%------------------------------------------------------------------------------
% File     : ITP040_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    : indexedLists.ax [Gau19]
%          : HL4040_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  325 ( 106 unt; 167 typ;   0 def)
%            Number of atoms       :  286 ( 177 equ)
%            Maximal formula atoms :    9 (   0 avg)
%            Number of connectives :  131 (   3   ~;   6   |;  49   &)
%                                         (  25 <=>;  48  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :   16 (   3 avg)
%            Number of types       :   13 (  12 usr)
%            Number of type conns  :  145 (  87   >;  58   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  154 ( 154 usr;  68 con; 0-4 aty)
%            Number of variables   :  647 ( 634   !;  13   ?; 647   :)
% SPC      : TF0_SAT_EQU_NAR

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

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

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

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

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

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

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: u ).

tff(c_2Earithmetic_2E_2B_2E1,type,
    c_2Earithmetic_2E_2B_2E1: du > u ).

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

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

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

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

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

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: u ).

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

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: u ).

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

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

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

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

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

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

tff(c_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: u ).

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

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: u ).

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

tff(c_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_2E0: u ).

tff(c_2Ecombin_2EC_2E2,type,
    c_2Ecombin_2EC_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

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

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

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

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: u ).

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

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: u ).

tff(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: ( du * du * du ) > u ).

tff(c_2EindexedLists_2EFOLDRi_2E0,type,
    c_2EindexedLists_2EFOLDRi_2E0: u ).

tff(c_2EindexedLists_2EFOLDRi_2E3,type,
    c_2EindexedLists_2EFOLDRi_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EFRONT_2E0,type,
    c_2Elist_2EFRONT_2E0: u ).

tff(c_2Elist_2EFRONT_2E1,type,
    c_2Elist_2EFRONT_2E1: du > u ).

tff(c_2Elist_2EGENLIST_2E0,type,
    c_2Elist_2EGENLIST_2E0: u ).

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

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: ( du * du ) > u ).

tff(c_2Elist_2ELAST_2E0,type,
    c_2Elist_2ELAST_2E0: u ).

tff(c_2Elist_2ELAST_2E1,type,
    c_2Elist_2ELAST_2E1: du > u ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: u ).

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

tff(c_2EindexedLists_2ELIST__RELi_2E0,type,
    c_2EindexedLists_2ELIST__RELi_2E0: u ).

tff(c_2EindexedLists_2ELIST__RELi_2E3,type,
    c_2EindexedLists_2ELIST__RELi_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: u ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: du > u ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: u ).

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

tff(c_2EindexedLists_2EMAP2i_2E0,type,
    c_2EindexedLists_2EMAP2i_2E0: u ).

tff(c_2EindexedLists_2EMAP2i_2E3,type,
    c_2EindexedLists_2EMAP2i_2E3: ( du * du * du ) > u ).

tff(c_2EindexedLists_2EMAP2ia_2E0,type,
    c_2EindexedLists_2EMAP2ia_2E0: u ).

tff(c_2EindexedLists_2EMAP2ia_2E4,type,
    c_2EindexedLists_2EMAP2ia_2E4: ( du * du * du * du ) > u ).

tff(c_2EindexedLists_2EMAPi_2E0,type,
    c_2EindexedLists_2EMAPi_2E0: u ).

tff(c_2EindexedLists_2EMAPi_2E2,type,
    c_2EindexedLists_2EMAPi_2E2: ( du * du ) > u ).

tff(c_2EindexedLists_2EMAPi__ACC_2E0,type,
    c_2EindexedLists_2EMAPi__ACC_2E0: u ).

tff(c_2EindexedLists_2EMAPi__ACC_2E4,type,
    c_2EindexedLists_2EMAPi__ACC_2E4: ( du * du * du * du ) > u ).

tff(c_2Earithmetic_2EMIN_2E0,type,
    c_2Earithmetic_2EMIN_2E0: u ).

tff(c_2Earithmetic_2EMIN_2E2,type,
    c_2Earithmetic_2EMIN_2E2: ( du * du ) > u ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

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

tff(c_2Elist_2EREVERSE_2E0,type,
    c_2Elist_2EREVERSE_2E0: u ).

