = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) ) ) ) )
     => ( ! [V5x_2E0: u,V3a_2E0: u] :
            ( ( 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 ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ V5x_2E0 )
              = ( s @ A_27a @ V3a_2E0 ) ) )
       => ( ! [V3a_2E0: u,V4b_2E0: u,V2f_2E0: u,V5x_2E0: u] :
              ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) )
              = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) )
         => ! [V0is__fmap_27_2E0: u] :
              ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) ) ) )
                & ! [V2f_2E0: u,V3a_2E0: u,V4b_2E0: u] :
                    ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) )
                      & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) ) ) ) ) )
             => ! [V6a0_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V6a0_2E0 ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V6a0_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eis__fmap__ind,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V1a_2E0: u] :
          ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) )
          = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) ) ) ) )
     => ( ! [V5x_2E0: u,V3a_2E0: u] :
            ( ( 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 ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ V5x_2E0 )
              = ( s @ A_27a @ V3a_2E0 ) ) )
       => ( ! [V3a_2E0: u,V4b_2E0: u,V2f_2E0: u,V5x_2E0: u] :
              ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) )
              = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F2_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) )
         => ! [V0is__fmap_27_2E0: u] :
              ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) ) ) )
                & ! [V2f_2E0: u,V3a_2E0: u,V4b_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27b @ V4b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V2f_2E0 ) ) ) ) ) ) ) )
             => ! [V6a0_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V6a0_2E0 ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ tyop_2Emin_2Ebool ) @ V0is__fmap_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V6a0_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eis__fmap__rules,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V0a_2E0: u] :
          ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0a_2E0 ) ) )
          = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINR_2E1 @ ( s @ tyop_2Eone_2Eone @ ( i_mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Eone_2Eone ) ) ) ) )
     => ( ! [V4x_2E0: u,V2a_2E0: u] :
            ( ( 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 ) ) @ F2_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ V4x_2E0 )
              = ( s @ A_27a @ V2a_2E0 ) ) )
       => ( ! [V2a_2E0: u,V3b_2E0: u,V1f_2E0: u,V4x_2E0: u] :
              ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1f_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) )
              = ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F2_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1f_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ F0_2E0 ) ) ) )
            & ! [V1f_2E0: u,V2a_2E0: u,V3b_2E0: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1f_2E0 ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Eis__fmap_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) ) ) ) @ F1_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ A_27b @ V3b_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ tyop_2Eone_2Eone ) ) @ V1f_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__FEMPTY__1,axiom,
    ! [A_27a: d,A_27b: d,V0g_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) ) ).

thf(thm_2Efinite__map_2EFUNION__FEMPTY__2,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ).

thf(thm_2Efinite__map_2EFUNION__FUPDATE__1,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__FUPDATE__2,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EEQ__FDOM__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0g_2E0: u,V1f_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0g_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUPDATE__EQN,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) ) ) )
    <=> ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) ) ) ) )
        | ( ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
            = ( s @ A_27b @ V0y_2E0 ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1r_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESTRONG__DRESTRICT__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1r_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1r_2E0: u,V2x_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2ENOT__FDOM__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1P_2E0: u,V2Q_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__IS__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESTRONG__DRESTRICT__FUPDATE__THM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1r_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__UNIV,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__EQ__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2s1_2E0: u,V3s2_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s1_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3s2_2E0 ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3s2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3s2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FUNION,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1m1_2E0: u,V2m2_2E0: u,V3k_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1m1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2m2_2E0 ) ) ) @ ( s @ A_27b @ V3k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1m1_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2m2_2E0 ) @ ( s @ A_27b @ V3k_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__CASES,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
      | ? [V1g_2E0: u,V2x_2E0: u,V3y_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__NOT__IN__DOM,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1fm_2E0: u] :
      ( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0v_2E0: u,V1k_2E0: u,V2fm_2E0: u,V3f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27c @ V0v_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V3f_2E0 ) @ ( s @ A_27c @ V0v_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__COMMUTES,axiom,
    ! [A_27a: d,A_27b: d,V0k2_2E0: u,V1k1_2E0: u,V2fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V0k2_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ A_27a @ V0k2_2E0 ) ) ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__IDEM,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) @ ( s @ A_27a @ V0k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0k_2E0: u,V1g_2E0: u,V2fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) @ ( s @ A_27a @ V0k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FUPDATE__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u,V2v_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27b @ V2v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FLOOKUP__THM,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1k1_2E0: u,V2k2_2E0: u] :
          ( ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V1k1_2E0 )
            = ( s @ A_27a @ V2k2_2E0 ) ) )
     => ! [V0fm_2E0: u,V1k1_2E0: u,V2k2_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FLOOKUP__NEQ,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k1_2E0: u,V2k2_2E0: u] :
      ( ( (~)
        @ ( ( s @ A_27a @ V1k1_2E0 )
          = ( s @ A_27a @ V2k2_2E0 ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FAPPLY__THM,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1k1_2E0: u,V2k2_2E0: u] :
          ( ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V1k1_2E0 )
            = ( s @ A_27a @ V2k2_2E0 ) ) )
     => ! [V0fm_2E0: u,V1k1_2E0: u,V2k2_2E0: u] :
          ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) )
          = ( s @ A_27b @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FAPPLY__NEQ,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k1_2E0: u,V2k2_2E0: u] :
      ( ( (~)
        @ ( ( s @ A_27a @ V1k1_2E0 )
          = ( s @ A_27a @ V2k2_2E0 ) ) )
     => ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FAPPLY,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u] :
      ( ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
      = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FUPDATE__THM,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1k1_2E0: u,V2k2_2E0: u] :
          ( ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) )
        <=> ( ( s @ A_27a @ V1k1_2E0 )
            = ( s @ A_27a @ V2k2_2E0 ) ) )
     => ! [V0fm_2E0: u,V1k1_2E0: u,V2k2_2E0: u,V3v_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( 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 ) ) @ F0_2E0 ) @ ( s @ A_27a @ V1k1_2E0 ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FUPDATE__NEQ,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k1_2E0: u,V2k2_2E0: u,V3v_2E0: u] :
      ( ( (~)
        @ ( ( s @ A_27a @ V1k1_2E0 )
          = ( s @ A_27a @ V2k2_2E0 ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) @ ( s @ A_27a @ V2k2_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k2_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k1_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1k_2E0: u,V2v_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2Ef__o__ASSOC,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0h_2E0: u,V1g_2E0: u,V2f_2E0: u] :
      ( ( ! [V3x_2E0: u,V4y_2E0: u] :
            ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V4y_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ V3x_2E0 )
              = ( s @ A_27a @ V4y_2E0 ) ) )
        & ! [V5x_2E0: u,V6y_2E0: u] :
            ( ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0h_2E0 ) @ ( s @ A_27c @ V5x_2E0 ) ) )
              = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0h_2E0 ) @ ( s @ A_27c @ V6y_2E0 ) ) ) )
          <=> ( ( s @ A_27c @ V5x_2E0 )
              = ( s @ A_27c @ V6y_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0h_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27d ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27d ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V0h_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFINITE__PRED__11,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V0g_2E0: u,V3f_2E0: u,V4x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3f_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0g_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3f_2E0 ) ) ) ) ) ) ) )
     => ! [V0g_2E0: u] :
          ( ! [V1x_2E0: u,V2y_2E0: u] :
              ( ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0g_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
                = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0g_2E0 ) @ ( s @ A_27a @ V2y_2E0 ) ) ) )
            <=> ( ( s @ A_27a @ V1x_2E0 )
                = ( s @ A_27a @ V2y_2E0 ) ) )
         => ! [V3f_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 ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V3f_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFAPPLY__f__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1g_2E0: u,V0f_2E0: u,V2x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( 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_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
     => ! [V0f_2E0: u,V1g_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 ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
         => ! [V3x_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ) )
             => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
                = ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Ef__o__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u,F4_2E0: u,F2_2E0: u,F3_2E0: u,F1_2E0: u] :
      ( ! [V3g_2E0: u,V0fm_2E0: u,V4x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) @ ( s @ A_27c @ V4x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V4x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) @ ( s @ A_27c @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ) )
     => ( ! [V3g_2E0: u,V6x_2E0: u,V1k_2E0: u] :
            ( ( 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_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27c @ V6x_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) )
          <=> ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) @ ( s @ A_27c @ V6x_2E0 ) ) )
              = ( s @ A_27a @ V1k_2E0 ) ) )
       => ( ! [V3g_2E0: u,V1k_2E0: u,V6x_2E0: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27c @ V6x_2E0 ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V6x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27c @ V6x_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) )
         => ( ! [V3g_2E0: u,V5x_2E0: u,V1k_2E0: u] :
                ( ( 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_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27c @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) )
              <=> ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) @ ( s @ A_27c @ V5x_2E0 ) ) )
                  = ( s @ A_27a @ V1k_2E0 ) ) )
           => ( ! [V3g_2E0: u,V1k_2E0: u,V5x_2E0: u] :
                  ( ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) @ ( s @ A_27c @ V5x_2E0 ) ) )
                  = ( s @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V5x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ F3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27c @ V5x_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) )
             => ! [V0fm_2E0: u,V1k_2E0: u,V2v_2E0: u,V3g_2E0: u] :
                  ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ) ) ) )
                 => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V2v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) )
                    = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ ( c_2Ecombin_2EC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ c_2Ecombin_2EK_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27b @ V2v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Epair_2Eprod @ A_27c @ tyop_2Emin_2Ebool ) ) ) ) @ F2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Ef__o__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0g_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0g_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFDOM__f__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1g_2E0: u,V0f_2E0: u,V3x_2E0: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
     => ( ! [V1g_2E0: u,V0f_2E0: u,V2x_2E0: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( 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_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
       => ! [V0f_2E0: u,V1g_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 ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) )
           => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__FUN__FMAP,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u,V1f_2E0: u,V2P_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 ) @ V2P_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) ) ) @ ( s @ A_27a @ V0k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V0k_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FMAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1s_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 ) @ V1s_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FMAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1P_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 ) @ V1P_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUN__FMAP__EMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2ERRESTRICT__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1r_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27b @ V3y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1r_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ERRESTRICT__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2ERRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0fm2_2E0: u,V1fm1_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm2_2E0 ) ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm2_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0v_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) ) ) )
    <=> ? [V2k_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ A_27b @ V2k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0v_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__FRANGE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0x_2E0: u,V1g_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1g_2E0 ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V2f_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1g_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFINITE__FRANGE,axiom,
    ! [A_27a: d,A_27b: d,V0fm_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 ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FRANGE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2y_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27b @ V2y_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFRANGE__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFRANGE_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__o__f,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V2f_2E0: u,V3v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2f_2E0 ) ) ) @ ( s @ A_27c @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2f_2E0 ) @ ( s @ A_27c @ V3v_2E0 ) ) ) ) ) )
     => ! [V0k_2E0: u,V1fm_2E0: u,V2f_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ A_27b @ V0k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V1fm_2E0 ) @ ( s @ A_27b @ V0k_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Eoption_2Eoption @ A_27a ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2f_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__o__f,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0h_2E0: u,V1g_2E0: u,V2f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ V1g_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ V0h_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27c ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27d ) @ V0h_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__o__f,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1P_2E0: u,V2f_2E0: u,V3x_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3x_2E0 ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3x_2E0 ) ) ) @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V2f_2E0 ) @ ( s @ A_27b @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V3x_2E0 ) ) ) ) ) ) ) ) ) ) )
     => ! [V0m_2E0: u,V1P_2E0: u,V2f_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) @ V1P_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0m_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2Eo__f__FAPPLY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) )
     => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
        = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__o__f,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__FDOM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Ef__o__f__FEMPTY__2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2Ef__o__f__FEMPTY__1,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EFEVERY__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1k_2E0: u,V2f_2E0: u,V3P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0v_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1k_2E0 ) @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1f_2E0: u,V2x_2E0: u,V3y_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) )
    <=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1s_2E0: u,V2k_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ A_27a @ V2k_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__eq__flookup,axiom,
    ! [A_27a: d,A_27b: d,V0f2_2E0: u,V1f1_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f1_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f2_2E0 ) )
    <=> ! [V2x_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f1_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f2_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__EXT,axiom,
    ! [A_27a: d,A_27b: d,V0f2_2E0: u,V1f1_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f1_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f2_2E0 ) )
    <=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f1_2E0 ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27b ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f2_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__FUNION,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V3v_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) @ ( s @ A_27a @ V3v_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V3v_2E0 ) ) ) )
     => ! [V0k_2E0: u,V1f2_2E0: u,V2f1_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f2_2E0 ) ) ) @ ( s @ A_27b @ V0k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2f1_2E0 ) @ ( s @ A_27b @ V0k_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f2_2E0 ) @ ( s @ A_27b @ V0k_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27a ) ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUPDATE__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V1x_2E0 ) @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) ) ) )
    <=> ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) )
        | ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0y_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0v_2E0: u,V1k_2E0: u,V2g_2E0: u,V3f_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2g_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3f_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0v_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2g_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V0v_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__UPDATE,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2k1_2E0: u,V1k2_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V2k1_2E0 ) ) ) @ ( s @ A_27b @ V1k2_2E0 ) ) ) )
        <=> ( ( s @ A_27b @ V2k1_2E0 )
            = ( s @ A_27b @ V1k2_2E0 ) ) )
     => ! [V0v_2E0: u,V1k2_2E0: u,V2k1_2E0: u,V3fm_2E0: u] :
          ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V3fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ V2k1_2E0 ) @ ( s @ A_27a @ V0v_2E0 ) ) ) ) ) @ ( s @ A_27b @ V1k2_2E0 ) ) )
          = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ F0_2E0 ) @ ( s @ A_27b @ V2k1_2E0 ) ) ) @ ( s @ A_27b @ V1k2_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V0v_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V3fm_2E0 ) @ ( s @ A_27b @ V1k2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__EMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0k_2E0: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ A_27b @ V0k_2E0 ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) ) ).