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

tff(c_2Ecombin_2ES_2E0,type,
    c_2Ecombin_2ES_2E0: u ).

tff(c_2Ecombin_2ES_2E2,type,
    c_2Ecombin_2ES_2E2: ( du * du ) > u ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: u ).

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

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

tff(c_2EindexedLists_2EdelN_2E0,type,
    c_2EindexedLists_2EdelN_2E0: u ).

tff(c_2EindexedLists_2EdelN_2E2,type,
    c_2EindexedLists_2EdelN_2E2: ( du * du ) > u ).

tff(c_2EindexedLists_2Efindi_2E0,type,
    c_2EindexedLists_2Efindi_2E0: u ).

tff(c_2EindexedLists_2Efindi_2E2,type,
    c_2EindexedLists_2Efindi_2E2: ( du * du ) > u ).

tff(c_2EindexedLists_2EfupdLast_2E0,type,
    c_2EindexedLists_2EfupdLast_2E0: u ).

tff(c_2EindexedLists_2EfupdLast_2E2,type,
    c_2EindexedLists_2EfupdLast_2E2: ( du * du ) > u ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

tff(c_2Ecombin_2Eo_2E1,type,
    c_2Ecombin_2Eo_2E1: du > u ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

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

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

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

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

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

tff(mono_2Ec_2Earithmetic_2E_2B_2E0,type,
    mono_2Ec_2Earithmetic_2E_2B_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2E_2B_2E1,type,
    mono_2Ec_2Earithmetic_2E_2B_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

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

tff(mono_2Ec_2Earithmetic_2E_2D_2E0,type,
    mono_2Ec_2Earithmetic_2E_2D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

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

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Enum_2E0_2E0,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eprim__rec_2E_3C_2E0,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Earithmetic_2E_3C_3D_2E0,type,
    mono_2Ec_2Earithmetic_2E_3C_3D_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Earithmetic_2EBIT1_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

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

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 ).

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

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EMIN_2E0,type,
    mono_2Ec_2Earithmetic_2EMIN_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2EMIN_2E2,type,
    mono_2Ec_2Earithmetic_2EMIN_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2ENUMERAL_2E0,type,
    mono_2Ec_2Earithmetic_2ENUMERAL_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

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

tff(mono_2Ec_2Enum_2ESUC_2E0,type,
    mono_2Ec_2Enum_2ESUC_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

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

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EZERO_2E0,type,
    mono_2Ec_2Earithmetic_2EZERO_2E0: mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq1_2Ec_2Earithmetic_2E_2B_2E1,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2E_2B_2E1(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E0,X0_2E0) ) ).

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

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

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

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

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

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

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

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

tff(arityeq1_2Ec_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)))) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EAPPEND_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Ecombin_2EC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),c_2Elist_2ECONS_2E0),s(A_27b,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c))),c_2Elist_2ECONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),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_2E0)))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27c)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2Elist_2EFOLDR_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2EindexedLists_2EFOLDRi_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))),c_2EindexedLists_2EFOLDRi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2EindexedLists_2EFOLDRi_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(A_27a,X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27a))),c_2EindexedLists_2EFOLDRi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(A_27a,X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) ) ).

tff(arityeq3_2Ec_2EindexedLists_2EFOLDRi_2E3_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0),s(A_27b,X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),A_27b))),c_2EindexedLists_2EFOLDRi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))),s(A_27b,X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2EFRONT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EFRONT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

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

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27b))),c_2Elist_2EGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(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)))) ) ).

tff(arityeq1_2Ec_2Elist_2ELAST_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2ELAST_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

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

tff(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)))) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),X0_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27c),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2EindexedLists_2ELIST__RELi_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_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,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_2EindexedLists_2ELIST__RELi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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)))) ) ).

tff(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))) ) ).