thf(thm_2Efinite__map_2EFMERGE__EQ__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1g_2E0: u,V2f_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
    <=> ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) )
        & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__DRESTRICT,axiom,
    ! [A_27a: d,A_27b: d,V0vs_2E0: u,V1st2_2E0: u,V2st1_2E0: u,V3f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2st1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1st2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0vs_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2st1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0vs_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1st2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0vs_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__ASSOC,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EASSOC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Efinite__map_2EFMERGE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2EASSOC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__COMM,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2ECOMM_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Efinite__map_2EFMERGE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ecombin_2ECOMM_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__NO__CHANGE,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1f2_2E0: u,V2f1_2E0: u] :
      ( ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) )
      <=> ! [V3x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) ) ) ) ) )
              & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
                = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) )
      & ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) )
      <=> ! [V4x_2E0: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) ) ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V4x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
              & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2f1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) @ ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) )
                = ( s @ A_27b @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__FMERGE,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2m_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V2m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__FUNION,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1y_2E0: u] :
          ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ F0_2E0 ) @ ( s @ A_27b @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
          = ( s @ A_27b @ V0x_2E0 ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUNION_2E0 )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ ( c_2Efinite__map_2EFMERGE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ F0_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FMERGE,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1f_2E0: u,V2g_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V2g_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFMERGE__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0m_2E0: u,V1f_2E0: u] :
      ( ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) )
      & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFMERGE_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFUNION__IDEMPOT,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0h_2E0: u,V1s1_2E0: u,V2s2_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1s1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2s2_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__EQ__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0h_2E0: u,V1h1_2E0: u,V2h2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1h1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h2_2E0 ) ) ) ) ) )
        & ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1h1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h2_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h2_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1h1_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EIN__FDOM__FOLDR__UNION,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1hL_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ c_2Efinite__map_2EFUNION_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ V1hL_2E0 ) ) ) ) ) ) ) )
    <=> ? [V2h_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ V1hL_2E0 ) ) ) ) ) )
          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2h_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__FUNION__DRESTRICT__COMPL,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2ECOMPL_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__IDEMPOT,axiom,
    ! [A_27a: d,A_27b: d,V0s_2E0: u,V1vs_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1vs_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1vs_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V1vs_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2ESUBMAP__FUNION__ABSORPTION,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EMAP__KEYS__witness,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0m_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ V0m_2E0 ) ) ) )
        <=> ! [V1f_2E0: u,V2fm_2E0: u] :
              ( ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) ) )
                = ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) ) ) )
              & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
               => ! [V3x_2E0: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) ) ) )
                   => ( ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ V0m_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
                      = ( s @ A_27c @ ( c_2Efinite__map_2EFAPPLY_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V2fm_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) ) ) ) ) )
     => ( ! [V4f_2E0: u,V5fm_2E0: u] :
            ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V5fm_2E0 ) ) )
            = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V5fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V5fm_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( c_2Epred__set_2ELINV_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V5fm_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V5fm_2E0 ) ) ) ) ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ c_2Ebool_2EARB_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V5fm_2E0 ) ) ) ) ) ) ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ELET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) ) ) @ F1_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EMAP__KEYS__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ).