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

tff(arityeq3_2Ec_2EindexedLists_2EMAP2i_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_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(tyop_2Enum_2Enum,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_2EindexedLists_2EMAP2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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))) ) ).

tff(arityeq3_2Ec_2EindexedLists_2EMAP2i_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),c_2EindexedLists_2EMAP2i_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))),s(tyop_2Elist_2Elist(A_27c),X2_2E0))) ) ).

tff(arityeq4_2Ec_2EindexedLists_2EMAP2ia_2E4_2Emono_2EA_27c_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27b),X3_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_2Enum_2Enum,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(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27c))))),c_2EindexedLists_2EMAP2ia_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) ) ).

tff(arityeq4_2Ec_2EindexedLists_2EMAP2ia_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27b),X2_2E0),s(tyop_2Elist_2Elist(A_27c),X3_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))))),c_2EindexedLists_2EMAP2ia_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))),s(tyop_2Elist_2Elist(A_27c),X3_2E0))) ) ).

tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))),c_2EindexedLists_2EMAPi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),c_2EindexedLists_2EMAPi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27a))),c_2EindexedLists_2EMAPi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2EindexedLists_2EMAPi_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27b))),c_2EindexedLists_2EMAPi_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(A_27c),X1_2E0))) ) ).

tff(arityeq4_2Ec_2EindexedLists_2EMAPi__ACC_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u,X3_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi__ACC_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Elist_2Elist(A_27a),X2_2E0),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27a))))),c_2EindexedLists_2EMAPi__ACC_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Elist_2Elist(A_27a),X2_2E0))),s(tyop_2Elist_2Elist(A_27b),X3_2E0))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EMIN_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMIN_2E2(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2EMIN_2E0,X0_2E0),X1_2E0) ) ).

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

tff(arityeq1_2Ec_2Elist_2EREVERSE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EREVERSE_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2ES_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b))),c_2Ecombin_2ES_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2EindexedLists_2EdelN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2EindexedLists_2EdelN_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2EindexedLists_2Efindi_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum)),c_2EindexedLists_2Efindi_2E0),s(A_27a,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2EindexedLists_2EfupdLast_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),c_2EindexedLists_2EfupdLast_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))) = 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))) ) ).

tff(arityeq1_2Ec_2Ecombin_2Eo_2E1_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Emin_2Efun_28A_27b_2CA_27b_29_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2CA_27b_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27c_2CA_27a_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(X1_2E0)))) ) ).

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

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

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

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

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

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

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

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

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

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

tff(thm_2EindexedLists_2EMAPi__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V1f_2E0: u,V2h_2E0: u,V3t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Elist_2Elist(A_27b),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(A_27b,V2h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Elist_2Elist(A_27b),V3t_2E0))))) ) ) ).

tff(thm_2EindexedLists_2EMAPi__ACC__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2a_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi__ACC_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),V2a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V2a_2E0))) )
      & ! [V3f_2E0: u,V4i_2E0: mono_2Etyop_2Enum_2Enum,V5a_2E0: u,V6h_2E0: u,V7t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi__ACC_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V3f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Elist_2Elist(A_27a),V5a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V6h_2E0),s(tyop_2Elist_2Elist(A_27b),V7t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi__ACC_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V3f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V4i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V3f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)))),s(A_27b,V6h_2E0))),s(tyop_2Elist_2Elist(A_27a),V5a_2E0))),s(tyop_2Elist_2Elist(A_27b),V7t_2E0))) ) ) ).

tff(thm_2EindexedLists_2EFOLDRi__def,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u,V1a_2E0: u] : ( s(A_27a,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V0f_2E0),s(A_27a,V1a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))) = s(A_27a,V1a_2E0) )
      & ! [V2f_2E0: u,V3a_2E0: u,V4h_2E0: u,V5t_2E0: u] : ( s(A_27a,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(A_27b,V4h_2E0))),s(A_27a,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(A_27a,V3a_2E0),s(tyop_2Elist_2Elist(A_27b),V5t_2E0))))) ) ) ).

tff(thm_2EindexedLists_2Efindi__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1x_2E0: u,V2h_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2h_2E0)))))
        <=> ( s(A_27a,V1x_2E0) = s(A_27a,V2h_2E0) ) )
     => ( ! [V0x_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))) = mono_2Ec_2Enum_2E0_2E0 )
        & ! [V1x_2E0: u,V2h_2E0: u,V3t_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum(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,V1x_2E0))),s(A_27a,V2h_2E0)))),mono_2Ec_2Enum_2E0_2E0,mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0)))))) ) ) ) ).

tff(thm_2EindexedLists_2EdelN__def,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V1i_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1i_2E0))
        <=> ( V1i_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V0i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
        & ! [V1i_2E0: mono_2Etyop_2Enum_2Enum,V2h_2E0: u,V3t_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V1i_2E0))),s(tyop_2Elist_2Elist(A_27a),V3t_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V3t_2E0))))))) ) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__def,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1x_27_2E0: u,V2x_27_27_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_27_2E0),s(tyop_2Elist_2Elist(A_27b),V2x_27_27_2E0)))))
    <=> ! [V3LIST__RELi_27_2E0: u] :
          ( ! [V4a0_2E0: u,V5a1_2E0: u] :
              ( ( ( ( s(tyop_2Elist_2Elist(A_27a),V4a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
                  & ( s(tyop_2Elist_2Elist(A_27b),V5a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) )
                | ? [V6h1_2E0: u,V7h2_2E0: u,V8l1_2E0: u,V9l2_2E0: u] :
                    ( ( s(tyop_2Elist_2Elist(A_27a),V4a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6h1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) )
                    & ( s(tyop_2Elist_2Elist(A_27b),V5a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V9l2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V7h2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) )
                    & p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0x_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))))),s(A_27a,V6h1_2E0))),s(A_27b,V7h2_2E0)))))
                    & p(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)),V3LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V8l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V9l2_2E0))))) ) )
             => p(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)),V3LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V5a1_2E0))))) )
         => p(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)),V3LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V1x_27_2E0))),s(tyop_2Elist_2Elist(A_27b),V2x_27_27_2E0))))) ) ) ).

tff(thm_2EindexedLists_2EMAPi__ACC__MAPi,axiom,
    ! [A_27a: d,A_27b: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2f_2E0: u,V3a_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi__ACC_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V3a_2E0),s(tyop_2Elist_2Elist(A_27b),V1l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(A_27a),V3a_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E1(V0n_2E0))))),s(tyop_2Elist_2Elist(A_27b),V1l_2E0))))) ) ).

tff(thm_2EindexedLists_2EMAPi__compute,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi__ACC_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0l_2E0))) ) ).

tff(thm_2EindexedLists_2ELT__SUC,axiom,
    ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1m_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,mono_2Ec_2Enum_2ESUC_2E1(V1m_2E0)))
    <=> ( ( V0n_2E0 = mono_2Ec_2Enum_2E0_2E0 )
        | ? [V2n0_2E0: mono_2Etyop_2Enum_2Enum] :
            ( ( V0n_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V2n0_2E0) )
            & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2n0_2E0,V1m_2E0)) ) ) ) ).

tff(thm_2EindexedLists_2EMEM__MAPi,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u,V2l_2E0: u] :
      ( p(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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V2l_2E0)))))))))
    <=> ? [V3n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l_2E0))))))
          & ( s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27b),V2l_2E0))))) ) ) ) ).

tff(thm_2EindexedLists_2EMAPi__CONG,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2f1_2E0: u,V3f2_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V0l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V1l2_2E0) )
        & ! [V4x_2E0: u,V5n_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0)))))))
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)))),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V3f2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)))),s(A_27a,V4x_2E0))) ) ) )
     => ( s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V3f2_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))) ) ) ).

tff(thm_2EindexedLists_2EMAPi__CONG_27,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2f2_2E0: u,V3f1_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) )
     => ( ! [V4x_2E0: u,V5n_2E0: mono_2Etyop_2Enum_2Enum] :
            ( ( s(A_27a,V4x_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))) )
           => ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V5n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))))
             => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V3f1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)))),s(A_27a,V4x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5n_2E0)))),s(A_27a,V4x_2E0))) ) ) )
       => ( s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V3f1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))) ) ) ) ).

tff(thm_2EindexedLists_2ELENGTH__MAPi,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1l_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))) ) ).

tff(thm_2EindexedLists_2EMAP__MAPi,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2l_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),V1g_2E0),s(tyop_2Elist_2Elist(A_27c),V2l_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),V1g_2E0))),s(tyop_2Elist_2Elist(A_27c),V2l_2E0))) ) ).

tff(thm_2EindexedLists_2EEL__MAPi,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))))
     => ( s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) ) ) ).