thf(thm_2Efinite__map_2EMAP__KEYS__FUPDATE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1fm_2E0: u,V2k_2E0: u,V3v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27c @ V3v_2E0 ) ) ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27b @ A_27c ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ A_27c @ V3v_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EMAP__KEYS__using__LINV,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1fm_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Ef__o__f_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ ( c_2Efinite__map_2EFUN__FMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( c_2Epred__set_2ELINV_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EMAP__KEYS__BIJ__LINV,axiom,
    ! [A_27a: d,V0t_2E0: u,V1f: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Epred__set_2EBIJ_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V1f @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1f ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Epred__set_2ELINV_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V1f @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Enum_2Enum ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ V0t_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ tyop_2Enum_2Enum @ A_27a ) @ V0t_2E0 ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__MAP__KEYS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
      ( ! [V1k_2E0: u,V2f_2E0: u,V0m_2E0: u,V3x_2E0: u] :
          ( ( 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 @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V1k_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
        <=> ( ( ( s @ A_27b @ V1k_2E0 )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) ) ) ) ) )
     => ! [V0m_2E0: u,V1k_2E0: u,V2f_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
         => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) @ ( s @ A_27b @ V1k_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Eoption_2EOPTION__BIND_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2Esome_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V1k_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Eoption_2Eoption @ A_27c ) ) @ ( c_2Efinite__map_2EFLOOKUP_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFLOOKUP__MAP__KEYS__MAPPED,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0m_2E0: u,V1k_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Eoption_2Eoption @ A_27c ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0m_2E0 ) @ ( s @ A_27a @ V1k_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDRESTRICT__MAP__KEYS__IMAGE,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0s_2E0: u,V1fm_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EINJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EDRESTRICT_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0s_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EDOMSUB__MAP__KEYS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0s_2E0: u,V1fm_2E0: u,V2f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EBIJ_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ A_27a @ V0s_2E0 ) ) ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27c ) @ ( c_2Efinite__map_2EMAP__KEYS_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1fm_2E0 ) @ ( s @ A_27a @ V0s_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FUPDATE__same,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0v2_2E0: u,V1v1_2E0: u,V2k_2E0: u,V3f2_2E0: u,V4f1_2E0: u,V5R_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V5R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V4f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V3f2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V5R_2E0 ) @ ( s @ A_27a @ V1v1_2E0 ) ) ) @ ( s @ A_27b @ V0v2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V5R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V4f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27a @ V1v1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27b @ V0v2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FUPDATE__LIST__same,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R_2E0: u,V1ls1_2E0: u,V2ls2_2E0: u,V3f1_2E0: u,V4f2_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V4f2_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27c ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1ls1_2E0 ) ) )
          = ( s @ ( tyop_2Elist_2Elist @ A_27c ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27c ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ V2ls2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2ELIST__REL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ A_27a ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1ls1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A_27b ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ A_27b ) @ c_2Epair_2ESND_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ V2ls2_2E0 ) ) ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) ) @ V1ls1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V4f2_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) ) @ V2ls2_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FEMPTY,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V0R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FEMPTY2,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1R_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f_2E0 ) ) ) )
      <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) )
      <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0f_2E0 )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ c_2Efinite__map_2EFEMPTY_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__refl,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1R_2E0: u] :
      ( ! [V2x_2E0: u] : ( 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 ) ) @ V1R_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27b @ A_27a ) @ V0x_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FUNION__rels,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f4_2E0: u,V1f3_2E0: u,V2f2_2E0: u,V3f1_2E0: u,V4R_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V2f2_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f3_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f4_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V3f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f3_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V2f2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f4_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FUPDATE__I,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0v2_2E0: u,V1v1_2E0: u,V2k_2E0: u,V3f2_2E0: u,V4f1_2E0: u,V5R_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V5R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V4f1_2E0 ) @ ( s @ A_27c @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V3f2_2E0 ) @ ( s @ A_27c @ V2k_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V5R_2E0 ) @ ( s @ A_27a @ V1v1_2E0 ) ) ) @ ( s @ A_27b @ V0v2_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V5R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V4f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27a ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27a @ V1v1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V3f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27c @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27c @ V2k_2E0 ) @ ( s @ A_27b @ V0v2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__mono,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f2_2E0: u,V1f1_2E0: u,V2R2_2E0: u,V3R1_2E0: u] :