tff(thm_2EindexedLists_2EMAPi__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0l1_2E0: u,V1l2_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) ) ).

tff(thm_2EindexedLists_2EMAPi__GENLIST,axiom,
    ! [A_27a: d,A_27b: d,V0l_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27b),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),c_2Ecombin_2ES_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2EC_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Elist_2EEL_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ).

tff(thm_2EindexedLists_2EGENLIST__CONG,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f2_2E0: u,V2f1_2E0: u] :
      ( ! [V3m_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3m_2E0,V0n_2E0))
         => ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m_2E0)))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m_2E0)))) ) )
     => ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) ) ) ).

tff(thm_2EindexedLists_2EFOLDR__MAPi,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2a_2E0: u,V3l_2E0: u] : ( s(A_27b,c_2Elist_2EFOLDR_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAPi_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),V1g_2E0),s(tyop_2Elist_2Elist(A_27c),V3l_2E0))))) = s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V0f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27c,A_27a)),V1g_2E0))),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27c),V3l_2E0))) ) ).

tff(thm_2EindexedLists_2EFOLDRi__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2a_2E0: u,V3f_2E0: u] : ( s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f_2E0),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))) = s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f_2E0),s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))))),s(A_27b,V2a_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) ) ).

tff(thm_2EindexedLists_2EFOLDRi__CONG,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2f2_2E0: u,V3f1_2E0: u,V4a2_2E0: u,V5a1_2E0: u] :
      ( ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) )
     => ( ! [V6n_2E0: mono_2Etyop_2Enum_2Enum,V7e_2E0: u,V8a_2E0: u] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V6n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))))
           => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V7e_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l2_2E0)))))))
             => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(A_27a,V7e_2E0))),s(A_27b,V8a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V2f2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(A_27a,V7e_2E0))),s(A_27b,V8a_2E0))) ) ) )
       => ( ( s(A_27b,V5a1_2E0) = s(A_27b,V4a2_2E0) )
         => ( s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f1_2E0),s(A_27b,V5a1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V2f2_2E0),s(A_27b,V4a2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))) ) ) ) ) ).

tff(thm_2EindexedLists_2EFOLDRi__CONG_27,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2f2_2E0: u,V3f1_2E0: u,V4a2_2E0: u,V5a1_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),V1l1_2E0) = s(tyop_2Elist_2Elist(A_27a),V0l2_2E0) )
        & ! [V6n_2E0: mono_2Etyop_2Enum_2Enum,V7a_2E0: u] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V6n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))))
           => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))),s(A_27b,V7a_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V2f2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))))),s(A_27b,V7a_2E0))) ) )
        & ( s(A_27b,V5a1_2E0) = s(A_27b,V4a2_2E0) ) )
     => ( s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V3f1_2E0),s(A_27b,V5a1_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))) = s(A_27b,c_2EindexedLists_2EFOLDRi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V2f2_2E0),s(A_27b,V4a2_2E0),s(tyop_2Elist_2Elist(A_27a),V0l2_2E0))) ) ) ).

tff(thm_2EindexedLists_2EMEM__findi,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l_2E0: u] :
      ( p(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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))))
     => p(mono_2Ec_2Eprim__rec_2E_3C_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,V0x_2E0),s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0)))))) ) ).

tff(thm_2EindexedLists_2Efindi__EL,axiom,
    ! [A_27a: d,V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) )
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))) = V1n_2E0 ) ) ).

tff(thm_2EindexedLists_2EEL__findi,axiom,
    ! [A_27a: d,V0l_2E0: u,V1x_2E0: u] :
      ( p(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_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))))
     => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,c_2EindexedLists_2Efindi_2E2(s(A_27a,V1x_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(A_27a,V1x_2E0) ) ) ).

tff(thm_2EindexedLists_2EdelN__shortens,axiom,
    ! [A_27a: d,V0l_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = mono_2Ec_2Earithmetic_2E_2D_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))) ) ) ).

tff(thm_2EindexedLists_2EEL__delN__BEFORE,axiom,
    ! [A_27a: d,V0l_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2j_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V1i_2E0,V2j_2E0))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2j_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) )
     => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2j_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ) ).

tff(thm_2EindexedLists_2EEL__delN__AFTER,axiom,
    ! [A_27a: d,V0l_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2j_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V2j_2E0,V1i_2E0))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Earithmetic_2E_2B_2E2(V1i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) )
     => ( s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EdelN_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2j_2E0)),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V1i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ) ).

tff(thm_2EindexedLists_2EfupdLast__ind,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ( ! [V1f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))
        & ! [V2f_2E0: u,V3h_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0)))))))
        & ! [V4f_2E0: u,V5h_2E0: u,V6v4_2E0: u,V7v5_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6v4_2E0),s(tyop_2Elist_2Elist(A_27a),V7v5_2E0)))))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V4f_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V6v4_2E0),s(tyop_2Elist_2Elist(A_27a),V7v5_2E0))))))))) ) )
     => ! [V8v_2E0: u,V9v1_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),V0P_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),V8v_2E0))),s(tyop_2Elist_2Elist(A_27a),V9v1_2E0))))) ) ).

tff(thm_2EindexedLists_2EfupdLast__def,axiom,
    ! [A_27a: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V1h_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0),s(A_27a,V1h_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
      & ! [V3v5_2E0: u,V4v4_2E0: u,V5h_2E0: u,V6f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4v4_2E0),s(tyop_2Elist_2Elist(A_27a),V3v5_2E0))))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V6f_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V4v4_2E0),s(tyop_2Elist_2Elist(A_27a),V3v5_2E0))))))) ) ) ).

tff(thm_2EindexedLists_2EfupdLast__EQ__NIL,axiom,
    ! [A_27a: d,V0x_2E0: u,V1f_2E0: u] :
      ( ( ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0x_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ( ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0x_2E0))) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ) ).

tff(thm_2EindexedLists_2EfupdLast__FRONT__LAST,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0l_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))
        <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
     => ! [V0l_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EfupdLast_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EFRONT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),V1f_2E0),s(A_27a,c_2Elist_2ELAST_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__rules,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
      & ! [V1h1_2E0: u,V2h2_2E0: u,V3l1_2E0: u,V4l2_2E0: u] :
          ( ( p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))))),s(A_27a,V1h1_2E0))),s(A_27b,V2h2_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27b),V4l2_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V4l2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V2h2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))))))) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__ind,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1LIST__RELi_27_2E0: u] :
      ( ( p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
        & ! [V2h1_2E0: u,V3h2_2E0: u,V4l1_2E0: u,V5l2_2E0: u] :
            ( ( p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))))),s(A_27a,V2h1_2E0))),s(A_27b,V3h2_2E0)))))
              & p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0))))) )
           => p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V5l2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))))))) ) )
     => ! [V6a0_2E0: u,V7a1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))
         => p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0))))) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__strongind,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1LIST__RELi_27_2E0: u] :
      ( ( p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0)))))
        & ! [V2h1_2E0: u,V3h2_2E0: u,V4l1_2E0: u,V5l2_2E0: u] :
            ( ( p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))))),s(A_27a,V2h1_2E0))),s(A_27b,V3h2_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0)))))
              & p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V4l1_2E0))),s(tyop_2Elist_2Elist(A_27b),V5l2_2E0))))) )
           => p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V4l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V5l2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))))))) ) )
     => ! [V6a0_2E0: u,V7a1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0)))))
         => p(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)),V1LIST__RELi_27_2E0),s(tyop_2Elist_2Elist(A_27a),V6a0_2E0))),s(tyop_2Elist_2Elist(A_27b),V7a1_2E0))))) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__cases,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1a0_2E0: u,V2a1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1a0_2E0),s(tyop_2Elist_2Elist(A_27b),V2a1_2E0)))))
    <=> ( ( ( s(tyop_2Elist_2Elist(A_27a),V1a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
          & ( s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) )
        | ? [V3h1_2E0: u,V4h2_2E0: u,V5l1_2E0: u,V6l2_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27a),V1a0_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V5l1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h1_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))) )
            & ( s(tyop_2Elist_2Elist(A_27b),V2a1_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V6l2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4h2_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))))) )
            & p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V5l1_2E0))))),s(A_27a,V3h1_2E0))),s(A_27b,V4h2_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V5l1_2E0),s(tyop_2Elist_2Elist(A_27b),V6l2_2E0))))) ) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__LENGTH,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V0R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
     => ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__EL__EQN,axiom,
    ! [A_27a: d,A_27b: d,V0l2_2E0: u,V1l1_2E0: u,V2R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V2R_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))))
    <=> ( ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))) = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V0l2_2E0)))) )
        & ! [V3i_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3i_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
           => p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V2R_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3i_2E0)),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))))))) ) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__thm,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1t_2E0: u,V2l_2E0: u,V3h_2E0: u,V4R_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27b),V0x_2E0)))))
      <=> ( s(tyop_2Elist_2Elist(A_27b),V0x_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0) ) )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))),s(tyop_2Elist_2Elist(A_27b),V2l_2E0)))))
      <=> ? [V5h_27_2E0: u,V6t_27_2E0: u] :
            ( ( s(tyop_2Elist_2Elist(A_27b),V2l_2E0) = s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V5h_27_2E0),s(tyop_2Elist_2Elist(A_27b),V6t_27_2E0))) )
            & p(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(A_27a,V3h_2E0))),s(A_27b,V5h_27_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Elist_2Elist(A_27a),V1t_2E0),s(tyop_2Elist_2Elist(A_27b),V6t_27_2E0))))) ) ) ) ).