      ( ! [V4x_2E0: u,V5y_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R1_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27b @ V5y_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R2_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) @ ( s @ A_27b @ V5y_2E0 ) ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R2_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__OPTREL__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f2_2E0: u,V1f1_2E0: u,V2R_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) ) ) )
    <=> ! [V3k_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ A_27c @ V3k_2E0 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) @ ( s @ A_27c @ V3k_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__rel__FLOOKUP__imp,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f2_2E0: u,V1f1_2E0: u,V2R_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__rel_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) ) ) )
     => ( ! [V3k_2E0: u] :
            ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ A_27c @ V3k_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ c_2Eoption_2ENONE_2E0 ) )
           => ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) @ ( s @ A_27c @ V3k_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ c_2Eoption_2ENONE_2E0 ) ) )
        & ! [V4k_2E0: u,V5v1_2E0: u] :
            ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27a ) @ V1f1_2E0 ) @ ( s @ A_27c @ V4k_2E0 ) ) )
              = ( s @ ( tyop_2Eoption_2Eoption @ A_27a ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27a @ V5v1_2E0 ) ) ) )
           => ? [V6v2_2E0: u] :
                ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27c @ A_27b ) @ V0f2_2E0 ) @ ( s @ A_27c @ V4k_2E0 ) ) )
                  = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V6v2_2E0 ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R_2E0 ) @ ( s @ A_27a @ V5v1_2E0 ) ) ) @ ( s @ A_27b @ V6v2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__UPTO______EMPTY,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EEMPTY_2E0 ) ) ) )
    <=> ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__UPTO______EQ,axiom,
    ! [A_27a: d,A_27b: d,V0vs_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0vs_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2ks_2E0: u,V3k_2E0: u,V4v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2ks_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDELETE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2ks_2E0 ) @ ( s @ A_27a @ V3k_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH______NO__DELETE,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2ks_2E0: u,V3k_2E0: u,V4v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2ks_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2ks_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__SING,axiom,
    ! [A_27a: d,A_27b: d,V0f1_2E0: u,V1f2_2E0: u,V2ks_2E0: u,V3k_2E0: u,V4v_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2ks_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2Efmap__EQ__UPTO_2E3 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ A_27b @ V4v_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINSERT_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2ks_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2Eo__f__FUNION,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f2_2E0: u,V1f1_2E0: u,V2f_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1f1_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0f2_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V1f1_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Eo__f_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27b ) @ V2f_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27c ) @ V0f2_2E0 ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFDOM__FOLDR__DOMSUB,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V2k_2E0: u,V3m_2E0: u] :
          ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3m_2E0 ) ) )
          = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2Efdomsub_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V3m_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) ) )
     => ! [V0ls_2E0: u,V1fm_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Elist_2EFOLDR_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EDIFF_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Efinite__map_2EFDOM_2E1 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ V0ls_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__SUBMAP,axiom,
    ! [A_27a: d,A_27b: d,V0fm0_2E0: u,V1fm_2E0: u,V2P_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2ESUBMAP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm0_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm0_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFEVERY__ALL__FLOOKUP,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u,V1f_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Efinite__map_2EFEVERY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) ) ) )
    <=> ! [V2k_2E0: u,V3v_2E0: u] :
          ( ( ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Efinite__map_2EFLOOKUP_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1f_2E0 ) @ ( s @ A_27a @ V2k_2E0 ) ) )
            = ( s @ ( tyop_2Eoption_2Eoption @ A_27b ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A_27b @ V3v_2E0 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V2k_2E0 ) @ ( s @ A_27b @ V3v_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__CANCEL,axiom,
    ! [A_27a: d,A_27b: d,V0ls1_2E0: u,V1fm_2E0: u,V2ls2_2E0: u] :
      ( ! [V3k_2E0: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls1_2E0 ) ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A_27a @ V3k_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2ls2_2E0 ) ) ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2ls2_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V1fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V2ls2_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__EQ__FUNION,axiom,
    ! [A_27a: d,A_27b: d,V0fm_2E0: u,V1kv_2E0: u] :
      ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) ) )
      = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUNION_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ c_2Efinite__map_2EFEMPTY_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ V1kv_2E0 ) ) ) @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V0fm_2E0 ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__APPEND__COMMUTES,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2fm_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EDISJOINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( c_2Elist_2ELIST__TO__SET_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1l2_2E0 ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0l1_2E0 ) ) ) ) ) ).

thf(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__PERM,axiom,
    ! [A_27a: d,A_27b: d,V0ls_2E0: u,V1ls_27_2E0: u,V2fm_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Elist_2EALL__DISTINCT_2E1 @ ( s @ ( tyop_2Elist_2Elist @ A_27a ) @ ( c_2Elist_2EMAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ A_27a ) @ c_2Epair_2EFST_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esorting_2EPERM_2E2 @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_27_2E0 ) ) ) ) )
     => ( ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V0ls_2E0 ) ) )
        = ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ ( c_2Efinite__map_2EFUPDATE__LIST_2E2 @ ( s @ ( tyop_2Efinite__map_2Efmap @ A_27a @ A_27b ) @ V2fm_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ V1ls_27_2E0 ) ) ) ) ) ).

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