tff(thm_2EindexedLists_2ELIST__RELi__APPEND__I,axiom,
    ! [A_27a: d,A_27b: d,V0m2_2E0: u,V1m1_2E0: u,V2l2_2E0: u,V3l1_2E0: u,V4R_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Earithmetic_2E_2B_2E1(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0))))))))),s(tyop_2Elist_2Elist(A_27a),V1m1_2E0),s(tyop_2Elist_2Elist(A_27b),V0m2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2EindexedLists_2ELIST__RELi_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),V4R_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V3l1_2E0),s(tyop_2Elist_2Elist(A_27a),V1m1_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0),s(tyop_2Elist_2Elist(A_27b),V0m2_2E0))))))) ) ).

tff(thm_2EindexedLists_2EMAP2i__ind,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
      ( ( ! [V1f_2E0: u,V2v0_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V2v0_2E0)))))
        & ! [V3f_2E0: u,V4v5_2E0: u,V5v6_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V3f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4v5_2E0),s(tyop_2Elist_2Elist(A_27b),V5v6_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))))
        & ! [V6f_2E0: u,V7h1_2E0: u,V8t1_2E0: u,V9h2_2E0: u,V10t2_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V6f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))))),s(tyop_2Elist_2Elist(A_27b),V8t1_2E0))),s(tyop_2Elist_2Elist(A_27c),V10t2_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V6f_2E0))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V7h1_2E0),s(tyop_2Elist_2Elist(A_27b),V8t1_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V9h2_2E0),s(tyop_2Elist_2Elist(A_27c),V10t2_2E0))))))) ) )
     => ! [V11v_2E0: u,V12v1_2E0: u,V13v2_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V11v_2E0))),s(tyop_2Elist_2Elist(A_27b),V12v1_2E0))),s(tyop_2Elist_2Elist(A_27c),V13v2_2E0))))) ) ).

tff(thm_2EindexedLists_2EMAP2i__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0v0_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V0v0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V2v6_2E0: u,V3v5_2E0: u,V4f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V4f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V3v5_2E0),s(tyop_2Elist_2Elist(A_27b),V2v6_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V5t2_2E0: u,V6t1_2E0: u,V7h2_2E0: u,V8h1_2E0: u,V9f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V9f_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V8h1_2E0),s(tyop_2Elist_2Elist(A_27b),V6t1_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V7h2_2E0),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V9f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(A_27b,V8h1_2E0))),s(A_27c,V7h2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V9f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Enum_2ESUC_2E0)))),s(tyop_2Elist_2Elist(A_27b),V6t1_2E0),s(tyop_2Elist_2Elist(A_27c),V5t2_2E0))))) ) ) ).

tff(thm_2EindexedLists_2EMAP2i__NIL2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l1_2E0: u,V1f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0),s(tyop_2Elist_2Elist(A_27b),V0l1_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2EindexedLists_2ELENGTH__MAP2i,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1l1_2E0: u,V2l2_2E0: u] : ( j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27c),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))) = mono_2Ec_2Earithmetic_2EMIN_2E2(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0)))),j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) ) ).

tff(thm_2EindexedLists_2EEL__MAP2i,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1l1_2E0: u,V2l2_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))))
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V3n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),V2l2_2E0)))))) )
     => ( s(A_27c,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27c),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V0f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V2l2_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)))),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0))))),s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Elist_2Elist(A_27b),V2l2_2E0))))) ) ) ).

tff(thm_2EindexedLists_2EMAP2ia__ind,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0P_2E0: u] :
      ( ( ! [V1f_2E0: u,V2i_2E0: mono_2Etyop_2Enum_2Enum,V3v0_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2i_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0))),s(tyop_2Elist_2Elist(A_27c),V3v0_2E0)))))
        & ! [V4f_2E0: u,V5i_2E0: mono_2Etyop_2Enum_2Enum,V6v7_2E0: u,V7v8_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V4f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5i_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V6v7_2E0),s(tyop_2Elist_2Elist(A_27b),V7v8_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0)))))
        & ! [V8f_2E0: u,V9i_2E0: mono_2Etyop_2Enum_2Enum,V10h1_2E0: u,V11t1_2E0: u,V12h2_2E0: u,V13t2_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V8f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V9i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Elist_2Elist(A_27b),V11t1_2E0))),s(tyop_2Elist_2Elist(A_27c),V13t2_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V8f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9i_2E0)))),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V10h1_2E0),s(tyop_2Elist_2Elist(A_27b),V11t1_2E0))))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V12h2_2E0),s(tyop_2Elist_2Elist(A_27c),V13t2_2E0))))))) ) )
     => ! [V14v_2E0: u,V15v1_2E0: mono_2Etyop_2Enum_2Enum,V16v2_2E0: u,V17v3_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Ebool)))),V0P_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V14v_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V15v1_2E0)))),s(tyop_2Elist_2Elist(A_27b),V16v2_2E0))),s(tyop_2Elist_2Elist(A_27c),V17v3_2E0))))) ) ).

tff(thm_2EindexedLists_2EMAP2ia__def,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0v0_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ENIL_2E0),s(tyop_2Elist_2Elist(A_27c),V0v0_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V3v8_2E0: u,V4v7_2E0: u,V5i_2E0: mono_2Etyop_2Enum_2Enum,V6f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V6f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5i_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V4v7_2E0),s(tyop_2Elist_2Elist(A_27b),V3v8_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) )
      & ! [V7t2_2E0: u,V8t1_2E0: u,V9i_2E0: mono_2Etyop_2Enum_2Enum,V10h2_2E0: u,V11h1_2E0: u,V12f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V12f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9i_2E0)),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2ECONS_2E2(s(A_27b,V11h1_2E0),s(tyop_2Elist_2Elist(A_27b),V8t1_2E0))),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ECONS_2E2(s(A_27c,V10h2_2E0),s(tyop_2Elist_2Elist(A_27c),V7t2_2E0))))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V12f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9i_2E0)))),s(A_27b,V11h1_2E0))),s(A_27c,V10h2_2E0))),s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V12f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V9i_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Elist_2Elist(A_27b),V8t1_2E0),s(tyop_2Elist_2Elist(A_27c),V7t2_2E0))))) ) ) ).

tff(thm_2EindexedLists_2EMAP2ia__NIL2,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l1_2E0: u,V1i_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1i_2E0)),s(tyop_2Elist_2Elist(A_27b),V0l1_2E0),s(tyop_2Elist_2Elist(A_27c),c_2Elist_2ENIL_2E0))) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ).

tff(thm_2EindexedLists_2EMAP2i__compute,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0l2_2E0: u,V1l1_2E0: u,V2f_2E0: u] : ( s(tyop_2Elist_2Elist(A_27c),c_2EindexedLists_2EMAP2i_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) = s(tyop_2Elist_2Elist(A_27c),c_2EindexedLists_2EMAP2ia_2E4(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l1_2E0),s(tyop_2Elist_2Elist(A_27b),V0l2_2E0))) ) ).

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